acalculator

How much energy is it?

Type a power and a time, a force and a distance, or a mass with its speed and height. The energy calculator gives the energy in joules, kilowatt-hours, kilocalories, BTU and foot-pounds.

Your numbers

Units
Energy from
Energy (J)
10,800,000

That is 10,800,000 J of energy, or 3 kWh.

Energy (kWh)
3
Energy (kcal)
2,581.26
Energy (BTU)
10,236.4
Energy (ft·lbf)
7,965,670

Energy (J): 10,800,000. That is 10,800,000 J of energy, or 3 kWh.

How to calculate

Computes energy from power and time (E = P × t), from force and distance (W = F × d), or the mechanical energy of a moving, raised mass (½mv² + mgh), in joules, kWh, kcal, BTU and ft·lbf.

Example with the default inputs (Energy from Power × time, Power 1,500 W, Time 2 h): That is 10,800,000 J of energy, or 3 kWh.

Method: E = P × t; W = F × d; E = ½ m v² + m g h.

  • Power × time: the power is steady over the whole time. Force × distance: a steady force that points along the motion.
  • Motion and height: kinetic energy ½ m v² (classical, well below light speed) plus gravitational potential energy m g h near a planet’s surface.
  • Exact unit sizes: 1 hp = 550 ft·lbf/s; 1 BTU = 1,055.05585262 J; 1 kcal = 4,184 J; 1 kWh = 3,600,000 J; 1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m; 1 mph = 0.44704 m/s.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Energy from Power × time, Power 1,500 W, Time 2 h gives Energy (J) 10,800,000, Energy (kWh) 3.Source: OpenStax, University Physics Volume 1, §7.4 Power (P = W ÷ t), https://openstax.org/books/university-physics-volume-1/pages/7-4-power
  2. Energy from Force × distance, Force 22.48 lbf, Distance 32.81 ft gives Energy (J) 1,000, Energy (kcal) 0.239006.Source: OpenStax, University Physics Volume 1, §7.1 Work (W = F d for a constant force along the motion), https://openstax.org/books/university-physics-volume-1/pages/7-1-work
  3. Energy from Motion and height, Mass 2,205 lb, Speed 44.74 mph, Height 32.81 ft, Gravity (m/s²) 9.80665 gives Energy (J) 298,066.5, Kinetic energy (J) 200,000, Potential energy (J) 98,066.5.Source: OpenStax, University Physics Volume 1, §8.3 Conservation of Energy (E = K + U), https://openstax.org/books/university-physics-volume-1/pages/8-3-conservation-of-energy
  4. Energy from Power × time, Power 1,055 W, Time 1 h gives Energy (BTU) 3,600, Energy (kWh) 1.055056.Source: OpenStax, University Physics Volume 1, §7.4 Power (P = W ÷ t), https://openstax.org/books/university-physics-volume-1/pages/7-4-power; NIST SP 811 (1 BTU = 1,055.05585262 J), https://www.nist.gov/pml/special-publication-811

How it works

Pick how to find the energy E, in joules:

  • Power × time: E = P × t, with P in watts and t in seconds.
  • Force × distance: W = F × d, with F in newtons and d in meters.
  • Motion and height: E = ½ × m × v² + m × g × h, with m in kg, v in m/s, h in m and g in m/s² (9.80665 by default). The page also shows the two parts, kinetic ½ m v² and potential m g h.

The energy shows in joules, kilowatt-hours (J ÷ 3,600,000), kilocalories (J ÷ 4,184), BTU (J ÷ 1,055.05585262) and foot-pounds (J ÷ 1.3558179483314004).

Unit sizes: 1 kW = 1,000 W; 1 MW = 10⁶ W; 1 hp = 550 × 0.3048 × 4.4482216152605 = 745.69987158227022 W; 1 BTU/h = 1,055.05585262 ÷ 3,600 W. 1 min = 60 s; 1 h = 3,600 s; 1 d = 86,400 s. 1 kN = 1,000 N; 1 lbf = 4.4482216152605 N; 1 kgf = 9.80665 N. 1 km = 1,000 m; 1 cm = 0.01 m; 1 ft = 0.3048 m; 1 in = 0.0254 m; 1 mi = 1,609.344 m. 1 g = 0.001 kg; 1 lb = 0.45359237 kg; 1 t = 1,000 kg. 1 km/h = 1/3.6 m/s; 1 mph = 0.44704 m/s; 1 ft/s = 0.3048 m/s.

Exact arithmetic. Each value is read as the exact decimal you typed, in its unit, and every unit size is exact, so the energy is an exact fraction until it is rounded for display.

Output format. Every value shows 6 significant figures; values of 10¹⁵ or more, or below 10⁻⁶, show in scientific form.

When there is no answer. An energy so small that it is below the smallest number a computer can hold (about 5 × 10⁻³²⁴ J).

Assumptions

  • A steady power, a steady force along the motion, and classical motion near a planet’s surface.
  • Power up to 10¹² W; time up to 10¹⁰ s; force up to 10¹² N; distance up to 10⁹ m; mass up to 10⁹ kg; speed 0 to 10⁶ m/s; height 0 to 10⁷ m; gravity 0.001 to 1,000 m/s².

Worked examples by hand

A 1,500 W heater for 2 hours. E = 1,500 × 7,200 = 10,800,000 J = 3 kWh.

100 N over 10 m. W = 100 × 10 = 1,000 J = 1,000 ÷ 4,184 = 0.239006 kcal.

A 1,000 kg car at 20 m/s, 10 m up. ½ × 1,000 × 20² = 200,000 J; 1,000 × 9.80665 × 10 = 98,066.5 J; total 298,066.5 J.

1,055.05585262 W for an hour. E = 1,055.05585262 × 3,600 = 3,798,201.069432 J = 3,600 BTU = 1.05505585262 kWh.

Other questions people ask

How do I calculate energy from power and time?

Multiply them: E = P × t. With the power in watts and the time in seconds, the energy is in joules. A 1,500 W heater running for 2 hours uses 1,500 × 7,200 = 10,800,000 J, which is 1.5 kW × 2 h = 3 kWh.

How is work related to energy?

Work is energy moved by a force: W = F × d for a steady force along the motion. Pushing with 100 N for 10 m does 1,000 J of work.

What is mechanical energy?

The sum of kinetic energy (½ m v²) and potential energy (m g h). A 1,000 kg car at 20 m/s and 10 m up has 200,000 J + 98,066.5 J = 298,066.5 J.

How many joules are in a kWh?

One kilowatt-hour is 1,000 W for 3,600 s: 3,600,000 J, or 3.6 MJ.

How many joules are in a calorie?

A small calorie is 4.184 J. A food Calorie is a kilocalorie, 4,184 J. So 1,000 J is about 0.239 kcal.

What is a BTU?

The British thermal unit, used for heating and cooling, is 1,055.05585262 J exactly (the International Table BTU). One kWh is about 3,412 BTU.