Physics
Kinetic Energy Calculator
Find the kinetic energy of a moving object from its mass and velocity using KE = ½·m·v² — or rearrange to solve for mass or velocity. Mix any units, see the working, and get a relatable sense of how big the answer is.
Kinetic energy
KE = ½mv²Solve for
Kinetic energy
578.704
about the same as a car at 50 mph (~80 km/h)
in joules
578,704 J
mass
1,500 kg
velocity
27.7778 m/s
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The basics
What is kinetic energy?
Kinetic energy is the energy an object has purely because it is moving. Bring something to a stop and that energy has to go somewhere — into heat, sound, or deformation. It depends on just two things, mass and speed, but speed counts far more because it enters the formula squared.
KE = ½ · m · v²
The formula
Half the mass times the velocity squared. With m in kilograms and v in metres per second, the energy comes out in joules.
½ · 2 kg · (3 m/s)² = 9 J
v doubles → KE ×4
Speed dominates
Because velocity is squared, doubling the speed quadruples the energy, while doubling the mass only doubles it. This is why crashes get so much worse at higher speeds.
10 → 20 m/s multiplies energy by 4
Method
How to calculate it by hand
Four short steps turn a mass and a speed into an energy in joules.
- 1
Convert to SI units
Put the mass in kilograms and the speed in metres per second. Mixed units (grams, mph, km/h) must be converted first — the calculator above does this for you.
m → kg, v → m/s - 2
Square the velocity
Multiply the speed by itself. This single step is why a small change in v makes a big change in energy.
v² = v · v - 3
Multiply by the mass
Multiply the squared velocity by the mass m.
m · v² - 4
Take half
Halve the result. The number you get is the kinetic energy in joules.
KE = ½ · m · v²
Worked examples
Solve for any variable
The same formula answers three different questions — find the energy, the mass, or the velocity — by rearranging it. Each tab works the example from the formula.
Given m = 2 kg, v = 3 m/s
KE = ½ · m · v²
KE = ½ · 2 · 3²
KE = ½ · 2 · 9
KE = 9 J
Rearranging
Three forms of one formula
Algebra lets you solve KE = ½·m·v² for whichever quantity you are missing.
KE = ½ · m · v²
Energy
The standard form. Use it when you know the mass and the speed.
2 kg at 3 m/s → 9 J
m = 2 · KE / v²
Mass
Solve for mass when you know the energy and the speed.
100 J at 5 m/s → 8 kg
v = √(2 · KE / m)
Velocity
Solve for speed when you know the energy and the mass.
90 J for 5 kg → 6 m/s
Where it shows up
Why it matters
Kinetic energy is the currency that motion trades in — it appears anywhere something moves and then has to stop.
braking distance ∝ v²
Road safety
Stopping distance grows with the square of speed, because the brakes must dissipate all the kinetic energy. Small speed increases need much longer to stop.
½ ρ A v³
Wind & turbines
The power available in moving air scales with velocity cubed — kinetic energy per unit of air times how fast it arrives — so wind farms favour windier sites.
KE → heat
Engineering
Crumple zones, run-off ramps, and flywheels are all about absorbing or storing kinetic energy safely rather than letting it release all at once.
Quick chart
How much energy do everyday things have?
A lookup of common objects at typical speeds. Nudge the speed multiplier to watch the squared-velocity law in action — twice the speed, four times the energy.
Speed multiplierActual speeds
| Object | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Walking person | 70 kg | 5 km/h | 67.5154 J |
| Cyclist | 80 kg | 25 km/h | 1.92901 kJ |
| Sprinter (Usain Bolt) | 86 kg | 44 km/h | 6.42346 kJ |
| Car in town | 1,500 kg | 50 km/h | 144.676 kJ |
| Car on highway | 1,500 kg | 100 km/h | 578.704 kJ |
| Tennis serve (ball) | 57 g | 200 km/h | 87.963 J |
| Bullet (9 mm) | 8 g | 1,300 km/h | 521.605 J |
| Passenger jet (cruise) | 80,000 kg | 900 km/h | 2,500 MJ |
Worth knowing
Rules and edge cases
A handful of facts that make kinetic energy easier to reason about.
KE ≥ 0
Never negative
Because the velocity is squared, kinetic energy is always zero or positive. Direction of travel makes no difference — only how fast.
KE = 0 at rest
Stationary means zero
An object that is not moving has no kinetic energy at all, however heavy it is.
W = ΔKE
The work–energy theorem
The net work done on an object equals its change in kinetic energy. Push something to speed it up; the work you do becomes its kinetic energy.
KE = p² / 2m
Link to momentum
Kinetic energy relates to momentum p = m·v by KE = p² / 2m — handy in collision problems.
frame-dependent
It depends on the observer
Speed is measured relative to something, so a coffee on a moving train has kinetic energy for someone on the platform but none for a fellow passenger.
rotational KE
Spinning counts too
Rotating objects carry rotational kinetic energy, ½·I·ω², which adds to the energy of straight-line motion for things that roll.
Common mistakes
Where it goes wrong
The usual slips when plugging numbers into KE = ½·m·v².
forgot to square
Squaring only v, not the units
The velocity is squared, not the mass. Square the speed first, then multiply by the mass and by one half.
g vs kg
Leaving mass in grams
A 145 g ball is 0.145 kg. Using 145 in the formula overstates the energy a thousandfold. Convert mass to kilograms first.
km/h vs m/s
Skipping the speed conversion
100 km/h is about 27.8 m/s, not 100. Divide km/h by 3.6 to get metres per second before squaring.
dropping the ½
Forgetting the one-half
The factor of one half is part of the formula. Leaving it out doubles every answer.
FAQ
Common questions
Kinetic energy is the energy an object has because it is moving. Any object with mass that is in motion carries kinetic energy, and the faster or heavier it is, the more it has. A stationary object has zero kinetic energy.
The kinetic energy of an object is KE = ½·m·v², where m is its mass and v is its speed. Take half of the mass, then multiply by the velocity squared. With mass in kilograms and velocity in metres per second, the result is in joules.
First write the formula KE = ½·m·v². Put the mass and velocity into SI units (kilograms and metres per second). Square the velocity, then multiply one half by the mass and the squared velocity. The answer is in joules.
Velocity is squared because energy grows with the square of speed: doubling the velocity quadruples the kinetic energy. It comes from the work–energy theorem — the distance needed to reach a speed scales with the square of that speed, so the energy stored does too.
Rearrange KE = ½·m·v² to v = √(2·KE / m). Divide twice the kinetic energy by the mass, then take the square root. Switch this calculator to ‘Solve for: Velocity’ to do it automatically.
Rearrange the formula to m = 2·KE / v². Multiply the kinetic energy by two and divide by the velocity squared. Switch the calculator to ‘Solve for: Mass’ to compute it from an energy and a speed.
A joule (J) is the SI unit of energy. It is the standard unit for kinetic energy when mass is in kilograms and velocity is in metres per second. One thousand joules is a kilojoule (kJ); roughly 4.18 J equals one calorie.
Kinetic energy is the energy of motion (KE = ½·m·v²), while potential energy is stored energy due to position or state — for example gravitational potential energy, PE = m·g·h. As an object falls, potential energy converts into kinetic energy, but the total stays the same.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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