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Kinetic Energy Calculator

Enter mass and velocity, or moment of inertia and angular velocity, to calculate kinetic energy.

Input Information

Result

Enter values and press Calculate.

Kinetic Energy Calculator is a physics tool that accurately calculates the energy an object has by virtue of its motion. A stationary object has zero kinetic energy, but the moment it starts moving it gains kinetic energy, which is determined by the object’s mass and velocity.

Key feature of kinetic energy is that it is proportional to the square of velocity. Doubling the speed makes the kinetic energy four times larger, and tripling it makes it nine times larger — exponentially. This is why speeding is dangerous and why collision damage increases.

This calculator is designed to compute two main types of kinetic energy. Translational kinetic energy is the energy of an object moving from one point to another, and rotational kinetic energy is the energy of an object rotating about a specific axis.

This calculator serves as an educational tool that helps students understand the law of conservation of energy, and as a practical tool that gives engineers accurate energy data for machine system design, vehicle crash analysis, and sports science research.

Term Glossary

Kinetic Energy
The energy an object has due to motion; proportional to mass and the square of velocity, with unit joule (J).
Moment of Inertia
In rotational motion, how far the mass is distributed from the rotation axis; unit kg·m².
Angular Velocity
The angle a rotating object turns per unit time, with unit rad/s.

  1. Enter mass → Enter the object’s mass in kilograms (kg).
  2. Enter velocity → Enter the velocity in meters per second (m/s).
  3. Calculate → Click the Calculate button.
  4. View result → Check the kinetic energy in joules (J).

2kg 물체, 3m/s

KE = ½ × 2kg × (3m/s)² = 9J

Car (1000 kg, 20 m/s)

KE = ½ × 1000kg × (20m/s)² = 200,000J (200kJ)

Baseball (0.05 kg, 40 m/s)

KE = ½ × 0.05kg × (40m/s)² = 40J

Linear (Translational) Kinetic Energy Formula

KE=12mv2KE = \tfrac{1}{2} m v^{2}
  • KE: kinetic energy, unit joule (J)
  • m: object mass, unit kilogram (kg)
  • v: object velocity, unit meters per second (m/s)

Rotational Kinetic Energy Formula

KE=12Iω2KE = \tfrac{1}{2} I \omega^{2}
  • I: moment of inertia, unit kg·m²
  • ω: angular velocity, unit radian per second (rad/s)

Example

What is the kinetic energy of a 2 kg ball moving at 10 m/s?

KE=12×2 kg×(10 m/s)2=100 JKE = \tfrac{1}{2} \times 2\,\text{kg} \times (10\,\text{m/s})^2 = 100\,\text{J}

Therefore the kinetic energy is 100 joules (J).

Work-Energy Theorem

The total work done on an object equals the change in its kinetic energy. Positive work increases kinetic energy; negative work decreases it.

Real-Life Applications

  • Traffic and Safety

    Doubling the speed makes kinetic energy four times larger. Braking distance and collision damage increase fourfold, which is the basis of safety testing.

  • Sports Science

    Golf swings, tennis serves, and soccer kicks all use the principle of kinetic energy; efficient energy transfer is key to performance.

  • Renewable Energy

    Wind, hydro, and wave power generators convert natural kinetic energy into electrical energy.

⚠️ Theory of Relativity

The formula KE = ½mv² is classical mechanics and valid when speed is much lower than the speed of light. At relativistic speeds, Einstein’s special relativity must be used.

Law of Conservation of Energy

Energy changes form but is neither created nor destroyed.

  • Potential → kinetic: a falling object’s potential energy converts to kinetic energy
  • Kinetic → heat: kinetic energy converts to heat via friction
  • Kinetic → elastic: kinetic energy stored by a spring

QWhy is the kinetic energy formula ½mv²?

The formula ½mv² is derived from the work (force × distance) needed to accelerate an object from rest to velocity v. That work is stored as energy, which is why the ½ coefficient appears.

QWhy is velocity squared?

Because velocity is squared, doubling the speed quadruples the kinetic energy. This is why braking distance and collision damage rise sharply with speeding.

QWhat does the joule (J) mean?

The joule (J) is the international standard unit of energy and work. One joule is the energy needed to move an object 1 meter with a force of 1 newton.

QWhat is the difference between kinetic energy and momentum?

Momentum (p = mv) is a vector quantity proportional to velocity and has direction. Kinetic energy (KE = ½mv²) is a scalar quantity proportional to the square of velocity with no direction.

QWhich affects kinetic energy more, mass or velocity?

Velocity has a larger impact. Doubling the velocity quadruples the kinetic energy, whereas doubling the mass only doubles it.

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