OneTaskBy Tim King · Updated
Energy Calculator
Kinetic, Potential, Power × Time and E = mc² in Joules
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How the Energy Calculator works
This energy calculator works out kinetic energy from mass and speed, potential energy from mass and height, electrical energy from power and time, or the energy locked in mass with E = mc². Every answer is given in joules with the working, then in kJ, Wh or kWh, kilocalories, electronvolts and tonnes of TNT so you can compare it with something familiar.
Energy is the same quantity whether it is a moving car, a raised weight, a kettle running for a few minutes or the mass of an atom, which is why it can all be measured in joules. Seeing one result in several units makes it easier to judge: a car at motorway speed carries about as much energy as a kettle uses in five minutes, and a single gram of matter holds as much as a large power station produces in a day.
How the energy calculator works
The formula for kinetic energy is ½mv², with mass in kilograms and speed in metres per second. Potential energy is mgh, using standard gravity g = 9.80665 m/s². Electrical energy is power in watts times time in seconds, and mass–energy is mc² with c = 299,792,458 m/s. For kinetic energy the page also shows the drop height that would give the same speed, and for potential energy the speed at impact if the object fell freely.
First example. A 1,500 kg car at 100 km/h (27.78 m/s) has ½ × 1,500 × 27.78² ≈ 578,800 J, about 579 kJ or 0.16 kWh. That equals a fall from 39.35 m, roughly a 13-storey building.
Second example. A 75 kg person 10 m up has 75 × 9.80665 × 10 = 7,355 J of potential energy and would land at 14.0 m/s, about 50 km/h, if they fell.
How many kWh does a 2 kW heater use in 90 minutes? 2,000 W × 5,400 s is 10.8 MJ, which is 3 kWh.
Kinetic energy of a 1,500 kg car and a 90 kg rider and bike by speed
| Speed (km/h) | Speed (m/s) | Car (kJ) | Car (Wh) | Rider and bike (kJ) | Same as a fall of (m) |
|---|---|---|---|---|---|
| 5 | 1.39 | 1.447 | 0.402 | 0.087 | 0.098 |
| 10 | 2.78 | 5.787 | 1.608 | 0.347 | 0.393 |
| 15 | 4.17 | 13.02 | 3.617 | 0.781 | 0.885 |
| 20 | 5.56 | 23.15 | 6.43 | 1.389 | 1.574 |
| 25 | 6.94 | 36.17 | 10.05 | 2.17 | 2.459 |
| 30 | 8.33 | 52.08 | 14.47 | 3.125 | 3.541 |
| 35 | 9.72 | 70.89 | 19.69 | 4.253 | 4.819 |
| 40 | 11.11 | 92.59 | 25.72 | 5.556 | 6.295 |
| 45 | 12.50 | 117.2 | 32.55 | 7.031 | 7.967 |
| 50 | 13.89 | 144.7 | 40.19 | 8.681 | 9.835 |
| 55 | 15.28 | 175.1 | 48.63 | 10.5 | 11.9 |
| 60 | 16.67 | 208.3 | 57.87 | 12.5 | 14.16 |
| 65 | 18.06 | 244.5 | 67.92 | 14.67 | 16.62 |
| 70 | 19.44 | 283.6 | 78.77 | 17.01 | 19.28 |
| 75 | 20.83 | 325.5 | 90.42 | 19.53 | 22.13 |
| 80 | 22.22 | 370.4 | 102.9 | 22.22 | 25.18 |
| 85 | 23.61 | 418.1 | 116.1 | 25.09 | 28.42 |
| 90 | 25.00 | 468.8 | 130.2 | 28.13 | 31.87 |
| 95 | 26.39 | 522.3 | 145.1 | 31.34 | 35.51 |
| 100 | 27.78 | 578.7 | 160.8 | 34.72 | 39.34 |
| 105 | 29.17 | 638 | 177.2 | 38.28 | 43.37 |
| 110 | 30.56 | 700.2 | 194.5 | 42.01 | 47.6 |
| 115 | 31.94 | 765.3 | 212.6 | 45.92 | 52.03 |
| 120 | 33.33 | 833.3 | 231.5 | 50 | 56.65 |
| 125 | 34.72 | 904.2 | 251.2 | 54.25 | 61.47 |
| 130 | 36.11 | 978 | 271.7 | 58.68 | 66.49 |
| 135 | 37.50 | 1,055 | 293 | 63.28 | 71.7 |
| 140 | 38.89 | 1,134 | 315.1 | 68.06 | 77.11 |
| 145 | 40.28 | 1,217 | 338 | 73 | 82.71 |
| 150 | 41.67 | 1,302 | 361.7 | 78.13 | 88.52 |
Tips and pitfalls
- Speed counts twice. Doubling speed quadruples kinetic energy, which is why braking distances grow so fast.
- Convert km/h to m/s. Divide km/h by 3.6 before using ½mv², or the answer is 13 times too big.
- Height is measured from the landing point. Potential energy depends on the drop, not the altitude above sea level.
- Watts are a rate. A watt is a joule per second, so energy needs a time as well as a power.
FAQ
How do you calculate kinetic energy?
Multiply half the mass in kilograms by the square of the speed in metres per second. A 70 kg cyclist at 10 m/s has ½ × 70 × 10² = 3,500 J. The square means speed matters much more than mass, so a small object moving fast can carry a lot of energy.
What is the formula for potential energy?
Gravitational potential energy is mass times gravity times height, PE = mgh. Lifting a 2 kg bag onto a 1.5 m shelf stores 2 × 9.81 × 1.5 ≈ 29.4 J. All of that becomes kinetic energy if it falls, less whatever is lost to air resistance on the way down.
How much energy is in 1 gram of matter?
Using E = mc², one gram is 0.001 × 299,792,458² ≈ 8.99 × 10¹³ J. That is about 25 million kWh, or roughly 21,500 tonnes of TNT. Real reactors and bombs convert only a tiny fraction of their fuel's mass into energy, so this is the theoretical maximum.
How many joules are in a kWh?
One kilowatt-hour is 1,000 watts for 3,600 seconds, which is 3,600,000 J or 3.6 MJ. Electricity bills use kWh because joules are inconveniently small: a kettle boiling a litre of water uses about 0.1 kWh, or around 360,000 J.
What is the difference between energy and power?
Energy is an amount, measured in joules or kWh. Power is how fast energy is used or delivered, measured in watts, where one watt is one joule per second. A 2 kW heater uses 2 kWh of energy in one hour and 1 kWh in half an hour.
See also: all Physics tools, Chemistry, Electronics.
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