Energy Unit Conversions — Joules, Calories, kWh and eV
Energy shows up in four genuinely different units depending on the field: the joule (J) is the SI unit used throughout physics and most of chemistry; the calorie (cal) is the traditional unit of thermochemistry and nutrition labels; the kilowatt-hour (kWh) is what your electricity bill is measured in; and the electron-volt (eV) is the unit of choice for atomic, nuclear and photon energies because joule-sized numbers there would be absurdly small. Converting cleanly between them is a real, exam-relevant skill — this article gives the exact factors and works through real numbers.
1 kcal (food Calorie) = 4184 J = 4.184 kJ
1 kWh = 3.6 × 10⁶ J = 3600 kJ = 3.6 MJ
1 eV = 1.602176634 × 10⁻¹⁹ J (exact, SI-defined via the elementary charge)
What each unit is for: the joule is 1 newton of force acting over 1 metre, or equivalently 1 watt sustained for 1 second — general-purpose and dimensionally simple. The calorie was originally defined as the energy to raise 1 g of water by 1°C, which is why it still dominates thermochemistry (bond enthalpies, heats of reaction) and food labelling (where "Calorie" with a capital C actually means kilocalorie). The kilowatt-hour is energy = power × time, convenient for billing because power (kW) and time (hours) are both everyday-sized numbers. The electron-volt is the kinetic energy gained by one electron accelerating through a 1-volt potential difference — it naturally fits atomic-scale energies like ionisation energy or photon energy without needing 10⁻¹⁹ everywhere.
J = 850 × 4.184 = 3556.4 J.
kJ = 3556.4 ÷ 1000 = 3.5564 kJ.
kJ = 150 × 4.184 = 627.6 kJ.
MJ = 627.6 ÷ 1000 = 0.6276 MJ.
J = 8 × 3.6 × 10⁶ = 2.88 × 10⁷ J (28.8 million joules) — a striking number that shows how large the joule is for everyday energy use, which is exactly why kWh exists as a practical unit instead.
J per photon = 2.5 × 1.602 × 10⁻¹⁹ = 4.005 × 10⁻¹⁹ J.
kJ/mol = (4.005 × 10⁻¹⁹ × 6.022 × 10²³) ÷ 1000 = (2.4122 × 10⁵) ÷ 1000 = 241.2 kJ/mol.
This "eV per particle → kJ/mol" step is exactly what photochemistry and bond-energy-from-photon-absorption problems require.
- Confusing "calorie" (cal, the chemistry unit) with "Calorie" (kcal, the food-label unit) — a factor-of-1000 error that's easy to make when a question doesn't capitalise carefully.
- Forgetting that kWh is a unit of energy, not power, despite containing "kilowatt" — power × time = energy is the reason, and it's worth writing that out rather than memorising kWh as a standalone fact.
- Using the rounded value 1.6 × 10⁻¹⁹ J for the eV-to-J conversion when a question demands more precision, or conversely over-specifying precision (using all 10 significant figures of the exact 2019-SI-redefinition value) when 3–4 s.f. is what's asked for.
- Forgetting the Avogadro's-number step when converting a per-particle energy (eV, or J per molecule) into the per-mole energy (kJ/mol) that thermochemistry equations expect.
| From | To | Multiply by |
|---|---|---|
| cal | J | 4.184 |
| kcal (Calorie) | kJ | 4.184 |
| kWh | J | 3.6 × 10⁶ |
| eV | J | 1.602 × 10⁻¹⁹ |
| eV per particle | kJ/mol | × Avogadro's number (6.022×10²³), then ÷1000 |
The calculator suite's unit converter has a dedicated Energy category for instant conversion between these units.
Open the Energy Converter →For structured practice connecting these conversions to real thermochemistry and photochemistry problems, ABC Chemistry runs Class 11–12 chemistry coaching through live online across India — see abcchemistry.in for details.