Atomic Mass Unit to Slug Converter
Convert atomic mass units to slugs with our free online weight converter.
Quick Answer
1 Atomic Mass Unit = 1.137831e-28 slugs
Formula: Atomic Mass Unit × conversion factor = Slug
Use the calculator below for instant, accurate conversions.
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All conversion formulas on UnitsConverter.io have been verified against NIST (National Institute of Standards and Technology) guidelines and international SI standards. Our calculations are accurate to 10 decimal places for standard conversions and use arbitrary precision arithmetic for astronomical units.
Atomic Mass Unit to Slug Calculator
How to Use the Atomic Mass Unit to Slug Calculator:
- Enter the value you want to convert in the 'From' field (Atomic Mass Unit).
- The converted value in Slug will appear automatically in the 'To' field.
- Use the dropdown menus to select different units within the Weight category.
- Click the swap button (⇌) to reverse the conversion direction.
How to Convert Atomic Mass Unit to Slug: Step-by-Step Guide
Converting Atomic Mass Unit to Slug involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
1 Atomic Mass Unit = 1.13783e-28 slugsExample Calculation:
Convert 5 atomic mass units: 5 × 1.13783e-28 = 5.68915e-28 slugs
Disclaimer: For Reference Only
These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.
Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.
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What Is an Atomic Mass Unit?
The atomic mass unit (symbol: u), also called the unified atomic mass unit or Dalton (symbol: Da), is a unit of mass used for expressing atomic and molecular masses.
Official definition: 1 u = exactly 1/12 of the mass of one unbound carbon-12 atom at rest in its ground state
Value in SI units: 1 u = 1.660 539 066 60 × 10⁻²⁷ kg (with uncertainty ±0.000 000 000 50 × 10⁻²⁷ kg)
Why Use Atomic Mass Units Instead of Kilograms?
Atomic and molecular masses in kilograms are extraordinarily small and unwieldy:
In kilograms (impractical):
- Hydrogen atom: 1.674 × 10⁻²⁷ kg
- Water molecule: 2.992 × 10⁻²⁶ kg
- Glucose molecule: 2.990 × 10⁻²⁵ kg
In atomic mass units (convenient):
- Hydrogen atom: 1.008 u
- Water molecule: 18.015 u
- Glucose molecule: 180.16 u
The atomic mass unit scales numbers to manageable sizes while maintaining precision for chemical calculations.
Carbon-12: The Reference Standard
Why carbon-12?
- Exact definition: ¹²C is defined as exactly 12 u (no uncertainty)
- Abundant: Carbon-12 comprises 98.89% of natural carbon
- Stable: Not radioactive, doesn't decay
- Central element: Carbon forms countless compounds, making it ideal for chemistry
- Integer mass: Convenient reference point (mass = 12 exactly)
Historical context: Before 1961, physicists and chemists used different oxygen-based standards, creating two incompatible atomic mass scales. Carbon-12 unified them.
Dalton vs. Unified Atomic Mass Unit
Two names, same unit:
Unified atomic mass unit (u):
- Official SI-accepted name
- Used primarily in chemistry and physics
- Symbol: u
Dalton (Da):
- Alternative name honoring John Dalton
- Used primarily in biochemistry and molecular biology
- Symbol: Da
- Convenient for large molecules (kilodaltons, kDa)
Relationship: 1 u = 1 Da (exactly equivalent)
Usage patterns:
- "The oxygen atom has a mass of 16.0 u" (chemistry)
- "The antibody protein has a mass of 150 kDa" (biochemistry)
Both refer to the same fundamental unit.
What Is a Slug?
The slug (symbol: sl or slug) is a unit of mass in the Foot-Pound-Second (FPS) system of imperial units. It is defined through Newton's second law of motion (F = ma):
1 slug = 1 lbf / (1 ft/s²)
In words: one slug is the mass that accelerates at one foot per second squared when a force of one pound-force is applied to it.
Exact Value
1 slug = 32.17404855... pounds-mass (lbm) ≈ 32.174 lbm
1 slug = 14.593902937206... kilograms ≈ 14.5939 kg
These values derive from the standard acceleration due to gravity: g = 32.174 ft/s² = 9.80665 m/s².
The Pound Confusion
The imperial system has a fundamental ambiguity: the word "pound" means two different things:
Pound-mass (lbm):
- A unit of mass (quantity of matter)
- An object has the same pound-mass everywhere in the universe
- Symbol: lbm
Pound-force (lbf):
- A unit of force (weight)
- The force exerted by one pound-mass under standard Earth gravity
- Symbol: lbf
- 1 lbf = 1 lbm × 32.174 ft/s² (weight = mass × gravity)
This creates confusion because in everyday language, "pound" can mean either, depending on context. The slug eliminates this ambiguity by serving as an unambiguous mass unit compatible with pound-force.
Why the Slug Matters: Making F = ma Work
Newton's second law: F = ma (Force = mass × acceleration)
Problem with pounds-mass and pounds-force: If you use lbm for mass and lbf for force, Newton's law becomes: F = ma / g_c
where g_c = 32.174 lbm·ft/(lbf·s²) is a dimensional conversion constant—ugly and error-prone!
Solution with slugs: Using slugs for mass and lbf for force, Newton's law works cleanly: F = ma (no extra constants needed!)
Example:
- Force: 10 lbf
- Acceleration: 5 ft/s²
- Mass: F/a = 10 lbf / 5 ft/s² = 2 slugs
- (Or in lbm: mass = 2 slugs × 32.174 = 64.348 lbm)
FPS System
The slug is part of the Foot-Pound-Second (FPS) system, also called the British Gravitational System or English Engineering System:
- Length: foot (ft)
- Force: pound-force (lbf)
- Time: second (s)
- Mass: slug (sl)
- Acceleration: feet per second squared (ft/s²)
This contrasts with the SI system (meter, kilogram, second, newton) and the pound-mass system (foot, pound-mass, second, poundal).
Note: The Atomic Mass Unit is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Slug belongs to the imperial/US customary system.
History of the Atomic Mass Unit and Slug
John Dalton and Atomic Theory (1803-1808)
John Dalton (1766-1844), an English chemist and physicist, revolutionized chemistry with his atomic theory (1803):
Dalton's key postulates:
- All matter consists of indivisible atoms
- Atoms of the same element are identical in mass and properties
- Atoms of different elements have different masses
- Chemical compounds form when atoms combine in simple whole-number ratios
Relative atomic masses: Dalton created the first table of atomic weights (1805-1808), assigning hydrogen a mass of 1 and expressing other elements relative to it:
- Hydrogen: 1
- Oxygen: 7 (incorrect; should be ~16, but Dalton thought water was HO, not H₂O)
- Carbon: 5 (incorrect)
Though Dalton's numerical values were often wrong (he didn't yet know correct chemical formulas), his conceptual framework established that elements have characteristic atomic masses.
Berzelius and Improved Atomic Weights (1810s-1820s)
Jöns Jacob Berzelius (Swedish chemist, 1779-1848) refined Dalton's work with meticulous experiments:
Achievements:
- Determined accurate atomic weights for over 40 elements by 1818
- Established oxygen = 100 as the standard (for convenience in calculation)
- Introduced modern chemical notation (H, O, C, etc.)
Berzelius' atomic weights were remarkably accurate, many within 1% of modern values.
Cannizzaro and Avogadro's Number (1860)
Stanislao Cannizzaro (Italian chemist, 1826-1910) resolved confusion about atomic vs. molecular weights at the Karlsruhe Congress (1860):
Key insight: Avogadro's hypothesis (1811)—equal volumes of gases contain equal numbers of molecules—allows distinguishing atomic from molecular masses
Result: By 1860s, chemists adopted consistent atomic weights based on oxygen = 16
The Oxygen Standard Era (1890s-1960)
Chemist's standard (1890s onward):
- Natural oxygen (mixture of ¹⁶O, ¹⁷O, ¹⁸O) = 16.0000 exactly
- Practical for analytical chemistry
- Used in atomic weight tables
Physicist's standard (1900s onward):
- Oxygen-16 isotope (¹⁶O) = 16.0000 exactly
- Used in mass spectrometry and nuclear physics
- More precise for isotope work
The problem: Natural oxygen is 99.757% ¹⁶O, 0.038% ¹⁷O, and 0.205% ¹⁸O
- Chemist's scale and physicist's scale differed by ~0.0003 (0.03%)
- Small but significant for precision work
Unification: Carbon-12 Standard (1961)
1960 IUPAP resolution (International Union of Pure and Applied Physics):
- Proposed carbon-12 as the new standard
- Physicist Alfred Nier championed the change
1961 IUPAC resolution (International Union of Pure and Applied Chemistry):
- Adopted carbon-12 standard
- Defined: 1 atomic mass unit = 1/12 the mass of ¹²C atom
Advantages of carbon-12:
- Unified physics and chemistry scales
- Carbon is central to organic chemistry
- Mass spectrometry reference (carbon calibration)
- Abundant, stable, non-radioactive
Notation evolution:
- Old: amu (atomic mass unit, ambiguous—which standard?)
- New: u (unified atomic mass unit, unambiguous—carbon-12 standard)
The Dalton Name (1960s-1980s)
1960s proposal: Several scientists suggested naming the unit after John Dalton
1980s acceptance: The name "Dalton" (Da) gained widespread use in biochemistry
1993 IUPAC endorsement: Officially recognized "Dalton" as an alternative name for the unified atomic mass unit
Modern usage:
- Chemistry/physics: Prefer "u" (atomic mass unit)
- Biochemistry: Prefer "Da" (Dalton), especially with kDa (kilodaltons) for proteins
Mass Spectrometry and Precision (1900s-Present)
Mass spectrometry (developed 1910s-1920s, refined continuously):
Thomson and Aston (1910s-1920s):
- J.J. Thomson and Francis Aston developed early mass spectrographs
- Discovered isotopes by precise mass measurement
- Aston won 1922 Nobel Prize in Chemistry
Modern precision:
- Mass spectrometry now measures atomic masses to 8-10 decimal places
- Essential for determining isotopic compositions
- Used to measure the carbon-12 standard with extraordinary accuracy
CODATA values: The Committee on Data for Science and Technology (CODATA) publishes official atomic mass unit values every few years, incorporating latest measurements:
- 2018 value: 1 u = 1.660 539 066 60(50) × 10⁻²⁷ kg
2019 SI Redefinition
Historic change: On May 20, 2019, the International System of Units (SI) was redefined based on fundamental physical constants rather than physical artifacts (like the kilogram prototype)
New kilogram definition: Based on the Planck constant (h = 6.626 070 15 × 10⁻³⁴ J·s, exact)
Impact on atomic mass unit: The atomic mass unit is now indirectly tied to fundamental constants through the kilogram's new definition, though it remains defined as 1/12 the mass of carbon-12
Practical effect: Minimal—atomic masses remain effectively unchanged, but now rooted in unchanging physical constants
The Imperial Weight-Mass Problem (Pre-1900)
Before the slug was invented, the imperial system created confusion between weight (force due to gravity) and mass (quantity of matter):
Common usage: "Pound" meant weight (what a scale measures on Earth)
- "This weighs 10 pounds" meant 10 pounds-force (10 lbf)
Scientific usage: "Pound" could mean mass (quantity of matter)
- "This has 10 pounds of mass" meant 10 pounds-mass (10 lbm)
The problem: Newton's laws of motion require distinguishing force from mass. Using "pound" for both led to:
- Confusion in physics calculations
- Need for awkward gravitational conversion constants
- Errors in engineering (mixing lbf and lbm)
Arthur Mason Worthington (1852-1916)
Arthur Mason Worthington was a British physicist and professor at the Royal Naval College, Greenwich, known for his pioneering work in:
- High-speed photography of liquid drops and splashes
- Physics education and textbook writing
- Developing clearer terminology for imperial units
Around 1900, Worthington recognized that the imperial system needed a mass unit analogous to the kilogram—a unit that would make Newton's second law (F = ma) work without conversion factors.
The Slug's Introduction (c. 1900-1920)
Worthington proposed the slug as a solution:
The name: "Slug" evokes sluggishness—the tendency of massive objects to resist acceleration (inertia). A more massive object is more "sluggish" in responding to forces.
The definition: 1 slug = mass that accelerates at 1 ft/s² under 1 lbf
The relationship: 1 slug = 32.174 lbm (approximately)
This ratio (32.174) is not arbitrary—it equals the standard acceleration due to gravity in ft/s² (g = 32.174 ft/s²). This means:
- On Earth's surface, a 1-slug mass weighs 32.174 lbf
- On Earth's surface, a 1-lbm mass weighs 1 lbf
Adoption in Engineering Education (1920s-1940s)
The slug gained acceptance in American and British engineering textbooks during the early 20th century:
Advantages recognized:
- Simplified dynamics calculations (F = ma without g_c)
- Clearer distinction between force and mass
- Consistency with scientific notation (separating weight from mass)
Textbook adoption: Engineering mechanics books by authors like Beer & Johnston, Meriam & Kraige, and Hibbeler introduced the slug to generations of engineering students
University courses: American aerospace and mechanical engineering programs taught dynamics using the FPS system with slugs
Aerospace Era Embrace (1940s-1970s)
The slug became essential in American aerospace during the mid-20th century:
NACA/NASA adoption (1940s-1970s):
- Aircraft performance calculations used slugs for mass
- Rocket dynamics required precise force-mass-acceleration relationships
- Apollo program documentation used slugs extensively
Military ballistics:
- Artillery trajectory calculations
- Rocket and missile design
- Aircraft carrier catapult systems
Engineering standards:
- ASME and SAE specifications sometimes used slugs
- Aerospace contractor documentation (Boeing, Lockheed, etc.)
Decline with Metrication (1960s-Present)
Despite its technical superiority, the slug declined for several reasons:
International metrication (1960s onward):
- Most countries adopted SI units (kilogram for mass, newton for force)
- International aerospace and scientific collaboration required metric
- Slug never gained traction outside English-speaking countries
Everyday unfamiliarity:
- People use pounds (lbm/lbf) in daily life, not slugs
- No one says "I weigh 5 slugs" (they say "160 pounds")
- Slug remained a technical unit, never entering popular vocabulary
Educational shifts:
- Even American universities increasingly teach SI units first
- Engineering courses present slugs as "alternative" or "legacy" units
Software standardization:
- Modern engineering software defaults to SI (kg, N, m)
- Maintaining slug support became maintenance burden
Where Slugs Survive Today
The slug persists in specific technical niches:
American aerospace engineering:
- Aircraft weight and balance calculations (sometimes)
- Rocket propulsion dynamics
- Legacy documentation from NASA programs
Mechanical engineering dynamics courses:
- Teaching Newton's laws in FPS units
- Demonstrating unit system consistency
Ballistics and defense:
- Military projectile calculations
- Explosive dynamics
Historical technical documentation:
- 20th-century engineering reports and specifications
- Understanding legacy systems and equipment
Common Uses and Applications: atomic mass units vs slugs
Explore the typical applications for both Atomic Mass Unit (imperial/US) and Slug (imperial/US) to understand their common contexts.
Common Uses for atomic mass units
1. Atomic Weights and Periodic Table
The periodic table lists atomic weights (average masses) of elements in atomic mass units:
Example: Carbon:
- Natural carbon contains 98.89% ¹²C (12.0000 u) and 1.11% ¹³C (13.0034 u)
- Weighted average: 0.9889 × 12.0000 + 0.0111 × 13.0034 = 12.0107 u
- Periodic table lists carbon's atomic weight as 12.011 u
Why atomic weights aren't integers: Most elements are mixtures of isotopes with different masses, so the average is non-integer
Usage: Every stoichiometry calculation in chemistry depends on atomic weights expressed in u or g/mol (numerically equal)
2. Molecular Mass Calculations
Molecular mass = sum of atomic masses of all atoms in the molecule
Example: Glucose (C₆H₁₂O₆):
- 6 carbon atoms: 6 × 12.011 = 72.066 u
- 12 hydrogen atoms: 12 × 1.008 = 12.096 u
- 6 oxygen atoms: 6 × 15.999 = 95.994 u
- Total: 72.066 + 12.096 + 95.994 = 180.156 u
Molar mass connection: 180.156 u per molecule = 180.156 g/mol (numerically identical!)
3. Mass Spectrometry
Mass spectrometry measures the mass-to-charge ratio (m/z) of ions:
Technique:
- Ionize molecules (add or remove electrons)
- Accelerate ions through electric/magnetic fields
- Separate by mass-to-charge ratio
- Detect and measure abundances
Output: Mass spectrum showing peaks at specific m/z values (in u/e or Da/e, where e = elementary charge)
Applications:
- Determining molecular formulas
- Identifying unknown compounds
- Measuring isotope ratios
- Protein identification in proteomics
- Drug testing and forensics
Example: A peak at m/z = 180 for glucose (C₆H₁₂O₆ = 180 u, charge = +1e)
4. Protein Characterization (Biochemistry)
Biochemists routinely express protein masses in kilodaltons (kDa):
SDS-PAGE (sodium dodecyl sulfate polyacrylamide gel electrophoresis):
- Separates proteins by molecular weight
- Gels calibrated with protein standards of known kDa
- "The unknown protein band migrates at ~50 kDa"
Protein databases:
- UniProt, PDB (Protein Data Bank) list protein masses in Da or kDa
- Essential for identifying proteins by mass
Clinical diagnostics:
- "Elevated levels of 150 kDa IgG antibodies detected" (immune response)
- Tumor markers identified by protein mass
5. Stoichiometry and Chemical Equations
Stoichiometry: Calculating quantities in chemical reactions
Example: Combustion of methane: CH₄ + 2O₂ → CO₂ + 2H₂O
Molecular masses:
- CH₄: 16.043 u
- O₂: 31.998 u
- CO₂: 44.010 u
- H₂O: 18.015 u
Mass balance: 16.043 + 2(31.998) = 44.010 + 2(18.015) = 80.039 u (both sides equal, confirming conservation of mass)
Practical calculation: To produce 44 grams of CO₂, you need 16 grams of CH₄ and 64 grams of O₂
6. Isotope Analysis
Isotopes: Atoms of the same element with different numbers of neutrons (different masses)
Examples:
- ¹²C: 12.0000 u (6 protons, 6 neutrons) — 98.89% of natural carbon
- ¹³C: 13.0034 u (6 protons, 7 neutrons) — 1.11% of natural carbon
- ¹⁴C: 14.0032 u (6 protons, 8 neutrons) — radioactive, trace amounts
Applications:
- Radiocarbon dating: ¹⁴C decay measures age of organic materials
- Climate science: ¹³C/¹²C ratios in ice cores track ancient temperatures
- Medical tracers: ¹³C-labeled compounds track metabolic pathways
- Forensics: Isotope ratios identify geographic origins of materials
7. Nuclear Physics and Mass Defect
Mass-energy equivalence (E = mc²): Mass and energy are interconvertible
Mass defect: The mass of a nucleus is slightly less than the sum of its individual protons and neutrons
Example: Helium-4 (⁴He):
- 2 protons: 2 × 1.007276 = 2.014552 u
- 2 neutrons: 2 × 1.008665 = 2.017330 u
- Sum: 4.031882 u
- Actual ⁴He nucleus mass: 4.001506 u
- Mass defect: 4.031882 - 4.001506 = 0.030376 u
Interpretation: The "missing" 0.030376 u was converted to binding energy that holds the nucleus together
Calculation: 0.030376 u × c² = 28.3 MeV (million electron volts)
This is the energy released when helium-4 forms from protons and neutrons (nuclear fusion).
When to Use slugs
1. Aerospace Engineering and Aircraft Dynamics
Aerospace engineers use slugs when working in imperial units for aircraft and spacecraft calculations:
Aircraft weight and balance:
- Empty weight: 100,000 lbs = 3,108 slugs
- Loaded weight: 175,000 lbs = 5,440 slugs
- Center of gravity calculations using slugs for mass distribution
Rocket dynamics (Newton's F = ma):
- Thrust: 750,000 lbf
- Mass: 50,000 slugs (initial), decreasing as fuel burns
- Acceleration: F/m = 750,000 lbf / 50,000 slugs = 15 ft/s²
Orbital mechanics:
- Satellite mass in slugs
- Thrust-to-weight calculations
- Momentum and angular momentum in slug·ft/s units
2. Mechanical Engineering Dynamics
Engineering students and professionals analyze motion using slugs:
Newton's second law problems:
- Force: 50 lbf
- Acceleration: 10 ft/s²
- Mass: F/a = 50/10 = 5 slugs (no gravitational constant needed!)
Momentum calculations (p = mv):
- Car mass: 77.7 slugs (2,500 lbs)
- Velocity: 60 ft/s
- Momentum: p = 77.7 × 60 = 4,662 slug·ft/s
Rotational dynamics (moment of inertia):
- I = mr² (with mass in slugs, radius in feet)
- Flywheel: mass = 10 slugs, radius = 2 ft
- I = 10 × 2² = 40 slug·ft²
3. Ballistics and Projectile Motion
Military and firearms engineers use slugs for projectile calculations:
Artillery shell trajectory:
- Shell mass: 0.932 slugs (30 lbs)
- Muzzle force: 50,000 lbf
- Acceleration: a = F/m = 50,000/0.932 = 53,648 ft/s²
Bullet dynamics:
- Bullet mass: 0.000466 slug (150 grains = 0.0214 lbm)
- Chamber pressure force: 0.5 lbf (approximate average)
- Barrel acceleration calculation
Recoil analysis:
- Conservation of momentum (m_gun × v_gun = m_bullet × v_bullet)
- Gun mass: 6.22 slugs (200 lbs)
- Calculating recoil velocity in ft/s
4. Physics Education and Problem Sets
High school and college physics courses teaching imperial units:
Demonstrating unit consistency:
- Showing that F = ma works directly with slugs
- Contrasting with the g_c requirement when using lbm
Inclined plane problems:
- Block mass: 2 slugs
- Angle: 30°
- Friction force calculations in lbf
Atwood machine:
- Two masses in slugs
- Pulley system acceleration
- Tension forces in lbf
5. Automotive Engineering
Vehicle dynamics calculations using imperial units:
Braking force analysis:
- Car mass: 93.2 slugs (3,000 lbs)
- Deceleration: 20 ft/s² (emergency braking)
- Required braking force: F = ma = 93.2 × 20 = 1,864 lbf
Acceleration performance:
- Engine force (at wheels): 3,000 lbf
- Car mass: 77.7 slugs (2,500 lbs)
- Acceleration: a = F/m = 3,000/77.7 = 38.6 ft/s²
Suspension design:
- Spring force (F = kx) in lbf
- Sprung mass in slugs
- Natural frequency calculations
6. Structural Dynamics and Vibration
Engineers analyzing oscillating systems in imperial units:
Simple harmonic motion:
- F = -kx (Hooke's law, force in lbf)
- m = mass in slugs
- Natural frequency: ω = √(k/m) where m is in slugs
Seismic analysis:
- Building mass: distributed load in slugs per floor
- Earthquake force (F = ma) with acceleration in ft/s²
Mechanical vibrations:
- Damping force proportional to velocity
- Mass-spring-damper systems with m in slugs
7. Fluid Dynamics and Hydraulics
Flow and pressure calculations when using imperial units:
Momentum of flowing fluid:
- Mass flow rate: ṁ = ρAv (density in slug/ft³, area in ft², velocity in ft/s)
- Force on pipe bend: F = ṁΔv (in lbf)
Pipe flow:
- Water density: 1.938 slug/ft³ (at 68°F)
- Pressure drop calculations
- Pump power requirements
Aerodynamic forces:
- Drag force (lbf) = ½ ρ v² A C_D
- Air density: 0.00238 slug/ft³ (sea level, standard conditions)
Additional Unit Information
About Atomic Mass Unit (u)
What is the value of 1 u (or Da) in kilograms?
Answer: 1 u = 1.660 539 066 60 × 10⁻²⁷ kg (with standard uncertainty ±0.000 000 000 50 × 10⁻²⁷ kg)
This extraordinarily precise value comes from measurements of carbon-12 atoms using mass spectrometry and relates to the newly defined kilogram (based on Planck's constant as of 2019).
Approximate value: 1 u ≈ 1.6605 × 10⁻²⁷ kg
In grams: 1 u ≈ 1.6605 × 10⁻²⁴ g
Memorization tip: "1.66 and exponent −27"
Uncertainty: The precision is about 0.3 parts per billion (extremely accurate!)
Source: CODATA 2018 recommended values (Committee on Data for Science and Technology)
Is the atomic mass unit (amu) the same as the Dalton (Da)?
Answer: Yes—in modern usage, u (unified atomic mass unit), amu, and Da (Dalton) all refer to the same unit
Historical context:
Pre-1961 (ambiguous):
- "amu" could mean the oxygen-based physics scale (¹⁶O = 16) or chemistry scale (natural O = 16)
- These differed by ~0.03%, causing confusion
1961 unification:
- IUPAC/IUPAP adopted carbon-12 standard
- "u" (unified atomic mass unit) replaced ambiguous "amu"
- 1 u = 1/12 mass of ¹²C atom
1970s-1993:
- "Dalton" (Da) proposed as an alternative name honoring John Dalton
- Gained popularity in biochemistry
Today:
- u: Official name, preferred in chemistry and physics
- Da: Alternative name, preferred in biochemistry (especially kDa for proteins)
- amu: Informal, but understood to mean "u" in modern contexts
Bottom line: 1 u = 1 Da = 1 amu (modern) — all identical
Why was Carbon-12 chosen as the standard for atomic mass?
Answer: Carbon-12 unified divergent physics and chemistry scales while being abundant, stable, and convenient
Historical problem (pre-1961):
- Physicists used ¹⁶O = 16.0000 exactly (pure isotope)
- Chemists used natural oxygen = 16.0000 exactly (isotope mixture)
- Natural oxygen is 99.757% ¹⁶O, 0.038% ¹⁷O, 0.205% ¹⁸O
- Result: Two incompatible atomic mass scales differing by ~0.03%
Carbon-12 advantages:
1. Unification: Resolved the physics-chemistry discrepancy with a single standard
2. Abundance: ¹²C comprises 98.89% of natural carbon (readily available)
3. Stability: Not radioactive (unlike ¹⁴C); doesn't decay
4. Integer mass: Defining ¹²C = 12 exactly gives a clean reference point
5. Chemical importance: Carbon is the basis of organic chemistry—central to life and synthetic compounds
6. Mass spectrometry: Carbon compounds are ubiquitous calibration standards
7. Convenience: Most atomic masses end up close to integers (approximately equal to mass number A)
Alternative considered: Hydrogen was Dalton's original choice, but hydrogen's mass (1.008 u) isn't exactly 1, and hydrogen forms fewer compounds than carbon or oxygen.
Result: Since 1961, all atomic weights worldwide are based on ¹²C = 12.0000 u (exact)
How does the atomic mass unit relate to Avogadro's number?
Answer: The atomic mass unit and Avogadro's number are defined such that mass in u equals molar mass in g/mol numerically
The elegant relationship:
Avogadro's constant: N_A = 6.022 140 76 × 10²³ mol⁻¹ (exact, as of 2019 SI redefinition)
Atomic mass unit: 1 u = 1/12 the mass of one ¹²C atom
Molar mass constant: M_u = 1 g/mol (by definition of the mole)
Mathematical relationship:
1 u = 1 g / N_A
Example:
- One carbon-12 atom: 12 u
- One mole of carbon-12 atoms: 12 g
- Number of atoms: 6.022 × 10²³
Practical consequence: To convert molecular mass (u) to grams, multiply by Avogadro's number:
- 1 water molecule: 18 u
- 1 mole of water: 18 g
- 18 g ÷ (6.022 × 10²³) = 2.99 × 10⁻²³ g per molecule ✓
Why this works: The definition of the mole (amount containing N_A entities) is coordinated with the definition of the atomic mass unit to make this numerical equality hold.
What is the difference between atomic mass and atomic weight?
Answer: Atomic mass refers to a specific isotope; atomic weight is the weighted average of all isotopes in natural abundance
Atomic mass (isotope-specific):
- Mass of one specific isotope
- Example: ¹²C has atomic mass = 12.0000 u (exact)
- Example: ¹³C has atomic mass = 13.0034 u
Atomic weight (element average):
- Weighted average of all naturally occurring isotopes
- Example: Natural carbon (98.89% ¹²C, 1.11% ¹³C) has atomic weight = 12.0107 u
- Listed on the periodic table
Calculation for carbon: Atomic weight = (0.9889 × 12.0000) + (0.0111 × 13.0034) = 12.0107 u
Why "weight" instead of "mass"? Historical naming; "atomic weight" actually refers to mass, not weight (force). The term persists despite being technically incorrect.
Relative atomic mass: Modern term preferred over "atomic weight" (same meaning, less confusing)
Important distinction: When doing precise isotope work (mass spectrometry, nuclear chemistry), use atomic masses of specific isotopes, not elemental atomic weights.
Can I use atomic mass units for objects larger than molecules?
Answer: Technically yes, but it's impractical—atomic mass units are too small for macroscopic objects
Practical range for atomic mass units:
- Atoms: 1-300 u (hydrogen to heaviest elements)
- Small molecules: 10-1,000 u
- Proteins: 1,000-10,000,000 u (1 kDa - 10 MDa)
- Viruses: up to ~1,000 MDa (1 gigadalton, GDa)
Beyond this: Use conventional mass units (grams, kilograms)
Example (why it's impractical):
- A grain of sand (~1 mg = 10⁻⁶ kg)
- In atomic mass units: 10⁻⁶ kg ÷ (1.66 × 10⁻²⁷ kg/u) ≈ 6 × 10²⁰ u
- This number is unwieldy!
Rule of thumb: Use atomic mass units for individual molecules or molecular complexes; switch to grams/kilograms for anything visible to the eye.
Extreme example: A 70 kg human = 4.2 × 10²⁸ u (42,000 trillion trillion u—utterly impractical!)
How accurate are modern atomic mass measurements?
Answer: Extraordinarily accurate—often 8-10 decimal places (parts per billion precision)
Modern mass spectrometry precision:
- Typical: 1 part per million (ppm) — 6 decimal places
- High-resolution: 1 part per billion (ppb) — 9 decimal places
- Ultra-high-resolution: 0.1 ppb — 10 decimal places
Example: Carbon-12:
- Defined as exactly 12.00000000000... u (infinite precision by definition)
Example: Hydrogen-1:
- Measured value: 1.00782503207 u (11 significant figures!)
- Uncertainty: ±0.00000000077 u
Why such precision matters:
1. Isotope identification: Distinguishing ¹²C¹H₄ (16.0313 u) from ¹³C¹H₃ (16.0344 u) requires high precision
2. Mass defect measurements: Nuclear binding energies calculated from tiny mass differences (0.1% of nuclear mass)
3. Molecular formula determination: Mass spectrometry can distinguish C₁₃H₁₂ from C₁₂H₁₂O from C₁₁H₁₆N (all ~168 u) with sufficient precision
4. Fundamental physics: Testing mass-energy equivalence, searching for physics beyond the Standard Model
Limitation: Even with extreme precision, natural isotopic variation (different ¹²C/¹³C ratios in different samples) limits practical accuracy to ~4-5 decimal places for most chemical applications.
Do protons and neutrons have exactly the same mass?
Answer: No—neutrons are slightly heavier than protons by about 0.14%
Precise values:
- Proton mass: 1.007276466621 u
- Neutron mass: 1.00866491595 u
- Difference: 0.00138845 u (neutron is heavier by ~1.4 MeV/c²)
Why this matters:
1. Neutron decay: Free neutrons decay into protons + electrons + antineutrinos with a half-life of ~10 minutes (neutron → proton + e⁻ + ν̄ₑ)
2. Nuclear stability: The mass difference affects which isotopes are stable vs. radioactive
3. Element synthesis: Mass differences determine which nuclear reactions can occur spontaneously in stars
Fun fact: Both are close to 1 u (within 1%), which is why atomic mass numbers (protons + neutrons) approximately equal atomic masses in u
Electron mass: Much lighter—only 0.000548580 u (~1/1836 of a proton)
Consequence: Atomic mass is almost entirely due to protons and neutrons; electrons contribute negligibly (<0.03%)
Why is the atomic mass of hydrogen 1.008 u instead of 1 u?
Answer: Because protons are slightly heavier than 1/12 of a carbon-12 atom, plus hydrogen atoms include an electron
Breakdown of hydrogen atom (¹H):
- Proton: 1.007276 u
- Electron: 0.000549 u
- Binding energy (negligible): −0.000015 u
- Total: 1.007825 u ≈ 1.008 u
Why isn't a proton exactly 1 u?
The atomic mass unit is defined as 1/12 the mass of carbon-12, which contains 6 protons + 6 neutrons + 6 electrons, minus the nuclear binding energy:
¹²C mass: 12 u (exact) = 6 protons + 6 neutrons + 6 electrons − binding energy
Solving: 1 nucleon (proton or neutron) ≈ 1.007-1.009 u (slightly more than 1 u)
Why the carbon-12 nucleus is lighter than 12 individual nucleons: Nuclear binding energy (E = mc²) converts ~0.1 u of mass into energy that holds the nucleus together
Result: Hydrogen (1 proton + 1 electron) ends up at 1.008 u, not 1.000 u
Will the definition of the atomic mass unit ever change?
Answer: Unlikely—the carbon-12 standard is stable, internationally accepted, and fundamental to chemistry
Why it's stable:
1. International agreement: IUPAC, IUPAP, and NIST all recognize ¹²C standard (since 1961)
2. Infrastructure: All atomic weight tables, databases, lab equipment calibrated to carbon-12
3. No compelling alternative: Carbon-12 works perfectly for chemistry and biochemistry
4. Historical continuity: Changing standards disrupts 60+ years of data
Recent change (2019 SI redefinition):
- The kilogram was redefined based on Planck's constant
- This indirectly affects the atomic mass unit (since 1 u is expressed in kg)
- But the change is at the 9th decimal place—completely negligible for chemistry
Future refinement: Values like 1.660539066(50) × 10⁻²⁷ kg will get more decimal places as measurements improve, but the carbon-12 definition (1 u = 1/12 m(¹²C)) won't change
Contrast with other standards:
- Meter: Redefined from physical bar to speed of light (1983)
- Kilogram: Redefined from physical cylinder to Planck constant (2019)
- Atomic mass unit: Based on fundamental particle (¹²C atom)—already a natural standard
Conclusion: The carbon-12 definition is here to stay for the foreseeable future (decades to centuries).
About Slug (sl)
How is the slug defined?
Answer: 1 slug = 1 lbf / (1 ft/s²) — the mass that accelerates at 1 ft/s² under 1 lbf
The slug is defined through Newton's second law (F = ma):
Rearranging: m = F/a
Definition: If a force of 1 pound-force produces an acceleration of 1 foot per second squared, the mass is 1 slug.
In equation form: 1 slug = 1 lbf / (1 ft/s²)
This makes Newton's law work cleanly: F (lbf) = m (slugs) × a (ft/s²)
Alternative definition (equivalent): 1 slug = 32.174 pounds-mass (lbm)
This number (32.174) comes from standard Earth gravity: g = 32.174 ft/s²
How many pounds-mass are in a slug?
Answer: 1 slug = 32.174 pounds-mass (lbm) exactly
This relationship derives from the gravitational constant:
Standard gravity: g = 32.17405 ft/s² (exactly, by definition)
Weight-mass relationship: Weight (lbf) = Mass (lbm) × g / g_c
where g_c = 32.174 lbm·ft/(lbf·s²) (dimensional conversion constant)
On Earth: A mass of 1 lbm experiences a weight of 1 lbf Therefore: A mass of 32.174 lbm experiences a weight of 32.174 lbf
But also: A mass of 1 slug experiences a weight of 32.174 lbf (by definition)
Conclusion: 1 slug = 32.174 lbm
Example:
- Person: 160 lbm
- In slugs: 160 ÷ 32.174 = 4.97 slugs
Why is the slug unit used?
Answer: To simplify F = ma calculations in imperial units by eliminating the need for gravitational conversion constants
The problem without slugs:
Using pounds-mass (lbm) and pounds-force (lbf) in Newton's law requires:
F = ma / g_c
where g_c = 32.174 lbm·ft/(lbf·s²)
This is awkward and error-prone!
The solution with slugs:
Using slugs for mass and lbf for force, Newton's law is simple:
F = ma (no conversion constant!)
Example comparison:
Force: 100 lbf Acceleration: 5 ft/s² Mass = ?
Without slugs (using lbm): m = F × g_c / a = 100 × 32.174 / 5 = 643.48 lbm
With slugs: m = F / a = 100 / 5 = 20 slugs
Much simpler! (Though 20 slugs = 643.48 lbm, same physical mass.)
How do I convert between slugs and kilograms?
Answer: 1 slug = 14.5939 kg (multiply slugs by 14.5939 to get kg)
Slugs to kilograms: kg = slugs × 14.5939
Examples:
- 1 slug = 14.5939 kg
- 5 slugs = 5 × 14.5939 = 72.97 kg
- 10 slugs = 10 × 14.5939 = 145.94 kg
Kilograms to slugs: slugs = kg ÷ 14.5939 (or kg × 0.0685218)
Examples:
- 10 kg = 10 ÷ 14.5939 = 0.685 slugs
- 70 kg = 70 ÷ 14.5939 = 4.80 slugs
- 100 kg = 100 ÷ 14.5939 = 6.85 slugs
Quick approximation:
- 1 slug ≈ 14.6 kg
- 1 kg ≈ 0.069 slugs (roughly 1/15th slug)
Why don't people use slugs in everyday life?
Answer: Slugs are awkward for everyday masses and unfamiliar to the general public
Practical reasons:
1. Unfamiliar numbers: Converting common weights to slugs produces strange values
- "I weigh 5.6 slugs" sounds odd compared to "180 pounds"
- A gallon of milk is "0.26 slugs" vs. "8.6 pounds"
2. No tradition: Unlike pounds (used for centuries in commerce), slugs were invented for technical calculations only
3. Pounds work fine for daily life: The lbf/lbm ambiguity doesn't matter when you're just measuring weight on a scale
4. Imperial persistence: Americans use pounds because of cultural tradition, not technical correctness
Technical fields use slugs precisely because they eliminate ambiguity in force-mass calculations, but this advantage is irrelevant for grocery shopping or body weight.
Cultural reality: People will continue saying "pounds" for everyday masses, while engineers quietly use slugs behind the scenes.
What's the difference between a slug and a pound?
Answer: Slug measures mass; pound can mean either mass (lbm) or force/weight (lbf)
Slug:
- Always a unit of mass
- 1 slug = 32.174 lbm = 14.5939 kg
- Measures quantity of matter (inertia)
- Used in F = ma calculations
Pound-mass (lbm):
- Unit of mass
- 1 lbm = 1/32.174 slug = 0.453592 kg
- Quantity of matter
Pound-force (lbf):
- Unit of force (weight)
- Force exerted by 1 lbm under standard Earth gravity
- 1 lbf = force needed to accelerate 1 slug at 1 ft/s²
Relationship on Earth:
- 1 slug has a mass of 32.174 lbm
- 1 slug weighs (exerts a force of) 32.174 lbf on Earth
- 1 lbm weighs 1 lbf on Earth
Key insight: The numerical coincidence (1 lbm weighs 1 lbf on Earth) obscures the fact that mass and force are different physical quantities. Slugs eliminate this confusion.
Is the slug still used in engineering?
Answer: Yes, but rarely—mainly in American aerospace and dynamics courses
Where slugs are still used:
1. Aerospace engineering:
- NASA and aerospace contractors for some calculations
- Aircraft dynamics and performance
- Rocket propulsion when working in imperial units
2. Engineering education:
- Mechanical engineering dynamics courses
- Teaching Newton's laws with imperial units
- Demonstrating unit consistency
3. Defense/ballistics:
- Military projectile calculations
- Weapons systems analysis
4. Legacy documentation:
- Understanding 20th-century engineering reports
- Maintaining older systems specified in FPS units
Where slugs are NOT used:
- International engineering (uses kilograms)
- Daily life (people use pounds)
- Most modern engineering software (defaults to SI units)
- Scientific research (exclusively metric)
Current status: Declining but not extinct; maintained for continuity with older American engineering systems
Can I weigh myself in slugs?
Answer: Technically yes, but practically no—scales measure force (weight), not mass
The technical issue:
Bathroom scales measure weight (force in lbf or kg-force), not mass:
- They use a spring that compresses under gravitational force
- The readout is calibrated to show "pounds" or "kilograms"
Converting scale reading to slugs:
If your scale says "160 pounds" (meaning 160 lbf weight):
- Your mass = 160 lbm / 32.174 = 4.97 slugs
Or if metric scale says "70 kg" (meaning 70 kg-force weight):
- Your mass = 70 kg / 14.5939 = 4.80 slugs
Why people don't do this:
- Unfamiliar: "I weigh 5 slugs" sounds strange
- Extra math: Requires division by 32.174
- No benefit: Pounds work fine for personal weight tracking
Correct statement: "My mass is 4.97 slugs" (not "I weigh 4.97 slugs"—weight is measured in lbf!)
How does the slug relate to Newton's second law?
Answer: The slug is defined to make F = ma work directly with pounds-force and ft/s²
Newton's second law: Force = mass × acceleration
In slug system (FPS units):
- Force in pound-force (lbf)
- Mass in slugs (sl)
- Acceleration in feet per second squared (ft/s²)
Result: F (lbf) = m (slugs) × a (ft/s²)
Example:
- Mass: 2 slugs
- Acceleration: 15 ft/s²
- Force: F = 2 × 15 = 30 lbf
Why this works: The slug is defined such that 1 lbf accelerates 1 slug at 1 ft/s²
Contrast with lbm system (more complicated): F (lbf) = m (lbm) × a (ft/s²) / g_c
where g_c = 32.174 lbm·ft/(lbf·s²)
Same example using lbm:
- Mass: 2 slugs = 64.348 lbm
- Acceleration: 15 ft/s²
- Force: F = 64.348 × 15 / 32.174 = 30 lbf (same result, more complex calculation)
The slug's purpose: Eliminate the g_c conversion factor!
What does "slug" mean and where does the name come from?
Answer: "Slug" evokes sluggishness or inertia—the resistance of mass to acceleration
Etymology:
The term was coined by British physicist Arthur Mason Worthington around 1900.
The metaphor:
- Sluggish = slow to respond, resistant to movement
- Inertia = the tendency of massive objects to resist acceleration
- A more massive object is more "sluggish"
The connection to physics:
Inertial mass is the property of matter that resists acceleration:
- Larger mass → greater "sluggishness" → harder to accelerate
- Smaller mass → less "sluggish" → easier to accelerate
Example:
- Push a shopping cart (low mass) → accelerates easily (not very sluggish)
- Push a truck (high mass in slugs) → accelerates slowly (very sluggish!)
Word choice reasoning: Worthington wanted a vivid, memorable term that conveyed the physical concept of inertia while fitting the imperial system of units (slug, pound, foot).
Alternative names considered: The unit could have been called "inertia pound" or "force-pound," but "slug" was catchier and emphasized the conceptual link to resistance to motion.
Why is 1 slug equal to 32.174 pounds-mass specifically?
Answer: Because 32.174 ft/s² is the standard acceleration due to Earth's gravity (g)
The relationship derives from weight-force:
Weight (lbf) = mass (lbm) × gravity (ft/s²) / g_c
where g_c = 32.174 lbm·ft/(lbf·s²) is the dimensional conversion constant
On Earth (g = 32.174 ft/s²):
- 1 lbm weighs: 1 lbm × 32.174 / 32.174 = 1 lbf
Also by definition:
- 1 slug weighs: 1 slug × 32.174 ft/s² = 32.174 lbf (from F = ma)
Combining these:
- If 1 lbm weighs 1 lbf, and 1 slug weighs 32.174 lbf...
- Then 1 slug must equal 32.174 lbm!
The number 32.174 is Earth's standard gravitational acceleration: g = 32.17405 ft/s² ≈ 32.174 ft/s²
Consequence: The slug naturally relates to pounds-mass through Earth's gravity, even though the slug is a mass unit (not dependent on gravity).
On other planets:
- Mass is still measured in slugs (unchanged)
- Weight changes (different g value)
- Example: 1 slug on Moon weighs only 5.32 lbf (not 32.174 lbf)
Will the slug eventually disappear?
Answer: Likely yes—it's declining rapidly as engineering shifts to SI units globally
Factors driving obsolescence:
1. International standardization:
- Global engineering collaborations require common units (SI/metric)
- Slug is unknown outside U.S./British contexts
2. Educational shifts:
- Even American universities teach SI units first
- Slugs relegated to "alternative units" or historical notes
3. Software migration:
- Modern CAD/simulation software defaults to metric (kg, N, m)
- Maintaining slug support is extra development cost
4. Generational change:
- Engineers trained in FPS/slug units are retiring
- New graduates work primarily in metric
5. Daily life disconnect:
- Slug never entered common vocabulary (unlike "pound")
- No cultural attachment to preserve it
Where it might persist longest:
- Legacy aerospace systems (maintaining old aircraft/rockets)
- Specialized defense applications
- Historical engineering documentation
- Educational examples showing unit system consistency
Likely outcome: Slug will become a "historical unit" known primarily to:
- Engineering historians
- Those maintaining 20th-century equipment
- Educators explaining evolution of unit systems
Similar to how poundals (another imperial force unit) are now essentially extinct despite once being scientifically "correct."
Conversion Table: Atomic Mass Unit to Slug
| Atomic Mass Unit (u) | Slug (sl) |
|---|---|
| 0.5 | 0 |
| 1 | 0 |
| 1.5 | 0 |
| 2 | 0 |
| 5 | 0 |
| 10 | 0 |
| 25 | 0 |
| 50 | 0 |
| 100 | 0 |
| 250 | 0 |
| 500 | 0 |
| 1,000 | 0 |
People Also Ask
How do I convert Atomic Mass Unit to Slug?
To convert Atomic Mass Unit to Slug, enter the value in Atomic Mass Unit in the calculator above. The conversion will happen automatically. Use our free online converter for instant and accurate results. You can also visit our weight converter page to convert between other units in this category.
Learn more →What is the conversion factor from Atomic Mass Unit to Slug?
The conversion factor depends on the specific relationship between Atomic Mass Unit and Slug. You can find the exact conversion formula and factor on this page. Our calculator handles all calculations automatically. See the conversion table above for common values.
Can I convert Slug back to Atomic Mass Unit?
Yes! You can easily convert Slug back to Atomic Mass Unit by using the swap button (⇌) in the calculator above, or by visiting our Slug to Atomic Mass Unit converter page. You can also explore other weight conversions on our category page.
Learn more →What are common uses for Atomic Mass Unit and Slug?
Atomic Mass Unit and Slug are both standard units used in weight measurements. They are commonly used in various applications including engineering, construction, cooking, and scientific research. Browse our weight converter for more conversion options.
For more weight conversion questions, visit our FAQ page or explore our conversion guides.
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Last verified: December 3, 2025