Kinetic energy calculator (and potential energy, work and power)
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Result
Work out the kinetic energy of a moving object, the speed that goes with a given kinetic energy, or the gravitational potential energy m·g·h. The work–energy mode gives the net work needed to change the speed of an object and the average net force over a distance, and the power mode divides work by time. Speeds can be entered in m/s, km/h or mph.
Step-by-step solution
Speed in m/s
Kinetic energy
Same energy as a fall from
Key formulas
- Kinetic energy
- Ek = ½mv²
- Potential energy
- Ep = mgh
- Energy balance
- Ek1 + Ep1 + W = Ek2 + Ep2 + losses
How to calculate kinetic energy
- Convert the speed to m/s: divide km/h by 3.6, or multiply mph by 0.447.
- Use KE = ½·m·v² with the mass in kg. The result is in joules: 1 J = 1 kg·m²/s².
- Gravitational potential energy near the Earth’s surface is PE = m·g·h, with g = 9.81 m/s² and the height h measured from a chosen reference level.
- Work–energy theorem: the net work done on an object equals the change in its kinetic energy, W = ½·m·v² − ½·m·v₀². Dividing by the distance gives the average net force.
- Power is the rate of doing work: P = W/t in watts. One mechanical horsepower is 745.7 W.
Questions and answers
Why does the speed count squared?
Because the work needed to reach a speed grows with the distance over which you accelerate, and that distance itself grows with the speed. Doubling the speed of a car gives four times the kinetic energy, and roughly four times the braking distance.
What is the difference between kinetic and potential energy?
Kinetic energy is energy of motion, ½·m·v². Potential energy is stored energy that depends on position, such as m·g·h for height or ½·k·x² for a spring. Without friction, energy moves between the two while their sum stays constant.
Can kinetic energy be negative?
No. Mass is positive and the speed is squared, so KE ≥ 0. The change in kinetic energy, and therefore the net work, can be negative when an object slows down.
What does the equivalent drop height mean?
The height from which the object would have to fall, without air resistance, to reach the same speed: h = v²/(2g). A car at 50 km/h has the same kinetic energy as a fall of almost 10 m.
Practise it yourself
Practise Work & energy
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.