Kinetic Energy Calculator
Find kinetic energy from mass and speed, or solve for the mass or velocity behind a given energy, in joules, kWh, calories or ft·lbf. Includes PE = mgh.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Kinetic Energy Calculator?
This kinetic energy calculator works out the energy of a moving object from KE = ½mv², or runs the formula backwards to find the speed or the mass that goes with a known energy. Type the mass in kilograms, grams, tonnes, pounds or ounces and the speed in m/s, km/h, mph, ft/s or knots, and read the answer in joules, kilojoules, watt-hours, kilowatt-hours, calories, foot-pounds, BTU or electronvolts.
Alongside the energy you get the momentum (p = mv), the height an object would have to fall to reach that speed, and the food-energy equivalent in kilocalories. If you enter a speed above 1% of the speed of light, the tool warns you and shows the relativistic value (γ − 1)mc², because ½mv² starts to undercount there.
A second tab handles gravitational potential energy, PE = mgh, solving for energy, mass or height on Earth, the Moon, Mars or with your own value of g. Both tabs update as you type and nothing you enter leaves the browser.
- Solve for kinetic energy, mass or speed
- Gravitational potential energy mgh with planet presets
- Ten energy units from eV to kWh and BTU
- Momentum, equivalent drop height and relativistic check
- Copy, share link and reset; runs entirely in your browser
How to use the Kinetic Energy Calculator
- Choose Kinetic energy or Potential energy at the top.
- Pick what to solve for: energy, mass or speed (or height on the potential energy tab).
- Enter the two known values and choose their units from the drop-downs next to each box.
- Read the answer in the result field and in the stat cards, which also show joules, kWh, km/h, mph and momentum.
- Change the output unit at any time; the result converts without retyping. Copy the results or share a link that reproduces the inputs.
Worked examples
A car at 50 km/h
Input
Mass 1,500 kg, speed 50 km/h
Output
144.68 kJ, momentum 20,833 kg·m/s, equivalent drop 9.84 m
13.889 m/s squared is 192.9, times 750 kg gives 144,676 J. At 100 km/h the same car carries 578.7 kJ, four times as much.
A pistol bullet
Input
Mass 8 g, speed 360 m/s
Output
518.4 J
Light objects carry large energies at high speed. The momentum is only 2.88 kg·m/s, which is why recoil is manageable while the impact energy is not.
Speed from energy
Input
Solve for speed; 100 J, 2 kg
Output
10 m/s
v = √(2KE/m) = √(200/2) = 10 m/s.
Potential energy on the Moon
Input
Potential tab; 10 kg, 5 m, Moon (1.62 m/s²)
Output
81 J, speed if dropped 4.02 m/s
On Earth the same lift stores 490.33 J. Weaker gravity means less energy stored and a slower fall.
Background and insight
Kinetic energy is the work needed to bring a mass from rest to a speed, and the work it can do while stopping. Integrating force over distance with F = ma gives ½mv², a result usually credited to Gaspard-Gustave Coriolis, who gave it that form in 1829; the joule (one newton acting over one metre) is the SI unit. Because speed is squared, the energy grows fast: doubling the speed quadruples the energy and the braking distance at a given deceleration.
Gravitational potential energy near a planet's surface is mgh, with g = 9.80665 m/s² as the conventional standard value on Earth (fixed by the 3rd CGPM in 1901). Only differences in height matter, so you choose where zero is. When an object falls without drag, mgh turns into ½mv², which is where the "equivalent drop height" v²/2g comes from: a car at 50 km/h carries the same energy it would gain by falling about 9.8 m.
The classical formula is an approximation of special relativity. Kinetic energy is really (γ − 1)mc², where γ = 1/√(1 − v²/c²). The two agree to better than 0.01% below about 3,000 km/s, so for anything on Earth ½mv² is exact for practical purposes. The calculator uses a series expansion at low speeds so the relativistic figure stays numerically accurate.
Common use cases
Physics homework
Check ½mv² and mgh answers in any unit, and see the working laid out step by step.
Vehicle safety
Compare the energy of a car at different speeds to see why a small increase in speed lengthens stopping distance so much.
Sports and ballistics
Work out the energy of a thrown ball, an arrow or a projectile from its mass and chronograph speed.
Energy storage
Estimate how much energy a raised weight or a flywheel-style moving mass holds, in joules or kWh.
Tips and limitations
- Speed must be relative to whatever the object hits. Two cars meeting head on at 50 km/h each have a closing speed of 100 km/h, but each still only carries its own ½mv².
- Kilocalories on food labels are kcal (Calories). 1 kcal = 4,184 J, so a 144 kJ car is about 35 kcal, a small reminder of how energy-dense food is.
- mgh assumes constant g, which is accurate to 0.1% for heights up to roughly 3 km. For orbits use the full gravitational potential −GMm/r.
- Rotating objects carry extra energy, ½Iω², on top of ½mv². A rolling ball has 40% more kinetic energy than a sliding one at the same speed.
- Kinetic energy is not conserved in collisions where things deform or heat up; momentum is. Use the momentum figure for collision problems.
Frequently asked questions
What is the formula for kinetic energy?
KE = ½ × m × v², with mass in kilograms and speed in metres per second giving joules. A 2 kg object at 3 m/s has ½ × 2 × 9 = 9 J.
How do I find velocity from kinetic energy?
Rearrange to v = √(2 × KE ÷ m). For 100 J and 2 kg, v = √(200 ÷ 2) = 10 m/s. Choose Speed under Solve for and the calculator does this for you.
Why does doubling the speed quadruple the energy?
Speed is squared in the formula, so twice the speed gives 2² = 4 times the energy. Three times the speed gives nine times the energy, which is why crash severity rises so steeply with speed.
What is the kinetic energy of a car at 60 mph?
A 1,500 kg car at 60 mph (26.82 m/s) has about 540 kJ, or 0.15 kWh. Enter the mass and speed with mph selected to see it for your own vehicle.
What is the difference between kinetic energy and momentum?
Momentum is mass times velocity and is conserved in every collision. Kinetic energy is half mass times velocity squared and is only conserved in perfectly elastic collisions; the rest turns into heat, sound and deformation.
When should I use the relativistic formula?
Only near the speed of light. Below about 1% of c (3,000 km/s) the classical and relativistic values differ by less than 0.01%. The calculator flags speeds above that and shows (γ − 1)mc².
How is potential energy related to kinetic energy?
Without air resistance, an object falling from height h turns all of its mgh into ½mv², so v = √(2gh). The potential energy tab shows this impact speed for any height.
Is there an in-depth guide to the Kinetic Energy Calculator?
Yes. “Kinetic Energy: ½mv², Speed Squared and Where the Energy Goes” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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