Kinetic energy is the energy an object possesses due to its motion. Any moving object — from a rolling ball to a speeding car — has kinetic energy. The faster an object moves and the more mass it has, the greater its kinetic energy. It is a scalar quantity measured in joules (J) in the SI system.

The classical kinetic energy formula is KE = ½mv², where m is the mass of the object (in kilograms) and v is its velocity (in meters per second). The factor ½ comes from the integral of momentum with respect to velocity. This formula applies to non-relativistic speeds — when velocities are far below the speed of light.

1. Identify the mass (m) of the object in kilograms (kg). Convert from other units if needed.
2. Determine the velocity (v) in meters per second (m/s). Convert from km/h, mph, or ft/s as necessary.
3. Square the velocity: Multiply v by itself (v²).
4. Multiply: KE = 0.5 × m × v².
5. Read the result in joules (J). Convert to your desired energy unit.

Velocity is squared because kinetic energy is derived from the work-energy theorem. When you accelerate an object, the work done equals force × distance. Since both force (F = ma) and the distance traveled depend on velocity, the relationship becomes quadratic. This means doubling the velocity quadruples the kinetic energy — a critical concept in vehicle safety and impact physics.

No, kinetic energy cannot be negative. Mass is always positive, and velocity squared (v²) is always non-negative regardless of direction. Therefore, KE = ½mv² is always ≥ 0. A stationary object (v = 0) has zero kinetic energy. If you encounter a negative KE value, check your inputs — it likely indicates an error.

Mass: kilograms (kg), grams (g), pounds (lb), ounces (oz).
Velocity: meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), feet per second (ft/s).
Energy output: joules (J), kilojoules (kJ), calories (cal), kilocalories (kcal), foot-pounds (ft·lb), electronvolts (eV).
All conversions are handled automatically with high precision.

• Walking person (70 kg, 1.4 m/s): ~69 J
• Sprinting athlete (70 kg, 10 m/s): ~3,500 J
• Compact car (1,200 kg, 30 m/s ≈ 108 km/h): ~540,000 J (540 kJ)
• Baseball pitch (0.145 kg, 45 m/s): ~147 J
• Bullet (0.01 kg, 400 m/s): ~800 J
• Commercial airplane (70,000 kg, 250 m/s): ~2.19 GJ

Kinetic energy is the energy of motion, while potential energy is stored energy due to position or configuration. For example, a ball held at height has gravitational potential energy (PE = mgh). When released, potential energy converts to kinetic energy as the ball accelerates downward. The sum of kinetic and potential energy in a closed system remains constant (conservation of mechanical energy).

This calculator uses the classical (Newtonian) kinetic energy formula KE = ½mv², which is accurate for everyday speeds. For speeds approaching the speed of light (≥ ~10% of c, or ~30,000,000 m/s), relativistic effects become significant, and the relativistic kinetic energy formula KE = (γ − 1)mc² should be used instead, where γ = 1/√(1 − v²/c²). For all practical terrestrial applications, the classical formula is perfectly adequate.

Kinetic energy is fundamental to understanding vehicle safety (braking distances increase with the square of speed), sports performance (why faster pitches are harder to hit), renewable energy (wind turbines convert kinetic energy of wind), and engineering design (impact resistance of materials). It also explains why a small increase in driving speed can dramatically increase the severity of a collision.