Energy, Work and Power Calculator: Kinetic and Potential

How to use it

Choose the Formula you need, for example Kinetic energy: E = ½mv².
Type the values you know into their boxes, for example Mass m 2 and Speed v 10, and leave exactly one box empty: the one to find.
Read the result in Solved value, and check All the values and How it is worked out.

The formulas

Kinetic energy is the energy a moving body has because of its motion. Potential energy is the energy a body has because of its height above a reference level. Work is the energy transferred by a force that moves its point of application, and power is the rate at which work is done.

kinetic energy   E = ½ m v²
potential energy E = m g h
work            W = F d cos θ
power           P = W ÷ t

1 J = 1 N × 1 m = 1 kg·m²/s²     1 W = 1 J/s

The kinetic energy grows with the square of the speed: twice the speed gives four times the energy.
The work needs the angle: a force at right angles to the motion does no work, and a force against the motion does negative work.
The unit of energy and work is the joule (J), and the unit of power is the watt (W), which is one joule per second.

Solving for any box

The calculator has three boxes filled and one empty. It uses the formula to find the empty one: by division when it is a factor, by a square root when the value is squared (as the speed is in kinetic energy), and by the arccosine for the angle. A value that gives a zero divisor, a negative square root or a cosine above 1 is reported, not shown as a number.

What the calculator does not cover

Work by a force that changes along the path, such as a spring: that needs the integral of the force over the distance.
Rotational and elastic energy, heat from friction, and the energy stored in a battery or a fuel.
Speeds near the speed of light, where the formula ½mv² is no longer exact.

Worked example: a car of 1500 kg at 20 m/s

With the formula E = ½mv² and m = 1500 kg, v = 20 m/s: E = ½ × 1500 × 20² = 300 000 J, which is 300 kJ. The car has 300 kJ of kinetic energy.

If the brakes take the car to rest, that energy is removed by the work of the brakes. A force of 6000 N over 50 m does W = 6000 × 50 × cos 180° = −300 000 J, the same energy with the sign showing that the force slows the car.

Quantity	Value
Mass m	1500 kg
Speed v	20 m/s
Energy E (calculated)	300 kJ
Force F, distance d and angle θ	6000 N, 50 m, 180°
Work W (calculated)	−300 kJ

Frequently asked questions

What is the difference between work and energy?

Work is energy that is transferred to or from a body by a force that moves it, while energy is what a body has. A force does work of the same size as the change of kinetic energy it causes, so the two are measured in the same unit, the joule.

Why is the speed squared in kinetic energy?

The work needed to bring a body from rest to speed v is the force times the distance, and the distance needed grows with v². So the energy grows with v², and doubling the speed multiplies the energy by four.

Why does the angle reduce the work?

Only the part of the force that lies along the motion does work, and that part is F cos θ. At 60° half the force does work, and at 90° none does.

What unit is power in?

Power is in watts (W). One watt is one joule per second, so 500 J in 10 s is 50 W. A power of 2.5 kW is 2500 W, and the calculator writes the result with the prefix that fits.

Can I type kWh for energy?

Yes. One kilowatt-hour is 3.6 million joules (3.6 MJ), so 1 kWh in 1 h is 1 kW. The calculator converts kWh and Wh to joules, and hours to seconds, before it works out the answer.

Why is g 9.80665 m/s²?

It is the standard gravity, defined as exactly 9.80665 m/s² by the General Conference on Weights and Measures in 1901. Gravity at a real place differs slightly from it, so the potential energy is an accurate figure at a reference level, not an absolute one.

Sources

Figures and text last checked on Tuesday, November 10, 2026.

Result

How it is worked out