What is the kinetic energy formula?

Kinetic energy is KE = ½ × m × v², where m is mass in kilograms and v is speed in metres per second. The result is in joules (J). One joule equals one kilogram times one metre-squared per second-squared (kg·m²/s²), which is the SI unit of energy.

How do I find velocity from kinetic energy and mass?

Rearrange the formula to v = √(2 × KE ÷ m). For example, if a 5 kg object has 250 J of kinetic energy, v = √(2 × 250 ÷ 5) = √100 = 10 m/s. Select "Velocity" in the Solve for dropdown and the calculator does this automatically.

How do I find mass from kinetic energy and velocity?

Rearrange to m = 2 × KE ÷ v². If an object moving at 20 m/s has 4 000 J of kinetic energy, m = 2 × 4000 ÷ 400 = 20 kg. Select "Mass" in the dropdown and the tool applies the formula and shows the working.

Why does doubling speed quadruple kinetic energy?

Because kinetic energy is proportional to v² (velocity squared), not v. If you double the speed, you multiply v² by 4, so kinetic energy increases by a factor of four. This is why road safety bodies focus on speed reduction — a 30 % drop in speed (from 100 km/h to 70 km/h) reduces crash energy by over 50 %.

What units can I use with this calculator?

Energy: millijoules, joules, kilojoules, megajoules. Mass: grams, kilograms, metric tonnes. Velocity: cm/s, m/s, km/h, mph, ft/s. All inputs are converted to base SI before calculation, so you can freely mix unit systems.

Is kinetic energy always positive?

Yes. Because KE = ½ m v² and both mass and v² are non-negative, kinetic energy is always zero or positive. A stationary object has zero kinetic energy regardless of its mass. The direction of motion does not affect the magnitude — only the speed matters.

Kinetic Energy Calculator

Kinetic energy is the energy an object possesses by virtue of its motion. It is one of the most fundamental concepts in classical mechanics and appears everywhere from vehicle crash analysis to roller-coaster design, bullet ballistics, and wind-turbine engineering. This calculator lets you solve KE = ½ m v² for any of its three variables — kinetic energy, mass, or velocity — with unit conversion, step-by-step working, and a reference speed table built in.

The formula and its rearrangements

The standard kinetic energy equation is:

KE = ½ × m × v²

where KE is kinetic energy in joules (J), m is mass in kilograms (kg), and v is speed in metres per second (m/s). Because there are three variables, the formula can be rearranged to solve for whichever one is unknown:

Solving for energy: KE = ½ m v²
Solving for mass: m = 2 KE ÷ v²
Solving for velocity: v = √(2 KE ÷ m)

The calculator applies whichever form matches your “Solve for” selection and displays the result in engineering notation (e.g. 4.50 kJ instead of 4500 J).

How it works

Select what you want to find, enter the other two quantities with their units, and the result appears instantly. The tool:

Converts all inputs to base SI (kg, m/s, J) using the selected unit prefix.
Applies the matching algebraic form of KE = ½ m v².
Displays the answer in a compact engineering-prefix format.
Shows a numbered list of every arithmetic step so you can verify the working by hand or use it in a homework write-up.
Renders a comparison table of kinetic energies at seven common speeds for your mass, giving you an intuitive feel for whether the result is reasonable.

The copy button exports the full step-by-step solution as plain text, ready to paste into a document or messaging app.

Worked example

A 70 kg cyclist is travelling at 30 km/h. What is their kinetic energy?

First convert 30 km/h to m/s: 30 ÷ 3.6 = 8.33 m/s.

Then apply the formula:

v² = 8.33² = 69.4 m²/s²
KE = ½ × 70 × 69.4 = 2 430 J ≈ 2.43 kJ

Now suppose the same cyclist accelerates to 60 km/h (16.67 m/s):

v² = 16.67² = 277.9 m²/s²
KE = ½ × 70 × 277.9 = 9 726 J ≈ 9.73 kJ

Doubling the speed has quadrupled the kinetic energy — from 2.43 kJ to 9.73 kJ. This illustrates the v² relationship that makes high-speed collisions so much more destructive than low-speed ones.

Speed	KE (70 kg rider)	Relative to 30 km/h
30 km/h	2.43 kJ	1×
60 km/h	9.73 kJ	4×
120 km/h	38.9 kJ	16×

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