Skip to content
Calcapedia
Menu
Science

Kinetic Energy Calculator

Find the kinetic energy of a moving object from its mass and speed, or solve for the mass or speed instead.

Level: Grades 8–9

Printable worksheet

Kinetic Energy Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for

Speed is a magnitude, so direction doesn't matter: KE depends on v².

Result

Kinetic energy

578.7037 kJ

Kinetic energy is 578.7037 kJ.

In joules
578,703.7037 J
In foot-pounds force
426,829.9475 ft·lbf
In kilocalories
138.3135 kcal
In kilowatt-hours
0.1608 kWh

See the step-by-step solution ↓

Step-by-step solution

  1. Convert speed to m/s (1 km/h = 0.277777777778 m/s)

    100 km/h×0.277777777778=27.777778 m/s

  2. Multiply half the mass by the speed squared; squaring is why speed matters so much more than mass

    12×1,500×27.7777782=578,703.703704 J

  3. Convert to kJ: divide by 1,000

    578,703.7037041,000=578.703704 kJ

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how much energy a moving object carries, from a rolling ball to a speeding car. Kinetic energy is the energy an object has because it is moving. For everyday speeds it equals one half of the mass times the speed squared, KE = ½mv². The square is the important part: doubling the speed quadruples the energy, which is why stopping distances grow so quickly with speed.

This calculator works in any direction. Give it a mass and a speed to get the energy, or give it an energy and one of the other two to find the missing value. Inputs can be in kilograms, grams, pounds or tonnes, and in meters per second, kilometers per hour, miles per hour or feet per second.

Where it's used

Why this math matters outside the classroom:

  • Speed and safety. Driver educators point out that doubling speed from 50 to 100 km/h gives a car four times the kinetic energy to shed.
  • Pitched baseball. A 0.145 kg baseball thrown at 40 m/s carries ½ × 0.145 × 40² = 116 J of kinetic energy.
  • Crash barriers. Highway engineers design barriers to absorb the kinetic energy of a vehicle of a given mass and speed.
  • Mass vs speed. Physics students find a 1,500 kg car at 20 m/s carries 300 kJ, then compare how mass and speed each change that figure.

Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether to solve for kinetic energy, mass or speed.
  2. Enter the two known values and pick a unit for each.
  3. Pick the unit for the answer; the result is also listed in the other available units.

What the inputs mean

Speed (v)
Only the size of the speed matters, because it is squared. 100 km/h is 27.78 m/s; 60 mph is exactly 26.8224 m/s.
Kinetic energy (KE)
1 kJ is 1,000 J. 1 ft·lbf is about 1.356 J, 1 kcal is 4,184 J, and 1 kWh is 3,600,000 J.

Formula and method

KE = ½ × m × v²
m = 2 × KE ÷ v²
v = √(2 × KE ÷ m)

KE is the kinetic energy, m is the mass and v is the speed. The small ² means "squared" (multiplied by itself), and √ is the square root. With mass in kilograms and speed in meters per second, the energy comes out in joules (J), the standard unit of energy. The calculator converts your inputs to those units first, then converts the answer to the unit you choose.

Solving for mass divides by v², so the speed must be above zero. Solving for speed takes a square root, which always gives the positive speed.

Worked example

A car with a mass of 1,500 kg is travelling at 100 km/h. How much kinetic energy does it have?

  1. Convert the speed: 100 km/h × (1000 ÷ 3600) = 27.7778 m/s.
  2. KE = ½ × 1500 × 27.7778² = 578,703.7 J.
  3. Convert to kilojoules: 578,703.7 ÷ 1000 = 578.7037 kJ.

Result: The car carries about 578.7 kJ of kinetic energy. At 50 km/h it would have a quarter of that.

Understanding the result

Kinetic energy is what brakes must turn into heat, and what a collision has to absorb. Comparing values at different speeds shows how sharply that load rises.

Joules are small units: lifting a 1 kg mass by about 10 cm takes roughly 1 J. Vehicle-scale energies are usually easier to read in kilojoules.

Assumptions and limitations

  • The object moves as a whole without spinning; rotational energy is not included.
  • Speed is measured relative to the frame you care about, usually the ground.
  • Speeds are far below the speed of light, so the classical formula applies.
  • Rotating parts such as wheels carry extra rotational kinetic energy that is not counted here.
  • At a significant fraction of the speed of light the relativistic formula is needed instead.
  • The result is energy of motion only; it says nothing about how that energy is dissipated in a collision.

Frequently asked questions

Why does doubling the speed quadruple the kinetic energy?

Because speed is squared in the formula. Twice the speed gives 2² = 4 times the energy, and three times the speed gives 9 times the energy.

Can kinetic energy be negative?

No. Mass is positive and the squared speed is never negative, so kinetic energy is zero for an object at rest and positive otherwise.

How is kinetic energy different from momentum?

Momentum is mass times velocity and has a direction; kinetic energy is half the mass times speed squared and has none. Two objects can share the same momentum but have very different energies.

What units should I use?

Any of the listed ones. Internally the calculation uses kilograms, meters per second and joules, which are the SI units that make the formula work without extra factors.

How this calculator is checked

Method: Classical translational kinetic energy, KE = ½mv², rearranged for m and v. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Kinetic Energy Calculator on your own website or blog for free. Paste this code where you want it to appear: