Energy Units Overview (J, kJ, cal, kcal, BTU, Wh)
1. Core Idea
All energy units scale from the joule. Convert any unit → joules → target unit. SI prefixes (k, M) are decimal powers; others (cal, BTU, ft·lb) use fixed factors.
2. Key Factors
- 1 kJ = 1000 J
- 1 cal = 4.184 J
- 1 kcal = 4184 J
- 1 Wh = 3600 J
- 1 kWh = 3.6×10⁶ J
- 1 BTU = 1055.06 J
- 1 ft·lb = 1.35582 J
- 1 N·m = 1 J
3. Quick Cross Conversions
| Unit | In Joules | Notes |
|---|---|---|
| kcal | 4184 | Food Calorie |
| kWh | 3.6×10⁶ | Electric energy billing |
| BTU | 1055.06 | Heating/cooling |
| ft·lb | 1.35582 | Mechanical work |
4. 3-Step Example
Convert 2.5 kWh to kcal
- kWh → J: 2.5 × 3.6×10⁶ = 9.0×10⁶ J
- Divide by 4184: 9.0×10⁶ ÷ 4184
- = 2152.3 kcal
5. Where Conversions Matter
Nutrition (kJ ↔ kcal), electricity billing (kWh ↔ kJ), HVAC sizing (BTU ↔ kWh), mechanical work (ft·lb ↔ J), battery specs (Wh ↔ J), physics labs (J ↔ kJ).
6. Accuracy & Tips
- Round nutrition: whole kcal / nearest 5 kJ.
- Engineering: keep 4–6 sig figs for factors (e.g., 1055.06).
- Chain conversions through joules to avoid compounding error.
- Mental: kcal ×4 ≈ kJ; Wh ×3.6 = kJ.
7. More Examples
| Source | Target | Result |
|---|---|---|
| 750 cal | kJ | 750×4.184 = 3138 kJ |
| 4200 J | kcal | 4200 ÷ 4184 = 1.00 kcal |
| 12 kWh | MJ | 12×3.6 = 43.2 MJ |
| 1500 ft·lb | J | 1500×1.35582 = 2033.7 J |
8. FAQ
J vs N·m?
Numerically identical; joule is energy, newton-meter is torque context.
kcal vs Cal?
On food labels Calorie (capital C) = kilocalorie = 1000 small calories.
Fast kWh → kJ?
Multiply by 3600 (add three zeros then ×3.6).