Units of energy

Because energy is defined via work then the SI unit for energy are the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton-metre and, in terms of SI base units:

1\ \mathrm{J} = 1\ \mathrm{kg} \left( \frac{\mathrm{m}}{\mathrm{s}} \right ) ^ 2 = 1\ \frac{\mathrm{kg} \cdot \mathrm{m}^2}{\mathrm{s}^2}

An energy unit that is used in atomic physics, particle physics and high energy physics is the electronvolt (eV). One eV  is equivalent to 1.60217653×10⁻¹⁹ J.

When large amounts of energy are involved, often TNT equivalent unit is used. 1 ton of TNT equivalent is equal to 4.2 × 10⁹ Joules. Therefore, 1 kT TNT is 4.2 × 10¹² Joules, and 1 MT TNT is 4.2 × 10¹⁵ Joules.

In spectroscopy the unit cm^-1 = 0.0001239 eV is used to represent energy since energy is inversely proportional to wavelength from the equation E = h \nu = h c/\lambda.

(Note that torque, which is typically expressed in newton-metres, has the same dimension and this is not a simple coincidence: a torque of 1 newton-metre applied on 1 radian requires exactly 1 newton-metre=joule of energy.)

Other units of energy

In cgs units, one erg is 1 g cm² s⁻², equal to 1.0×10⁻⁷ J.

The imperial/US units for both energy and work include the foot-pound force (1.3558 J), the British thermal unit (Btu) which has various values in the region of 1055 J, and the horsepower-hour (2.6845 MJ).

The energy unit used for everyday electricity, particularly for utility bills, is the kilowatt-hour (kW h), and one kW h is equivalent to 3.6×10⁶ J  (3600 kJ or 3.6 MJ).

The calorie equals the amount of heat necessary to raise the temperature of one gram of water by 1 Celsius degree, at a pressure of 1 atm. It is equal to 4.1868 J. Food energy is measured in kilocalories, commonly abbreviated as Calories (= 10³ calories).