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Kinetic Energy Calculator

Kinetic energy equals one-half times mass times velocity squared: KE = 0.5 x m x v². This fundamental physics formula calculates the energy an object possesses due to its motion. Select which variable to solve for, enter the two known values, and the calculator returns the result instantly.

Quick Answer

A 10 kg object moving at 5 m/s has a kinetic energy of 0.5 x 10 x 25 = 125 J. A 1,500 kg car traveling at 20 m/s (about 45 mph) has a kinetic energy of 300,000 J (300 kJ).

Common Examples

Input Result
m = 10 kg, v = 5 m/s KE = 125.00 J
m = 1,500 kg, v = 20 m/s KE = 300,000.00 J
KE = 500 J, v = 10 m/s m = 10.00 kg
KE = 200 J, m = 4 kg v = 10.00 m/s
m = 0.145 kg, v = 40 m/s KE = 116.00 J

How It Works

The Formula

The kinetic energy formula describes the energy of a moving object:

KE = ½ x m x v²

Where:

  • KE = kinetic energy in joules (J)
  • m = mass of the object in kilograms (kg)
  • v = velocity (speed) of the object in meters per second (m/s)

This equation can be rearranged to solve for any of the three variables:

  • Kinetic energy: KE = 0.5 x m x v²
  • Mass: m = 2 x KE / v²
  • Velocity: v = sqrt(2 x KE / m)

Key Properties of Kinetic Energy

Kinetic energy depends on the square of velocity, which means doubling the speed quadruples the kinetic energy. This is why highway speed collisions are far more destructive than low-speed impacts. A car going 60 mph has four times the kinetic energy of the same car going 30 mph.

Kinetic energy is always zero or positive. An object at rest (v = 0) has zero kinetic energy. Mass is always positive, and squaring the velocity eliminates any directional sign.

Units

In SI units, mass is in kilograms and velocity is in meters per second, giving kinetic energy in joules (J). One joule equals one kilogram-meter-squared per second-squared (kg x m² / s²).

Relationship to Work

The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W = ΔKE. This means the energy required to accelerate an object from rest to a given speed equals its kinetic energy at that speed.

Worked Example

For a 10 kg object moving at 5 m/s: KE = 0.5 x 10 x 5² = 0.5 x 10 x 25 = 125 J. To find the mass of an object with KE = 500 J and v = 10 m/s: m = 2 x 500 / 10² = 1,000 / 100 = 10 kg. To find the velocity of a 4 kg object with KE = 200 J: v = sqrt(2 x 200 / 4) = sqrt(100) = 10 m/s. For a baseball (0.145 kg) thrown at 40 m/s (about 90 mph): KE = 0.5 x 0.145 x 40² = 0.5 x 0.145 x 1,600 = 116 J.

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Frequently Asked Questions

What is kinetic energy?
Kinetic energy is the energy an object has because of its motion. Any object with mass that is moving has kinetic energy. The faster it moves or the more massive it is, the more kinetic energy it possesses. Kinetic energy is measured in joules (J) in the SI system.
Why is velocity squared in the formula?
The v-squared relationship comes from the work-energy theorem and Newton's second law. When you integrate force over distance to calculate work, the velocity term appears squared. Physically, this means that doubling the speed of an object requires four times the energy, and an object moving twice as fast takes four times the stopping distance.
What is the difference between kinetic and potential energy?
Kinetic energy is energy of motion, while potential energy is stored energy due to position or configuration. For example, a ball held at a height has gravitational potential energy (PE = mgh). When released, that potential energy converts to kinetic energy as the ball falls. The total mechanical energy (KE + PE) is conserved in the absence of friction and air resistance.
Can kinetic energy be negative?
No. Since mass is always positive and velocity is squared (eliminating any negative sign from direction), kinetic energy is always zero or positive. An object at rest has zero kinetic energy. There is no physical meaning to negative kinetic energy in classical mechanics.
How does kinetic energy relate to stopping distance?
Stopping distance is proportional to kinetic energy. Since KE depends on v-squared, doubling your speed quadruples the energy that brakes must dissipate, approximately quadrupling the stopping distance. This is a key reason why speed limits exist and why high-speed collisions are disproportionately more dangerous.