Kinetic Energy Calculator,
KE = ½mv², solve for energy, mass or velocity.

Physics guide

What is kinetic energy and how is it calculated?

Kinetic energy is the energy a body possesses because it is moving. Any object with mass that is in motion carries kinetic energy. It is a scalar quantity, meaning it has magnitude but no direction, and it is always zero or positive since mass and velocity squared are always non-negative.

The kinetic energy formula

The kinetic energy equation follows from Newton's laws of motion. Gaspard-Gustave de Coriolis helped formalise the ½mv² expression in the 1820s, and the name “kinetic energy” came later in the nineteenth century:

Where KE is kinetic energy in joules, m is mass in kilograms, and v is velocity in meters per second. Textbooks also write it as K or E_k; the equation is the same. The "½" factor arises from integration of Newton's second law over a displacement: applying a constant force to accelerate a mass from rest produces work equal to half the product of mass and velocity squared.

Solving for the three variables

The same equation can be rearranged to find any of the three variables when the other two are known:

The calculator detects which field you left empty and applies the correct rearrangement automatically. All inputs are converted to SI units (kg and m/s) before calculation, and the result is converted back to your chosen output unit.

Worked examples

Calculate kinetic energy

A 1,200 kg car travels at 25 m/s. Square the speed, multiply by the mass, then halve it:

Find velocity from kinetic energy

A 2 kg ball carries 500 J of kinetic energy. Rearrange for v:

That is about 80.5 km/h, or 50 mph.

Find mass from kinetic energy

An object moving at 6 m/s has 90 J of kinetic energy. Rearrange for m:

Why velocity matters more than mass

Because velocity is squared in the formula, doubling an object's speed quadruples its kinetic energy, while doubling its mass only doubles the kinetic energy. This is why vehicle collision physics emphasizes speed limits so strongly: a car traveling at 120 km/h carries four times the kinetic energy of the same car at 60 km/h.

Real-world examples

• Baseball pitch (145 g at 144 km/h): KE = ½ × 0.145 × 40² = 116 J. A small mass at high speed still carries a surprising amount of energy.
• Rifle bullet (10 g at 900 m/s): KE = ½ × 0.010 × 900² = 4050 J. Despite the tiny mass, the enormous velocity gives a bullet tremendous stopping power.
• Olympic sprinter (80 kg at 10 m/s): KE = ½ × 80 × 100 = 4000 J, roughly equivalent to the bullet. The mass compensates for the lower speed.
• Commercial airliner (300,000 kg at 250 m/s): KE = ½ × 300,000 × 62,500 = 9.375 × 10⁹ J = 9.375 GJ, which is about 2,600 kWh, roughly what a typical US home uses in three months.

The work-energy theorem

The work-energy theorem states that the net work done on an object equals the change in its kinetic energy:

This relationship is at the heart of classical mechanics. When you brake a car, the friction force does negative work, reducing the kinetic energy to zero. The amount of energy that must be dissipated as heat equals the initial kinetic energy, which is why stopping distance increases with the square of speed.

From kinetic energy to force

Kinetic energy is not a force, but the work-energy theorem turns it into one. Stopping an object means doing work equal to its kinetic energy, and work is force times distance (W = F × d). So the average force over a stopping distance d is:

Take the 1,200 kg car at 25 m/s from above, which carries 375,000 J. Brought to rest over 50 m, the average braking force is 375,000 / 50 = 7,500 N (about 1,690 lbf). Over just 25 m it is 15,000 N. Halving the stopping distance doubles the force, which is why crumple zones and airbags that lengthen the stop reduce the load on a body. The “Average stopping force” card in the calculator does this sum for you once a kinetic energy is shown.

This is an average that assumes a constant force. If you were looking for kinetic friction force (f = μ_k × N), that is a separate calculation based on the friction coefficient.

Units of kinetic energy

The SI unit of energy is the joule (J). One joule is the energy transferred when a force of one newton acts over a distance of one meter. Other useful units include:

• Kilojoule (kJ): 1000 J. Used for engineering and vehicle calculations.
• Kilowatt-hour (kWh): 3.6 million J. The unit on your electricity bill.
• Calorie (cal) and kilocalorie (kcal): Used in nutrition. One food calorie (kcal) = 4184 J.
• Electronvolt (eV): Tiny unit used in atomic and nuclear physics. 1 eV = 1.602 × 10^-19 J.
• BTU: British Thermal Unit, used in HVAC and engineering in the US. 1 BTU = 1055 J.

Unit notes

• Use kg and m/s inside the formula. The result is only in joules if mass is in kilograms and speed is in meters per second. The calculator converts for you.
• Speed conversions: divide km/h by 3.6 to get m/s, and multiply mph by 0.44704.
• Pounds here mean mass. 1 lb = 0.45359 kg. Do not use pounds-force (lbf) in this formula. Grams must be divided by 1,000.

Example with US units: a 160 lb player running at 15 mph has a mass of 160 × 0.45359 = 72.57 kg and a speed of 15 × 0.44704 = 6.706 m/s, so KE = ½ × 72.57 × 6.706² ≈ 1,632 J.

Relativistic kinetic energy

At everyday speeds, the classical formula KE = ½mv² is an excellent approximation. However, as objects approach a significant fraction of the speed of light, Einstein's special relativity becomes important. The relativistic kinetic energy is:

For speeds below 10% of the speed of light (30,000 km/s), the classical formula is within about 1% of the relativistic result. This calculator uses the classical formula, which suits everyday objects including aircraft, spacecraft (in orbit), and even most scientific projectiles.

Disclaimer

This calculator provides estimates for educational and planning use and is not a substitute for a licensed engineer or applicable codes. Do not use it for safety-critical decisions such as crash protection, braking or barrier design. It uses classical (Newtonian) mechanics, so it does not model relativistic effects at very high speeds, rotational energy, air resistance, or energy lost to heat, sound and deformation in real impacts. Displayed values are rounded. Consult a qualified engineer before relying on any figure.