Kinetic Energy Calculator

Calculate kinetic energy from mass and speed, or rearrange Ek = ½mv² to find mass or speed.

Your values

What do you want to calculate?
Kinetic energy (Ek) — joulesCalculated

The kinetic energy value to use in the formula.

145 kJ
Mass (m) — kilogramsEntered

Mass of the moving object. Choose a mass unit, not a force/weight unit.

Speed (v) — metres per secondEntered

Speed of the object. The formula uses speed magnitude, not direction.

Based on the two values entered. Speed uses magnitude, not direction.

A mass of 1.50 t moving at 13.8889 m/s has a classical kinetic energy of 145 kJ.

Formula used

Ek = ½ × m × v²
Ek = ½ × 1.50 t × (13.8889 m/s)² = 145 kJ

Units used

Mass, speed and kinetic energy: display value, exact base SI value, and whether each was entered or calculated
QuantityDisplay valueBase SI valueStatus
Kinetic energy (Ek)145 kJ144,676 JCalculated
Mass (m)1,500 kg1,500.00 kgEntered
Speed (v)50 km/h13.8889 m/s (≈ 50.0 km/h, ≈ 31.1 mph)Entered

How mass and speed changes affect energy

  • Doubling the mass to 3.00 t at the same speed doubles the energy to 289 kJ.
  • Halving the mass to 750 kg at the same speed halves the energy to 72.3 kJ.
  • Doubling the speed to 27.7778 m/s at the same mass quadruples the energy to 579 kJ.
  • Halving the speed to 6.94444 m/s at the same mass cuts the energy to a quarter, 36.2 kJ.

Based on the classical kinetic-energy formula for straight-line motion. Values are converted to SI units for the calculation.

How to use this calculator

Select what you want to calculate, enter the other two values, and choose the units that match your figures. The result updates automatically as you type — there is no separate calculate step. The calculator uses the classical kinetic-energy equation Ek = ½mv².

  1. Choose "Kinetic energy", "Mass" or "Speed" as the quantity to calculate — the other two quantity cards become editable inputs.
  2. Enter each known value and choose the unit it was measured in. The missing quantity recalculates as soon as both values are entered.
  3. Review the formula used, the units-used table, any warnings, and how the energy would change with a doubled or halved mass or speed.
  4. Change the mode at any time — your entered values are kept — or select "Reset" to start over, or "Use example" to load a worked example.

What is kinetic energy?

Kinetic energy is the energy an object has because it is moving. In classical (Newtonian) mechanics, the kinetic energy of an object moving in a straight line is:

Ek = ½ × m × v²
  • Ek — kinetic energy, in joules (J)
  • m — mass, in kilograms (kg)
  • v — speed, in metres per second (m/s)

A joule is defined from these same base units: 1 J = 1 kg·m²·s⁻² — one kilogram, moving at one metre per second, squared. Every other energy unit this calculator supports (kilojoules, kilowatt-hours, calories, foot-pounds force…) is a fixed multiple of the joule.

How is kinetic energy calculated from mass and speed?

Convert both figures to kilograms and metres per second, then apply Ek = ½mv². For a 1,500 kg car travelling at 50 km/h:

50 km/h = 50 ÷ 3.6 = 13.888… m/s, so Ek = ½ × 1,500 kg × (13.888… m/s)² = 144,675.93 J, or about 144.68 kJ.

Speed is always converted to metres per second first — energy scales with the square of speed, so an unconverted figure would give a wildly wrong answer.

How do you rearrange the formula to find mass or speed?

Starting from Ek = ½mv², the same relationship rearranges to solve for either input:

Kinetic energy formulas, rearranged for each quantity
Solving forFormula
Kinetic energyEk = ½ × m × v²
Massm = 2 × Ek ÷ v²
Speedv = √(2 × Ek ÷ m)

For example, 24 J of kinetic energy in a 3 kg object gives a speed of v = √(2 × 24 ÷ 3) = 4 m/s. And a kinetic energy of 450 J at 30 m/s gives a mass of m = 2 × 450 ÷ 30² = 1 kg.

Why does kinetic energy grow with the square of speed?

Because v is squared in Ek = ½mv², a change in speed has a much bigger effect on energy than the same change in mass. Doubling the mass at a fixed speed doubles the energy — a straight-line relationship. Doubling the speed at a fixed mass quadruples the energy, because 2² = 4. Halving the speed cuts the energy to a quarter. This is a mathematical property of the formula itself, not a real-world conclusion about impact severity, braking distance or safety.

How is this different from relativistic kinetic energy?

Ek = ½mv² is the classical (Newtonian) approximation, accurate at speeds much lower than the speed of light — everyday machinery, vehicles, sports and most physics coursework. Close to the speed of light, mass and energy behave differently and the relativistic kinetic-energy formula is needed instead. This calculator flags a result once speed reaches 1% of the speed of light, warns strongly from 10% upward, and refuses to calculate at or above the speed of light itself — but it never computes a relativistic answer. Relativistic kinetic energy is out of scope for this version of the calculator.

Does this calculator use metric or imperial units?

Both, on every input. Mass accepts micrograms, milligrams, grams, kilograms and metric tonnes alongside ounces, pounds, US short tons and UK long (Imperial) tons. Speed accepts metres per second, kilometres per hour, feet per second and knots alongside miles per hour. Energy accepts joules and its SI multiples alongside watt-hours, foot-pounds force, calories and kilocalories. Every figure is converted to kilograms, metres per second and joules before the formula runs, so mixing units — say, a mass in pounds with a speed in km/h — calculates correctly.

US and UK tons are never treated as the same unit: a US short ton is exactly 907.18474 kg, a UK long (Imperial) ton is exactly 1,016.0469088 kg, and a metric tonne is exactly 1,000 kg — three different masses that this calculator always labels in full, never as a bare "ton".

What does this calculator assume, and what does it not do?

This calculator assumes classical, non-relativistic, straight-line (translational) motion, with speed entered as a magnitude rather than a directional velocity. It does not model rotational kinetic energy, force, momentum, work, drag, friction, gravity or vectors, and it applies no real-world losses. It does not assess a collision, impact, injury, braking distance, vehicle safety, ballistics, lifting, material-strength or equipment-design question, and a figure from it should never be used alone to make one of those decisions — those need a real measurement, the relevant engineering standard, and a qualified assessment.

Frequently asked questions

What is the formula for kinetic energy?

The classical formula for kinetic energy is Ek = ½ × m × v², where Ek is kinetic energy in joules, m is mass in kilograms and v is speed in metres per second. It only applies to straight-line (translational) motion at speeds far below the speed of light — it does not include rotational energy.

How do I calculate kinetic energy from mass and speed?

Choose "Kinetic energy" as what to calculate, then enter the mass and speed with their units — the result updates automatically. The calculator converts both figures to kilograms and metres per second, then applies Ek = ½mv². For example, a 1,500 kg car at 50 km/h (13.89 m/s) has a kinetic energy of about 144.68 kJ.

How do I solve for speed if I know the kinetic energy and mass?

Choose "Speed" as what to calculate, then enter the kinetic energy and the mass. The calculator rearranges the formula to v = √(2 × Ek ÷ m). For example, 450 J of kinetic energy and a mass of 30 kg give a speed of √(2 × 450 ÷ 30) = 1 m/s.

How do I solve for mass if I know the kinetic energy and speed?

Choose "Mass" as what to calculate, then enter the kinetic energy and the speed. The calculator rearranges the formula to m = 2 × Ek ÷ v². For example, 24 J of kinetic energy at a speed of 4 m/s give a mass of 2 × 24 ÷ 4² = 3 kg.

Why does doubling the speed quadruple the kinetic energy?

Because speed is squared in the formula (Ek = ½mv²), doubling v multiplies v² by four, so the energy also multiplies by four. Doubling the mass with speed unchanged only doubles the energy, because mass appears to the first power, not squared. This is a mathematical property of the formula, not a statement about impact severity or safety.

What units does this calculator support?

Mass: micrograms, milligrams, grams, kilograms, metric tonnes, ounces, pounds, US short tons and UK long (Imperial) tons — kept distinct throughout, since a US ton (907.18474 kg) and a UK long ton (1,016.0469088 kg) are different masses. Speed: metres per second, kilometres per hour, miles per hour, feet per second and knots. Energy: millijoules, joules, kilojoules, megajoules, gigajoules, watt-hours, kilowatt-hours, foot-pounds force, calories and kilocalories (the "food Calories" on a nutrition label).

Can I use this calculator for a crash, impact or ballistics calculation?

No. This is a theoretical classical-physics calculator only. It does not assess a collision, impact, injury, braking distance, vehicle safety, ballistics, lifting, material-strength or equipment-design question, and none of those decisions should be made from this result alone. Real-world impact severity depends on force, duration, structure and many factors this calculator does not model.

What happens near the speed of light?

The classical formula Ek = ½mv² is only accurate at speeds far below the speed of light. This calculator flags a result once speed reaches 1% of the speed of light, and shows a stronger warning from 10% of the speed of light upward, because relativistic effects become significant there. It refuses to calculate at or above the speed of light itself, since the classical formula is not valid at that point. Version 1 of this calculator does not compute a relativistic result.

What is the difference between speed and velocity?

Speed is a magnitude — how fast something is moving, with no direction. Velocity is a vector — speed combined with a direction. This calculator uses speed magnitude only: it works entirely in straight-line, non-rotating motion and never resolves direction, vectors or components of velocity.