Rankine (°R) - Unit Information & Conversion
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What is a Rankine?
The Rankine scale (°R or °Ra) is an absolute thermodynamic temperature scale where zero represents absolute zero—the theoretical point at which all molecular motion ceases—while using Fahrenheit-sized degree increments of 1 degree Rankine = 1 degree Fahrenheit. Named after Scottish engineer William John Macquorn Rankine, who proposed it in 1859, the scale provides the thermodynamic advantages of an absolute scale (essential for calculations involving gas laws, heat engines, and entropy) while maintaining compatibility with the Fahrenheit measurements familiar to American and British engineers. The conversion between Rankine and Fahrenheit is straightforward: °R = °F + 459.67, meaning water freezes at 491.67 °R and boils at 671.67 °R at standard atmospheric pressure. While largely superseded by Kelvin in scientific contexts and international engineering, Rankine remains in use within certain American engineering disciplines—particularly aerospace, cryogenics, and thermodynamics textbooks—where working exclusively in U.S. customary units is preferred or traditional. The scale's persistence reflects the broader continuation of Fahrenheit in American industry, allowing absolute temperature calculations without converting to metric units.
History of the Rankine
The Rankine scale was proposed in 1859 by Scottish engineer and physicist William John Macquorn Rankine (1820-1872), a professor at the University of Glasgow and one of the founders of the science of thermodynamics. Rankine developed the scale shortly after William Thomson (Lord Kelvin) introduced his absolute temperature scale in 1848. While Kelvin's scale used Celsius degree increments and was ideal for scientific work in metric countries, Rankine recognized that engineers in Britain and America—who worked primarily with Fahrenheit measurements—needed an equivalent absolute scale that didn't require constant conversion. By setting zero at absolute zero (−459.67 °F) while maintaining Fahrenheit degree intervals, Rankine created a scale that simplified thermodynamic calculations (like the Carnot efficiency formula: η = 1 - T_cold/T_hot) for engineers using British imperial units. The scale was particularly influential in 19th and early 20th century engineering, appearing prominently in steam engine design, thermodynamic cycle analysis, and heat transfer calculations. The American Society of Mechanical Engineers (ASME) adopted Rankine for many standard tables and formulas through the mid-20th century. However, the 1960s push for metrication in most countries, combined with the global scientific community's preference for Kelvin, gradually diminished Rankine's usage outside the United States. Today, Rankine persists primarily in American aerospace engineering (rocket propulsion calculations), cryogenics (liquefied gas handling), specialized thermodynamics education, and legacy engineering documentation. Its continued existence parallels Fahrenheit's retention in American culture—a measurement system maintained by institutional inertia, industry standards, and educational tradition despite global metric adoption.
Quick Answer
The Rankine scale is an absolute temperature scale where 0 °R = absolute zero, using Fahrenheit-sized degrees
Conversion: °R = °F + 459.67
Key temperatures:
- Absolute zero: 0 °R (−459.67 °F, 0 K)
- Water freezes: 491.67 °R (32 °F, 273.15 K)
- Water boils: 671.67 °R (212 °F, 373.15 K)
Quick Comparison Table
| Temperature | Rankine | Fahrenheit | Celsius | Kelvin |
|---|---|---|---|---|
| Absolute zero | 0 °R | −459.67 °F | −273.15 °C | 0 K |
| Nitrogen boils | 139.3 °R | −320.4 °F | −195.8 °C | 77.35 K |
| Dry ice sublimes | 389.0 °R | −109.3 °F | −78.5 °C | 194.65 K |
| Water freezes | 491.67 °R | 32 °F | 0 °C | 273.15 K |
| Room temperature | 527.67 °R | 68 °F | 20 °C | 293.15 K |
| Body temperature | 558.27 °R | 98.6 °F | 37 °C | 310.15 K |
| Water boils | 671.67 °R | 212 °F | 100 °C | 373.15 K |
| Oven temperature | 859.67 °R | 400 °F | 204 °C | 477.15 K |
Definition
What Is the Rankine Scale?
The Rankine scale (symbol: °R or °Ra) is an absolute thermodynamic temperature scale where:
- Zero point: Absolute zero (0 °R = −459.67 °F), the theoretical lowest possible temperature where all molecular kinetic energy ceases
- Degree size: Equal to Fahrenheit degrees (1 °R increment = 1 °F increment)
- Named after: William John Macquorn Rankine (1820-1872), Scottish engineer and physicist
Absolute Temperature Scales
An absolute temperature scale begins at absolute zero rather than an arbitrary freezing point:
Absolute scales (start at absolute zero):
- Kelvin (K): Uses Celsius-sized degrees, 0 K = absolute zero, used worldwide in science
- Rankine (°R): Uses Fahrenheit-sized degrees, 0 °R = absolute zero, used in some U.S. engineering
Relative scales (start at arbitrary points):
- Celsius (°C): 0 °C = water's freezing point (at standard pressure)
- Fahrenheit (°F): 0 °F = freezing point of brine solution, 32 °F = water's freezing point
Why Absolute Scales Matter
Many fundamental physics equations require absolute temperatures because ratios and products become meaningful only when zero truly means "no thermal energy":
Ideal gas law: PV = nRT (T must be absolute) Carnot efficiency: η = 1 - T_cold/T_hot (requires absolute temperatures) Stefan-Boltzmann law: Power radiated ∝ T⁴ (absolute temperature to fourth power) Entropy calculations: ΔS = Q/T (T must be absolute to avoid division by zero)
Using relative scales (Fahrenheit, Celsius) in these equations produces nonsensical results. Absolute scales (Rankine, Kelvin) make the mathematics work correctly.
Official Definition
1 degree Rankine = 1 degree Fahrenheit (in size)
Relationship to Fahrenheit: °R = °F + 459.67
Relationship to Kelvin: °R = K × 9/5 (or °R = K × 1.8)
Relationship to Celsius: °R = (°C + 273.15) × 9/5
History
William John Macquorn Rankine (1820-1872)
William Rankine was a Scottish engineer, physicist, and professor at the University of Glasgow who made foundational contributions to thermodynamics, civil engineering, and molecular physics.
Key contributions:
- Formulated the Rankine cycle (1859), describing the ideal thermodynamic cycle for steam engines
- Developed the Rankine temperature scale (1859) as an absolute scale compatible with Fahrenheit
- Wrote influential textbooks on applied mechanics, steam engines, and civil engineering
- Co-founded the science of thermodynamics alongside Carnot, Clausius, Kelvin, and Joule
Rankine was a contemporary and correspondent of William Thomson (Lord Kelvin), who proposed the Kelvin absolute scale in 1848. The two scientists worked on similar thermodynamic problems but approached them from different engineering traditions—Kelvin from metric/Celsius contexts, Rankine from British imperial/Fahrenheit contexts.
The Need for an Absolute Scale (1840s-1850s)
The mid-19th century saw rapid developments in thermodynamics driven by the Industrial Revolution's reliance on steam engines:
Carnot's theorem (1824): Sadi Carnot demonstrated that heat engine efficiency depends on the temperature ratio between hot and cold reservoirs, implicitly requiring an absolute temperature scale
Joule's mechanical equivalent of heat (1843-1850): James Prescott Joule established that heat and mechanical work are interconvertible, laying foundations for the first law of thermodynamics
Thomson's (Kelvin's) absolute scale (1848): William Thomson proposed an absolute scale based on Carnot's theorem, using Celsius degree increments, with zero at −273.15 °C
These developments made clear that thermodynamic calculations required absolute temperature measurements, but Thomson's Kelvin scale was impractical for British and American engineers who worked exclusively in Fahrenheit.
Rankine's Proposal (1859)
In 1859, Rankine published his absolute temperature scale in engineering papers, presenting it as the practical solution for engineers who needed absolute temperatures but worked in imperial units:
Rankine's logic:
- Thermodynamic calculations require absolute zero as the baseline
- British and American engineers measure temperature in Fahrenheit
- Constantly converting Fahrenheit ↔ Celsius ↔ Kelvin introduces errors and inefficiency
- An absolute scale with Fahrenheit-sized degrees solves the problem elegantly
The result: 0 °R = absolute zero (−459.67 °F), with degree increments matching Fahrenheit
This allowed engineers to use familiar Fahrenheit measurements while accessing the mathematical benefits of absolute temperature.
Adoption in Engineering (1860s-1960s)
The Rankine scale became standard in British and American engineering disciplines throughout the late 19th and first half of the 20th centuries:
Steam engineering: Rankine cycle analysis (for steam turbines, power plants) used Rankine temperatures for efficiency calculations
ASME standards: The American Society of Mechanical Engineers incorporated Rankine into standard tables for steam properties, refrigeration cycles, and combustion calculations
Aerospace engineering: Early rocket and jet engine development (1940s-1960s) used Rankine for combustion chamber and exhaust nozzle temperature calculations
Cryogenics: Liquefied gas industries (oxygen, nitrogen, hydrogen) used Rankine when working with U.S. measurement systems
Thermodynamics textbooks: Engineering thermodynamics texts published in the U.S. and U.K. through the 1960s routinely presented equations in both Kelvin and Rankine
Decline and Modern Usage (1960s-Present)
Several factors led to Rankine's decline:
International metrication (1960s-1980s): Most countries adopted SI units (including Kelvin), making Rankine unnecessary outside the United States
Scientific standardization: The global scientific community standardized on Kelvin, making it the universal absolute scale for research and international collaboration
U.S. engineering education shift: Even American engineering programs increasingly taught Kelvin as the primary absolute scale, relegating Rankine to historical footnotes
Computing and automation: Modern engineering software typically works in SI units (Kelvin), reducing incentive to maintain Rankine compatibility
Where Rankine Survives Today
Despite its decline, Rankine persists in specific niches:
American aerospace engineering: NASA and aerospace contractors occasionally use Rankine in rocket propulsion calculations when working with U.S. customary units (pounds-force, BTU, etc.)
Cryogenic engineering: Liquefied natural gas (LNG) facilities and industrial gas companies in the U.S. may use Rankine for process calculations
Legacy documentation: Older engineering manuals, equipment specifications, and technical standards still reference Rankine, requiring continued familiarity
Thermodynamics education: Some U.S. engineering thermodynamics courses teach Rankine alongside Kelvin to demonstrate absolute temperature concepts with Fahrenheit context
Historical research: Engineers and historians studying 19th-20th century technology encounter Rankine in original documents and must understand conversions
Real-World Examples
Cryogenic Temperatures (Below 200 °R)
Ultra-cold temperatures for liquefied gases and cryogenics:
- Absolute zero: 0 °R (theoretical limit, never achieved)
- Helium boiling point: 7.6 °R (−451.9 °F, 4.2 K)
- Hydrogen boiling point: 37.1 °R (−422.6 °F, 20.3 K)
- Nitrogen boiling point: 139.3 °R (−320.4 °F, 77.4 K)
- Oxygen boiling point: 162.7 °R (−297.3 °F, 90.2 K)
Applications: Rocket fuel storage, superconducting magnets, medical cryotherapy, industrial gas production
Cold Temperatures (200-450 °R)
Freezer temperatures and cold environments:
- Dry ice sublimation: 389.0 °R (−109.3 °F, 194.7 K)
- Arctic winter extreme: 405 °R (−55 °F, 230 K)
- Home freezer: 440-460 °R (−20 to 0 °F, 244-256 K)
- Refrigerator: 485 °R (25 °F, 269 K)
Applications: Food preservation, cold climate operations, refrigeration cycles
Temperate Temperatures (450-600 °R)
Everyday human environment temperatures:
- Water freezes: 491.67 °R (32 °F, 273.15 K) [exact]
- Cold winter day: 500 °R (40 °F, 278 K)
- Cool room: 520 °R (60 °F, 289 K)
- Room temperature: 527.67 °R (68 °F, 293.15 K)
- Warm room: 540 °R (80 °F, 300 K)
- Human body temperature: 558.27 °R (98.6 °F, 310.15 K)
- Hot summer day: 580 °R (120 °F, 322 K)
Applications: HVAC engineering, building design, human comfort analysis
Hot Temperatures (600-1000 °R)
Cooking, engines, industrial processes:
- Water boils: 671.67 °R (212 °F, 373.15 K) [exact]
- Moderate oven: 760 °R (300 °F, 422 K)
- Hot oven: 860 °R (400 °F, 478 K)
- Lead melts: 987 °R (528 °F, 600 K)
Applications: Cooking, baking, metallurgy, heat treatment
Very Hot Temperatures (1000-3000 °R)
High-temperature industrial and combustion processes:
- Aluminum melts: 1679 °R (1220 °F, 933 K)
- Internal combustion engine exhaust: 1400-1800 °R (940-1340 °F, 778-1022 K)
- Natural gas flame: 3500 °R (3040 °F, 1950 K)
- Iron melts: 3031 °R (2572 °F, 1811 K)
Applications: Combustion analysis, furnace design, metallurgical processing
Extreme Temperatures (Above 3000 °R)
High-energy processes and stellar phenomena:
- Steel melts: 3200 °R (2740 °F, 1783 K)
- Jet engine combustor: 3000-4000 °R (2540-3540 °F, 1670-2100 K)
- Rocket combustion chamber: 5000-7000 °R (4540-6540 °F, 2780-3890 K)
- Sun''s surface: 10,340 °R (9880 °F, 5780 K)
- Lightning bolt: 54,000 °R (53,500 °F, 30,000 K)
Applications: Aerospace propulsion, plasma physics, astrophysics
Common Uses
1. Thermodynamic Cycle Analysis
Engineers analyzing heat engines and refrigeration cycles use Rankine when working in U.S. customary units:
Carnot efficiency calculation: η = 1 - T_cold/T_hot
Example (using Rankine for compatibility with imperial units):
- Hot reservoir: 1160 °R (700 °F, combustion chamber)
- Cold reservoir: 540 °R (80 °F, ambient air)
- Maximum efficiency: η = 1 - 540/1160 = 1 - 0.465 = 53.5%
If you incorrectly used Fahrenheit (relative scale) instead: η = 1 - 80/700 = 88.6% ← Wrong! (impossibly high)
Rankine (absolute scale) gives the correct physical result.
Ideal gas law (PV = nRT): Requires absolute temperature T in Rankine or Kelvin Refrigeration coefficient of performance: COP = T_cold/(T_hot - T_cold), requires absolute T Entropy change: ΔS = Q/T, requires absolute T
2. Aerospace and Rocket Propulsion
NASA and aerospace contractors sometimes use Rankine in rocket engine calculations when working entirely in imperial units:
Rocket nozzle expansion:
- Combustion chamber temperature: 6000 °R (5540 °F, liquid hydrogen/oxygen combustion)
- Nozzle exit temperature: 1500 °R (1040 °F, after expansion)
- Temperature ratio used in thrust calculations: 1500/6000 = 0.25
Specific impulse calculations: Rocket performance metrics sometimes expressed in U.S. units (pounds-force, BTU, Rankine)
Reentry heating analysis: Atmospheric friction temperatures calculated in Rankine for Space Shuttle and Apollo programs
3. Cryogenic and Liquefied Gas Engineering
Engineers working with liquefied natural gas (LNG), liquid nitrogen, or liquid oxygen may use Rankine in American industrial contexts:
LNG storage:
- Methane boiling point: 201.1 °R (−258.6 °F, 111.7 K)
- Storage tank insulation must maintain temperatures below 210 °R
Nitrogen liquefaction: Process temperatures from ambient (528 °R) down to liquid nitrogen (140 °R)
Oxygen separation: Cryogenic air separation units cool air from 520 °R to 163 °R (oxygen boiling point)
4. Steam Power and HVAC Engineering
Historical and some modern steam system calculations use Rankine:
Steam turbine efficiency: Calculating ideal Rankine cycle efficiency for power plants Boiler performance: Heat transfer calculations involving steam temperatures in Rankine HVAC refrigeration cycles: Coefficient of performance calculations requiring absolute temperatures
5. Combustion and Internal Combustion Engines
Engine designers analyzing combustion processes may use Rankine when working in U.S. units:
Compression ratio effects: Calculating temperature rise during compression stroke Exhaust temperatures: Modeling exhaust gas temperatures for turbocharger design Flame temperatures: Analyzing combustion chamber temperatures in Rankine for compatibility with BTU energy units
6. Materials Science and Heat Treatment
Metallurgists and materials engineers working with U.S. specifications:
Heat treatment processes: Tempering, annealing, and hardening temperatures sometimes specified in Rankine in older American standards Thermal expansion: Calculating expansion coefficients with temperature in Rankine Phase transitions: Melting and solidification temperatures in absolute scale for thermodynamic calculations
7. Historical Engineering and Technical Documentation
Engineers working with legacy systems, historical restoration, or archival research:
Old ASME standards: Early 20th century steam tables and equipment specifications used Rankine Vintage aviation: WWII and early jet age aircraft engine documentation may use Rankine Technical history: Understanding historical engineering achievements requires Rankine fluency
Conversion Guide
Converting Fahrenheit to Rankine
Formula: °R = °F + 459.67
Why 459.67? Because absolute zero = −459.67 °F = 0 °R
Examples:
- 32 °F (water freezes) = 32 + 459.67 = 491.67 °R
- 212 °F (water boils) = 212 + 459.67 = 671.67 °R
- 68 °F (room temp) = 68 + 459.67 = 527.67 °R
- −40 °F (extremely cold) = −40 + 459.67 = 419.67 °R
- 0 °F (freezing brine) = 0 + 459.67 = 459.67 °R
Reverse (Rankine to Fahrenheit): °F = °R − 459.67
Converting Celsius to Rankine
Formula: °R = (°C + 273.15) × 9/5
Step-by-step:
- Convert Celsius to Kelvin: K = °C + 273.15
- Convert Kelvin to Rankine: °R = K × 9/5
Examples:
- 0 °C = (0 + 273.15) × 9/5 = 273.15 × 1.8 = 491.67 °R
- 100 °C = (100 + 273.15) × 9/5 = 373.15 × 1.8 = 671.67 °R
- 20 °C = (20 + 273.15) × 9/5 = 293.15 × 1.8 = 527.67 °R
- −273.15 °C = (−273.15 + 273.15) × 9/5 = 0 × 1.8 = 0 °R (absolute zero)
Reverse (Rankine to Celsius): °C = (°R × 5/9) − 273.15
Converting Kelvin to Rankine
Formula: °R = K × 9/5 (or °R = K × 1.8)
Why? Kelvin uses Celsius-sized degrees, Rankine uses Fahrenheit-sized degrees, and Fahrenheit degrees are 9/5 the size of Celsius degrees
Examples:
- 273.15 K (water freezes) = 273.15 × 1.8 = 491.67 °R
- 373.15 K (water boils) = 373.15 × 1.8 = 671.67 °R
- 293.15 K (room temp) = 293.15 × 1.8 = 527.67 °R
- 0 K (absolute zero) = 0 × 1.8 = 0 °R
- 100 K (cryogenic) = 100 × 1.8 = 180 °R
Reverse (Rankine to Kelvin): K = °R × 5/9 (or K = °R / 1.8)
Temperature Difference Conversions
Important distinction: Temperature differences (ΔT) convert differently than absolute temperatures
For temperature changes (not absolute temperatures):
- 1 °R change = 1 °F change (same degree size)
- 1 K change = 1 °C change (same degree size)
- 1 °R change = 5/9 K change (different degree sizes)
Example (temperature drop):
- Engine cools from 700 °F to 200 °F
- Temperature drop in Fahrenheit: ΔT = 700 − 200 = 500 °F
- Temperature drop in Rankine: ΔT = 500 °R (same value!)
- But absolute temperatures: 700 °F = 1159.67 °R, 200 °F = 659.67 °R
Don't confuse absolute temperature conversion with temperature difference conversion!
Common Conversion Mistakes
1. Using Fahrenheit Instead of Rankine in Absolute Temperature Equations
The Mistake: Plugging Fahrenheit directly into thermodynamic equations requiring absolute temperature
Why It Happens: Familiarity with Fahrenheit leads to forgetting the +459.67 offset
Example of the error (Carnot efficiency):
- Hot reservoir: 700 °F (1159.67 °R)
- Cold reservoir: 80 °F (539.67 °R)
- Wrong (using Fahrenheit): η = 1 - 80/700 = 88.6%
- Correct (using Rankine): η = 1 - 539.67/1159.67 = 53.5%
Impact: The wrong calculation gives impossibly high efficiency, violating the second law of thermodynamics!
Correct approach: Always convert Fahrenheit to Rankine (add 459.67) before using in thermodynamic equations
2. Confusing Temperature Differences with Absolute Temperatures
The Mistake: Adding 459.67 when converting temperature changes instead of absolute temperatures
Why It Happens: Misunderstanding when the offset applies
The Truth:
- Absolute temperature: Use the full conversion (°R = °F + 459.67)
- Temperature difference: Use equal values (1 °R change = 1 °F change)
Example:
- Object heats from 70 °F to 120 °F
- Temperature rise: ΔT = 50 °F
- Temperature rise in Rankine: ΔT = 50 °R (not 50 + 459.67!)
Correct understanding: The offset (459.67) shifts the scale but doesn't affect differences
3. Mixing Up Kelvin-Rankine Conversion Direction
The Mistake: Multiplying by 9/5 when you should divide, or vice versa
Why It Happens: Confusion about which scale is larger per degree
The Truth:
- Rankine uses larger degree intervals (Fahrenheit-sized)
- Kelvin uses smaller degree intervals (Celsius-sized)
- Going from smaller (K) to larger (°R): multiply by 9/5
- Going from larger (°R) to smaller (K): multiply by 5/9 (or divide by 9/5)
Mnemonic: "Rankine is bigger, so multiply by 9/5 when converting FROM Kelvin"
Example:
- Correct: 300 K × 9/5 = 540 °R ✓
- Wrong: 300 K × 5/9 = 166.67 °R ✗ (way too cold!)
4. Forgetting That Zero Points Align (Absolute Zero)
The Mistake: Thinking Rankine and Kelvin have different zero points like Celsius and Fahrenheit do
Why It Happens: Overgeneralizing from Fahrenheit-Celsius differences
The Truth: Both Rankine and Kelvin start at absolute zero:
- 0 °R = 0 K = absolute zero
- 0 °F ≠ 0 °C (these are different temperatures)
This means the relationship between Rankine and Kelvin is purely a scaling factor (9/5), with no offset.
Correct conversion: °R = K × 9/5 (no addition/subtraction needed)
5. Using Rankine Outside Its Intended Context
The Mistake: Using Rankine in international documentation or scientific papers expecting Kelvin
Why It Happens: Assuming U.S.-centric units are universally understood
The Truth: Rankine is almost exclusively used in American engineering niches. International audiences expect Kelvin.
Impact: Confusion, errors in international collaboration, rejection of technical papers
Correct approach:
- Use Kelvin for international scientific/engineering work
- Use Rankine only when working specifically in U.S. customary unit systems (BTU, pounds-force, etc.) or with legacy American documentation
6. Rounding Errors with 459.67 Constant
The Mistake: Rounding 459.67 to 460 for simplicity
Why It Happens: Thinking the 0.67 is negligible
The Truth: The 459.67 constant is exact (derived from the precise definition of absolute zero: −459.67 °F)
Impact on precision:
- Water freezing point (32 °F) → 32 + 460 = 492 °R (wrong by 0.33 °R)
- For high-precision engineering (aerospace, cryogenics), this error matters
Correct approach: Always use 459.67 (exact value), not 460
Rankine Conversion Formulas
To Celsius:
To Fahrenheit:
To Kelvin:
To Réaumur:
To Rømer:
To Newton:
To Delisle:
Frequently Asked Questions
Answer: 0 °R (exactly) Absolute zero is the lowest possible temperature, where all classical molecular motion ceases and a system has minimal quantum mechanical zero-point energy. On the Rankine scale, this is defined as exactly 0 °R. Absolute zero in other scales:
- Rankine: 0 °R (by definition)
- Fahrenheit: −459.67 °F
- Kelvin: 0 K (by definition)
- Celsius: −273.15 °C The Rankine scale, like Kelvin, is an absolute scale, meaning its zero point represents true zero thermal energy (in the classical thermodynamic sense), not an arbitrary freezing point like Celsius or Fahrenheit.
Convert Rankine
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