Kinetic energy is the energy an object has because it is moving. It equals the work needed to bring the object from rest up to its speed, and the work that brakes, a crash barrier or air resistance must remove to stop it again. This calculator solves KE = ½mv² for kinetic energy, mass or speed, and adds two comparisons that make the number tangible: the energy at double the speed and the height of a fall that would produce the same speed.
How to use the kinetic energy calculator
- Under Solve for, choose Kinetic energy, Mass or Speed.
- Enter Mass (m) in kg, g, mg, metric tonnes, lb, oz, US tons or stone.
- Enter Speed (v) in m/s, km/h, mph, ft/s or knots. Direction does not matter; a negative entry is treated as its magnitude.
- When solving for mass or speed, enter Kinetic energy (KE) in J, kJ, MJ, cal, kcal, Wh, kWh, BTU, ft·lbf, eV or erg.
- Choose the output unit under Show the result in. The result lists conversions, the momentum, the energy at twice the speed and the equivalent drop height (for speeds up to 3 km/s), plus a relativity note at very high speeds.
Kinetic energy formula
Rearranged for mass and speed:
The ½ comes from the work–energy link: a steady force F accelerating a mass from rest over a distance d does work Fd = mad, and since v² = 2ad, that work equals ½mv². Mass must be positive and kinetic energy cannot be negative. Solving for mass needs a non-zero speed and a positive energy, and speeds at or above the speed of light are rejected.
Worked example: a car at 100 km/h
A 1,500 kg car travels at 100 km/h.
Convert the speed: 100 ÷ 3.6 = 27.78 m/s, so v² ≈ 771.6 m²/s².
Kinetic energy: ½ × 1,500 × 771.6 ≈ 578,704 J = 578.7 kJ, about 0.161 kWh, 138.3 kcal or 426,830 ft·lbf.
At 200 km/h the same car would carry 2,314.8 kJ, four times as much.
Equivalent drop height: 39.3 m. Hitting a solid wall at 100 km/h involves the same energy as falling from a 13-story building.
The speed-squared effect
For the same 1,500 kg car:
| Speed | Kinetic energy | Equivalent drop | Compared with 50 km/h |
|---|---|---|---|
| 30 km/h | 52.1 kJ | 3.5 m | 0.36× |
| 50 km/h | 144.7 kJ | 9.8 m | 1× |
| 80 km/h | 370.4 kJ | 25.2 m | 2.56× |
| 100 km/h | 578.7 kJ | 39.3 m | 4× |
| 130 km/h | 978.0 kJ | 66.5 m | 6.76× |
Going from 100 to 130 km/h raises the speed by 30% but the energy by 69%. Brakes must remove all of that energy as negative work, braking force times distance, so with the same braking force the stopping distance scales with the energy. If the brakes hold a steady 9,000 N on this car, stopping from 100 km/h takes 578,704 ÷ 9,000 ≈ 64.3 m, while stopping from 130 km/h takes 978,009 ÷ 9,000 ≈ 108.7 m: 69% farther for 30% more speed. The driver’s reaction distance comes on top and grows only in proportion to speed.
Solving for speed or mass
- Speed: a 10 kg object carrying 500 J moves at √(2 × 500 ÷ 10) = 10 m/s, or 36 km/h.
- Mass: a meteoroid at 20 km/s carrying 400 MJ has a mass of 2 × 400,000,000 ÷ 20,000² = 2 kg. That energy matches about 96 kg of TNT, which is why even small objects striking at meteoric speeds are so destructive.
Drop height and the relativistic limit
The equivalent drop height is h = v² ÷ 2g with g = 9.80665 m/s², so it depends only on speed. It assumes no air drag and uniform gravity, which makes it a fair picture for vehicles and sports but meaningless for orbital speeds, where the figure would run into thousands of kilometers and gravity has weakened long before. Above 3 km/s (a drop of about 459 km) the calculator leaves the drop height out and says why in a note.
At extreme speeds the classical formula drifts from reality. The exact kinetic energy is (γ − 1)mc², where γ = 1 ÷ √(1 − v²/c²) and c = 299,792,458 m/s. Above 1% of light speed the calculator keeps ½mv² as the main result but adds a note with the relativistic value and the gap between them: at 10% of c the classical figure is about 0.76% low. Even the fastest spacecraft stay well under 0.1% of c, so for anything human-made ½mv² is exact enough.
Related calculators
Compare motion with height using the potential energy calculator, or find the vector quantity that goes with speed in the momentum calculator. The work calculator handles the force-times-distance side of the work–energy theorem.
Frequently asked questions
What is the kinetic energy formula?
KE = ½mv². With mass in kilograms and speed in meters per second, the result is in joules. A 1,500 kg car at 100 km/h (27.78 m/s) carries ½ × 1,500 × 27.78² ≈ 578.7 kJ.
Why does doubling the speed quadruple the kinetic energy?
Speed is squared in the formula, so twice the speed gives 2² = 4 times the energy and three times the speed gives 9 times. Mass appears only once, so doubling the mass merely doubles the energy.
Can kinetic energy be negative?
No. Mass is positive and the square of any speed is zero or positive, so kinetic energy never drops below zero. The calculator accepts a negative speed but uses only its magnitude.
What is the equivalent drop height?
It is the height an object would have to fall, with no air resistance, to reach the same speed: h = v² ÷ 2g. It does not depend on mass. A speed of 100 km/h matches a drop of about 39.3 m, roughly a 13-story building.
When does ½mv² stop being accurate?
Near a few percent of the speed of light. Whenever the speed tops 1% of light speed, the calculator adds a note with the exact relativistic value, (γ − 1)mc². At 10% of light speed, ½mv² comes out about 0.76% too low. Cars, bullets and even spacecraft are far below that range.