Joule (J) - Unit Information & Conversion

Quick Answer

What is a Joule? A joule (J) is the SI unit of energy equal to the work done by one newton of force over one meter, or one watt of power for one second. Lifting a small apple (100g) one meter requires ~1 joule. A food Calorie equals 4,184 joules. An AA battery stores ~10,000 joules (10 kJ). Your home uses ~100 million joules (100 MJ = 28 kWh) per day. Use our energy converter for instant joule conversions.

Quick Comparison Table

Unit	Energy in Joules	Relative to 1 J
1 joule (J)	1 J	1× (baseline)
1 kilojoule (kJ)	1,000 J	1,000×
1 megajoule (MJ)	1,000,000 J	1,000,000×
1 gigajoule (GJ)	1,000,000,000 J	1 billion×
1 calorie (thermochemical)	4.184 J	4.184×
1 Calorie (food kcal)	4,184 J	4,184×
1 watt-hour (Wh)	3,600 J	3,600×
1 kilowatt-hour (kWh)	3,600,000 J	3.6 million×
1 British thermal unit (BTU)	1,055 J	1,055×
1 electronvolt (eV)	1.602 × 10⁻¹⁹ J	1.602 × 10⁻¹⁹×

Quick context: Pressing a keyboard key uses ~0.15 joules. Your heartbeat performs ~1 joule of work. Boiling a liter of water requires ~420,000 joules (420 kJ).

Definition and Standards

SI Definition

The joule is the SI derived unit of energy, work, and heat, defined as:

1 joule = the energy transferred when a force of 1 newton acts through a distance of 1 meter

Mathematically:

• 1 J = 1 N·m (newton-meter)
• 1 J = 1 kg·m²/s² (SI base units)
• 1 J = 1 W·s (watt-second)
• 1 J = 1 Pa·m³ (pascal-cubic meter)

Multiple Equivalent Definitions

Mechanical work: 1 J = work done moving an object 1 meter against 1 newton force

Electrical energy: 1 J = energy dissipated passing 1 ampere through 1 ohm resistance for 1 second (1 J = 1 A² · Ω · s = 1 V · A · s)

Kinetic energy: 1 J = kinetic energy of a 2 kg mass moving at 1 m/s (KE = ½mv² = ½ × 2 × 1² = 1 J)

Gravitational potential energy: 1 J = energy to lift ~102 grams by 1 meter on Earth (PE = mgh = 0.102 kg × 9.8 m/s² × 1 m ≈ 1 J)

Thermal energy: 1 J ≈ 0.239 calories (energy to raise 0.239 grams of water by 1°C)

2019 SI Redefinition

The 2019 SI revision redefined the joule based on exact fundamental constants:

• Planck constant (h): Exactly 6.62607015 × 10⁻³⁴ J·s
• Speed of light (c): Exactly 299,792,458 m/s
• Caesium hyperfine frequency: Exactly 9,192,631,770 Hz

Since the joule is defined in terms of kilogram, meter, and second, and these are now defined via fundamental constants, the joule has absolute stability independent of physical artifacts.

Standard Multiples

Kilojoule (kJ): 1 kJ = 1,000 J

• Typical for food energy (1 food Calorie = 4.184 kJ)
• Small appliance energy consumption

Megajoule (MJ): 1 MJ = 1,000,000 J = 1,000 kJ

• Vehicle fuel energy (1 liter gasoline ≈ 32 MJ)
• Industrial processes, home daily energy use

Gigajoule (GJ): 1 GJ = 1,000,000,000 J = 1,000 MJ

• Large-scale energy systems
• Natural gas (1 cubic meter ≈ 38 MJ, 1 therm = 105.5 MJ)

Terajoule (TJ): 1 TJ = 10¹² J

• Power plant output (per day/month)
• National energy statistics

History and Evolution

The Mechanical Equivalent of Heat (1840s-1850s)

James Prescott Joule (1818-1889), an English brewer and amateur scientist, conducted groundbreaking experiments demonstrating that mechanical work and heat are equivalent.

Famous paddle-wheel experiment (1843-1850): Joule built apparatus where falling weights drove paddles that stirred water in an insulated container. He precisely measured:

• Mechanical work input (weight × distance fallen)
• Temperature rise of water
• Established ratio: ~772 foot-pounds of work = 1 BTU of heat
• Modern equivalent: 4.184 joules = 1 calorie

Joule's work was initially met with skepticism but eventually revolutionized thermodynamics by unifying heat and mechanical energy under the first law of thermodynamics (conservation of energy).

Lord Kelvin (William Thomson) and Rudolf Clausius incorporated Joule's findings into the foundation of thermodynamics in the 1850s-1860s.

Adoption as a Unit (1882)

The British Association for the Advancement of Science formally adopted "joule" as the unit of work at its 1882 meeting, honoring James Prescott Joule's contributions. The joule was defined as 10⁷ ergs (the CGS energy unit).

Early definition: 1 joule = 10⁷ erg = 10⁷ g·cm²/s²

This established the joule in the meter-kilogram-second (MKS) system, precursor to SI.

International System of Units (1960)

The 11th General Conference on Weights and Measures (CGPM) in 1960 established the International System of Units (SI), designating the joule as the official SI unit for energy, work, and heat.

Unified energy unit: The joule replaced multiple historical units:

• Calorie (thermochemistry, nutrition)
• Erg (CGS physics)
• Foot-pound (engineering)
• Watt-hour (electricity)
• BTU (heating/cooling)

Despite SI adoption, many of these units persist in specific contexts (food Calories, kWh for electricity billing, BTU for HVAC).

Modern Precision (1990s-2019)

1990 redefinition: Linked to the volt and ohm through quantum electrical standards (Josephson effect and quantum Hall effect), enabling unprecedented precision.

2019 SI revision: Redefined the joule via exact fundamental constants (Planck constant, speed of light), eliminating dependence on physical prototypes. This "New SI" provides ultimate stability—joule can be reproduced anywhere in the universe using only constants and measurement equipment.

Real-World Examples

Human Scale (1-1,000 J)

• Lifting an apple (100g) 1 meter: ~1 J
• Human heartbeat: ~1 J of mechanical work
• Typing keystroke: ~0.1-0.2 J
• Footstep (walking): ~40-60 J
• Jumping vertically 30 cm: ~150 J (70 kg person)
• Snapping fingers: ~2 J
• Blinking eyes: ~0.001 J
• Breathing cycle (rest): ~0.5-1 J

Daily Activities (kJ)

• Climbing one flight of stairs: ~2,000-3,000 J (2-3 kJ)
• Running 100 meters: ~400-500 J (0.4-0.5 kJ)
• Doing 10 pushups: ~500-1,000 J (0.5-1 kJ)
• Cycling 1 km: ~50,000-100,000 J (50-100 kJ)
• Daily human metabolic energy: ~8,000,000-10,000,000 J (8-10 MJ = 2,000-2,400 kcal)

Food and Nutrition (kJ)

• 1 food Calorie (kcal): 4,184 J = 4.184 kJ
• Small apple: ~250,000 J (250 kJ = 60 kcal)
• Banana: ~440,000 J (440 kJ = 105 kcal)
• Slice of bread: ~315,000 J (315 kJ = 75 kcal)
• Candy bar: ~1,000,000 J (1 MJ = 240 kcal)
• Big Mac: ~2,350,000 J (2.35 MJ = 563 kcal)
• Daily food intake: ~8,000,000-12,000,000 J (8-12 MJ = 2,000-3,000 kcal)

Electrical Energy (J to MJ)

• LED bulb (10W) for 1 hour: 36,000 J (36 kJ = 0.01 kWh)
• Incandescent bulb (60W) for 1 hour: 216,000 J (216 kJ = 0.06 kWh)
• Laptop (50W) for 8 hours: 1,440,000 J (1.44 MJ = 0.4 kWh)
• Smartphone battery (15 Wh): 54,000 J (54 kJ)
• AA battery: ~10,000 J (10 kJ)
• Car battery (60 Ah at 12V = 720 Wh): ~2,600,000 J (2.6 MJ)
• Home daily electricity (30 kWh): 108,000,000 J (108 MJ)

Transportation (MJ to GJ)

• Gasoline (1 liter): ~32,000,000 J (32 MJ)
• Diesel (1 liter): ~36,000,000 J (36 MJ)
• Natural gas (1 m³): ~38,000,000 J (38 MJ)
• Car fuel tank (50 liters gasoline): ~1,600,000,000 J (1.6 GJ)
• Electric car battery (60 kWh): ~216,000,000 J (216 MJ)
• Jet fuel (1 liter): ~35,000,000 J (35 MJ)

Large-Scale Energy (GJ to TJ)

• Natural gas (1 therm): 105,500,000 J (105.5 MJ)
• Ton of coal: ~24,000,000,000 J (24 GJ)
• Ton of TNT (explosive energy): ~4,184,000,000 J (4.184 GJ)
• Nuclear fission (1 kg uranium-235): ~8.2 × 10¹³ J (82,000 GJ = 82 TJ)
• Hiroshima bomb: ~63,000,000,000,000 J (63 TJ)

Common Uses

Physics and Science

The joule is the universal energy unit in scientific research:

Mechanics: Kinetic energy (KE = ½mv²), potential energy (PE = mgh), work (W = F·d)

Thermodynamics: Heat transfer, enthalpy, internal energy, entropy (S units: J/K)

Electromagnetism: Electrical energy (E = V·I·t), magnetic energy (E = ½LI²), capacitor energy (E = ½CV²)

Quantum mechanics: Energy levels in atoms/molecules (though electronvolts often preferred)

Relativity: Mass-energy equivalence E = mc² (in joules when using SI units)

Engineering Applications

Engineers use joules across all disciplines:

Mechanical engineering: Impact energy, spring energy (E = ½kx²), rotational energy (E = ½Iω²)

Civil engineering: Structural load energy, seismic energy absorption

Aerospace engineering: Rocket propulsion energy, orbital energy calculations

Chemical engineering: Heat of reaction, activation energy, process energy requirements

Materials science: Fracture energy, strain energy density

Electrical and Electronics

Joules quantify electrical energy consumption:

Power consumption: Energy (J) = Power (W) × Time (s)

• 100W light bulb for 1 hour = 100 × 3,600 = 360,000 J = 360 kJ

Battery capacity: Often listed in watt-hours (Wh), convert to joules by × 3,600

• 10 Wh battery = 10 × 3,600 = 36,000 J = 36 kJ

Capacitor energy: E = ½CV² (where C in farads, V in volts, E in joules)

Energy efficiency: Comparing joules input vs. joules output determines efficiency percentage

Nutrition and Food Science

Many countries mandate both kilojoules and Calories on nutrition labels:

Australia/New Zealand: Kilojoules (kJ) primary, Calories secondary

European Union: Often lists both kJ and kcal

Conversion: 1 food Calorie (kcal) = 4.184 kJ

Example: 500 kJ = 500 ÷ 4.184 ≈ 120 kcal (Calories)

Climate and Energy Policy

Joules (typically in TJ, PJ, EJ) measure large-scale energy:

National energy consumption: Reported in exajoules (EJ = 10¹⁸ J) annually

• World primary energy: ~600 EJ/year
• United States: ~100 EJ/year

Carbon footprint: kg CO₂ per GJ of energy source

Renewable energy: Solar irradiance (W/m² → J/m² over time)

Energy intensity: Economic output per joule consumed (GDP/GJ)

Sports and Exercise Science

Joules measure human energy expenditure:

Metabolic equivalent (MET): 1 MET = ~4.184 kJ/hour per kg body weight at rest

Cycling power meters: Measure work in kilojoules per ride

Weightlifting: Work = weight × height × 9.8 (in joules)

• Deadlift 100 kg to 1 meter height = 100 × 9.8 × 1 = 980 J

Running economy: Joules per meter traveled

Conversion Guide

Converting Joules to Other Energy Units

From joules (J) to:

• Kilojoules (kJ): J ÷ 1,000 = kJ
  • Example: 5,000 J ÷ 1,000 = 5 kJ
• Megajoules (MJ): J ÷ 1,000,000 = MJ
  • Example: 2,000,000 J ÷ 1,000,000 = 2 MJ
• Calories (cal, thermochemical): J ÷ 4.184 = cal
  • Example: 4,184 J ÷ 4.184 = 1,000 cal = 1 kcal
• Food Calories (kcal): J ÷ 4,184 = kcal
  • Example: 836,800 J ÷ 4,184 = 200 kcal
• Watt-hours (Wh): J ÷ 3,600 = Wh
  • Example: 36,000 J ÷ 3,600 = 10 Wh
• Kilowatt-hours (kWh): J ÷ 3,600,000 = kWh
  • Example: 3,600,000 J ÷ 3,600,000 = 1 kWh
• British thermal units (BTU): J ÷ 1,055.06 = BTU
  • Example: 10,550 J ÷ 1,055 = 10 BTU
• Electronvolts (eV): J ÷ 1.602 × 10⁻¹⁹ = eV
  • Example: 1.602 × 10⁻¹⁹ J = 1 eV

Converting to Joules

From calories (cal) to joules:

• cal × 4.184 = J
• Example: 100 cal × 4.184 = 418.4 J

From Calories (kcal, food) to joules:

• kcal × 4,184 = J
• Example: 50 kcal × 4,184 = 209,200 J

From watt-hours (Wh) to joules:

• Wh × 3,600 = J
• Example: 5 Wh × 3,600 = 18,000 J

From kilowatt-hours (kWh) to joules:

• kWh × 3,600,000 = J
• Example: 0.5 kWh × 3,600,000 = 1,800,000 J = 1.8 MJ

From BTU to joules:

• BTU × 1,055.06 = J
• Example: 10 BTU × 1,055 = 10,550 J

Power-Time-Energy Conversions

Energy = Power × Time

Watts to joules:

• Watts × seconds = joules
• Example: 100 W × 60 s = 6,000 J = 6 kJ

Joules to watts (requires time):

• J ÷ seconds = W
• Example: 10,000 J ÷ 100 s = 100 W

Common Conversion Mistakes

1. Confusing Watts and Joules

❌ Wrong: "My light bulb uses 60 joules" ✅ Right: "My light bulb uses 60 watts (60 joules per second)"

Why: Watts measure power (energy per time), joules measure energy. Must multiply watts by time (seconds) to get joules.

2. Incorrect kWh to Joules Conversion

❌ Wrong: "1 kWh = 1,000 watts × 3,600 seconds = 3,600 joules" ✅ Right: "1 kWh = 1,000 watts × 3,600 seconds = 3,600,000 joules = 3.6 MJ"

Why: Must convert kilowatts to watts first (× 1,000), then multiply by seconds.

3. Mixing Calories and Kilocalories

❌ Wrong: "100 Calories on food label = 100 × 4.184 = 418.4 joules" ✅ Right: "100 Calories (kcal) on food label = 100 × 4,184 = 418,400 joules = 418.4 kJ"

Why: Food "Calories" are kilocalories (kcal), so multiply by 4,184 not 4.184.

4. Forgetting Time in Power Calculations

❌ Wrong: "A 1,000W heater uses 1,000 joules" ✅ Right: "A 1,000W heater uses 1,000 joules per second, or 3,600,000 joules per hour"

Why: Power is energy per time. Must specify duration to calculate total energy.

5. Misapplying Force-Distance Work Formula

❌ Wrong: "Lifting 50 kg by 2 meters = 50 × 2 = 100 joules" ✅ Right: "Lifting 50 kg by 2 meters = 50 × 9.8 × 2 = 980 joules"

Why: Work = force × distance. Must multiply mass (kg) by gravity (9.8 m/s²) to get force (N), then multiply by distance (m).

6. Incorrect Kinetic Energy Calculation

❌ Wrong: "KE of 10 kg at 5 m/s = 10 × 5 = 50 joules" ✅ Right: "KE of 10 kg at 5 m/s = ½ × 10 × 5² = ½ × 10 × 25 = 125 joules"

Why: Kinetic energy = ½mv². Must square the velocity and include the ½ factor.