Calories (thermochemical) to joules (cal to J)

The formula

J = cal × 4.184

Where the factor comes from — each unit by its definition, then its size in SI:

• 1 cal = 4.184 × J = 4.184 J
• 1 J is the SI unit of energy.

Dividing the two SI sizes gives the factor: 4.184, exact — every step above is a definition, not a measurement. The reverse factor is 0.239005736138.

The SI unit of energy is the joule. Food labels use kilocalories, electricity bills kilowatt-hours, heating specs BTU and particle physics electronvolts — the same quantity in five costumes.

Worked examples

• A day's food (2000 kcal): 2,000,000 cal = 8,368,000 J — 2,000,000 × 4.184 = 8,368,000
• A 1 kW heater run for one hour (1 kWh): 860,421 cal = 3,600,000 J — 860,421 × 4.184 = 3,600,000
• Lifting 1 kg through 1 m at standard gravity: 2.34385 cal = 9.80665 J — 2.34385 × 4.184 = 9.80665
• A visible-light photon (2 eV): 7.65859 × 10⁻²⁰ cal = 3.20435 × 10⁻¹⁹ J — 7.65859 × 10⁻²⁰ × 4.184 = 3.20435 × 10⁻¹⁹

Frequently asked questions