Kinetic Energy Calculator
Find the kinetic energy of anything that moves, or the mass or speed from the other two, with KE = ½mv². Mix units freely. Advanced adds potential energy, drop height and impact speed, rough braking distance and light-speed physics.
KE = ½ × m × v²
The answer appears in the highlighted box; change its unit to see it another way. Mix units freely, for example pounds with km/h.
Height, potential energy and drops
Uses the mass and speed above, standard gravity g = 9.80665 m/s² and no air resistance.
Braking to a stop (rough)
The brakes must take out all the kinetic energy: distance = KE ÷ (mass × deceleration) = v² ÷ (2 × deceleration). Reaction time, slopes and ABS are not included.
Faster means much more energy
The same mass at other speeds. Energy grows with the square of the speed: double the speed, four times the energy.
| Speed | × speed | Kinetic energy | × energy |
|---|
Near the speed of light
How your kinetic energy is worked out
Your numbers: speed into m/s, square it, then multiply by half the mass.
- 1
Speed in m/s
100 km/h= 27.7778 m/s
- 2
Square the speed
27.7778 × 27.7778= 771.605 m²/s²
- 3
Half × mass × v²
½ × 1,000 kg ×771.605= 385,802 J
- 4
Into your unit
385,802 J= 385.8 kJ
Read more: the formula, worked examples, braking and light speed
Anything that moves carries energy. Speed it up and you put energy in; slow it down and the brakes, the air or whatever it hits must take that energy out, usually as heat and bent metal. Because the speed is squared, the energy climbs very fast as things go faster.
The formula
kinetic energy KE = ½ × mass m × speed v²
mass m = 2 × KE ÷ v²
speed v = √(2 × KE ÷ m)
momentum p = m × v
potential energy PE = m × g × h, g = 9.80665 m/s²
total mechanical energy = KE + PE
drop height for the same energy h = v² ÷ (2 × g)
impact speed from a drop v = √(2 × g × h)
braking distance d = v² ÷ (2 × a), a = μ × g
relativistic KE = (γ − 1) × m × c², γ = 1 ÷ √(1 − v² ÷ c²)
m in kg, v in m/s, h and d in m, KE in joules
Worked example
Kinetic energy (the default): a 1,000 kg car at 100 km/h. Speed: 100 ÷ 3.6 = 27.7778 m/s. Squared: (100 ÷ 3.6)² = 771.605 m²/s². Then KE = ½ × 1,000 × 771.605 = 385,802.47 J = 385.80 kJ = 0.10717 kWh = 92.21 kcal.
Momentum: 1,000 × 27.7778 = 27,777.78 kg·m/s.
Same energy as a drop of: h = 771.605 ÷ (2 × 9.80665) = 771.605 ÷ 19.6133 = 39.34 m, about a 13-storey building.
Mass: 1,000 J at 10 m/s. m = 2 × 1,000 ÷ 10² = 2,000 ÷ 100 = 20 kg.
Speed: 1,000 J in 5 kg. v = √(2 × 1,000 ÷ 5) = √400 = 20 m/s (72 km/h).
US units: a 3,000 lb car at 60 mph. 3,000 lb = 1,360.777 kg and 60 mph = 26.8224 m/s, so KE = ½ × 1,360.777 × 26.8224² = 489,499.5 J = 361,036 ft·lbf.
Potential and total energy: the same car on a 10 m high ramp. PE = 1,000 × 9.80665 × 10 = 98,066.5 J, so the total is 385,802.47 + 98,066.5 = 483,868.97 J. Dropped from rest from 10 m it would hit the ground at √(2 × 9.80665 × 10) = 14.00 m/s (50.42 km/h).
Braking (rough): on dry asphalt (μ ≈ 0.7) the deceleration is 0.7 × 9.80665 = 6.8647 m/s². Distance = 771.605 ÷ (2 × 6.8647) = 56.20 m, time = 27.7778 ÷ 6.8647 = 4.05 s, average force 1,000 × 6.8647 = 6,864.7 N. Check: 6,864.7 N × 56.20 m ≈ 385,802 J, the whole kinetic energy.
Near light speed: 1 kg at 10% of light speed (29,979,245.8 m/s). γ = 1 ÷ √(1 − 0.1²) = 1.0050378. Relativistic KE = 0.0050378 × 1 × 299,792,458² = 4.5278 × 10¹⁴ J, while ½mv² gives 4.4938 × 10¹⁴ J, about 0.76% too little.
Double the speed, four times the energy
The 1,000 kg car at different speeds:
| Speed | Kinetic energy | Compared with 100 km/h |
|---|---|---|
| 50 km/h | 96.451 kJ | 0.25× |
| 100 km/h | 385.8 kJ | 1× |
| 150 km/h | 868.06 kJ | 2.25× |
| 200 km/h | 1,543.2 kJ | 4× |
| 300 km/h | 3,472.2 kJ | 9× |
Everyday kinetic energies
Typical, rounded values worked out with ½mv².
| What | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Car at 100 km/h | 1,000 kg | 100 km/h | 385,800 J |
| Cyclist and bike at 25 km/h | 85 kg | 25 km/h | 2,050 J |
| Baseball pitch | 145 g | 90 mph | 117.4 J |
| Sprinter | 75 kg | 10 m/s | 3,750 J |
| Loaded truck | 40 t | 80 km/h | 9,877,000 J |
| Airliner | 70 t | 140 kt | 181,600,000 J |
Rough friction coefficients for braking
| Surface | μ (rough) | Braking distance from 100 km/h |
|---|---|---|
| Dry asphalt | 0.7 | 56.2 m |
| Wet asphalt | 0.4 | 98.4 m |
| Gravel | 0.35 | 112 m |
| Packed snow | 0.2 | 197 m |
| Ice | 0.1 | 393 m |
Notes
- Braking numbers are rough. Real tyre grip varies a lot with the tyre, its wear, the road, the temperature and the speed. Add the reaction distance (speed × about 1 to 1.5 s) for a full stopping distance. Never use these figures to judge a safe following distance.
- Drop heights, fall times and impact speeds ignore air resistance, so real falling objects are slower, especially light ones or long drops.
- Standard gravity g = 9.80665 m/s² is a defined value; real gravity is about 9.78 at the equator and 9.83 at the poles.
- Energy factors are exact by definition: 1 kWh = 3.6 MJ, 1 Wh = 3,600 J, 1 cal = 4.184 J (thermochemical, used on food labels, so 1 kcal = 4,184 J), 1 BTU = 1,055.05585262 J (International Table) and 1 ft·lbf = 1.3558179483 J.
- The speed of light c = 299,792,458 m/s exactly. Above 1% of c the calculator also shows the relativistic answer; nothing with mass can reach c.
Common questions
What is kinetic energy?
Kinetic energy is the energy something has because it is moving. It is the work you would have to do to get it from standing still up to its speed, and the work the brakes (or a wall) must take out to stop it. It is measured in joules: 1 J is the energy of a 2 kg mass moving at 1 m/s.
What is the kinetic energy formula?
KE = ½ × m × v². Mass m in kilograms and speed v in metres per second give the energy in joules. A 1,000 kg car at 100 km/h (27.78 m/s) has ½ × 1,000 × 27.78² = 385,802 J, about 386 kJ.
Why does doubling the speed give four times the energy?
Because the speed is squared. Twice the speed is 2² = 4 times the energy, and three times the speed is 9 times. That is why a crash at 100 km/h is far worse than one at 50 km/h, and why the braking distance (not counting reaction time) also grows four times.
How do I find the speed from kinetic energy?
Turn the formula around: v = √(2 × KE ÷ m). 1,000 J in a 5 kg mass gives √(2,000 ÷ 5) = √400 = 20 m/s.
How do I find the mass from kinetic energy?
m = 2 × KE ÷ v². 1,000 J at 10 m/s gives 2,000 ÷ 100 = 20 kg.
What is the difference between kinetic and potential energy?
Kinetic energy comes from moving; gravitational potential energy comes from height: PE = m × g × h with g = 9.80665 m/s². When something falls, height turns into speed. A car at 100 km/h has the same energy as if it were dropped from 39.3 m, ignoring air resistance.
When does ½mv² stop being right?
At speeds close to light. Relativity gives KE = (γ − 1) × m × c², where γ = 1 ÷ √(1 − v² ÷ c²). At 1% of light speed the difference is under 0.01%, at 10% about 0.76% and at half light speed about 24%. For anything on Earth, ½mv² is exact enough.
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