Kinetic Energy Calculator
Find the kinetic energy of any moving object. Enter the mass and velocity, or work backwards from energy to find speed or mass.
KE = ½ × m × v²
About Kinetic Energy:
Kinetic energy is the energy of motion. An object's kinetic energy depends on both its mass and the square of its velocity. Doubling velocity quadruples the kinetic energy.
How the Kinetic Energy Calculator Works
Select what you want to calculate: kinetic energy, mass, or velocity. Enter the known values in their respective fields. The calculator supports various units for mass (kg, g, lb) and velocity (m/s, km/h, mph, knots).
The calculator applies the classical kinetic energy formula: KE = ½mv², where m is mass and v is velocity. For relativistic speeds (approaching light speed), the relativistic formula is available.
Results display in joules with alternative units (calories, kWh, electron-volts) for context. The calculation steps show the formula substitution. A comparison shows equivalent energies (like TNT or food calories) for perspective.
When You'd Actually Use This
Vehicle crash analysis
Calculate energy in collisions. A car's kinetic energy must be dissipated in a crash. Higher speed means dramatically more energy (v² relationship).
Ballistics calculations
Determine projectile energy. Bullet kinetic energy affects penetration and stopping power. Hunters and ballisticians compare cartridge energies.
Sports performance analysis
Analyze ball or athlete energy. A baseball's kinetic energy affects how far it travels. Sprinters' kinetic energy relates to their speed and mass.
Wind turbine power estimation
Calculate kinetic energy in moving air. Wind power is proportional to air mass flow rate and v². Doubling wind speed octuples available power.
Physics problem solving
Solve mechanics problems involving energy. Use kinetic energy with potential energy for conservation of energy calculations.
Flywheel energy storage
Design rotating energy storage. Flywheels store kinetic energy. Energy capacity depends on moment of inertia and rotational speed squared.
What to Know Before Using
Kinetic energy scales with velocity squared.Double the speed, quadruple the energy. This is why high-speed crashes are so much more dangerous than low-speed ones.
KE is always positive.Mass is positive, v² is positive. Direction doesn't matter - a car has the same KE traveling east or west at the same speed.
Classical formula works for everyday speeds.Below about 10% of light speed, classical KE = ½mv² is accurate. For relativistic speeds, use KE = (γ - 1)mc².
Work-energy theorem connects force and KE.Net work done on an object equals its change in kinetic energy. This is often easier than using F = ma for complex problems.
Pro tip: Kinetic energy is frame-dependent. A ball has zero KE in its own frame, but significant KE in the frame of someone it's flying toward. Always specify your reference frame.
Common Questions
Why is there a ½ in the formula?
It comes from integrating F = ma over distance. Work = ∫F·dx = ∫ma·dx = ½mv². The ½ is a mathematical consequence of the derivation.
What's the unit of kinetic energy?
Joules (J) in SI. 1 J = 1 kg⋅m²/s² = 1 N⋅m. Other units: calories, BTU, kWh, electron-volts. The calculator shows conversions.
Can kinetic energy be negative?
No. Mass is always positive, and velocity squared is always positive. Kinetic energy is a scalar quantity that's always ≥ 0.
How does KE relate to momentum?
Momentum p = mv, KE = ½mv². So KE = p²/(2m). Momentum is a vector, KE is a scalar. Both are conserved in elastic collisions.
What about rotational kinetic energy?
Rotating objects have KE_rot = ½Iω², where I is moment of inertia and ω is angular velocity. Analogous to linear KE with mass→I, v→ω.
Why does speed affect KE more than mass?
KE is linear in mass but quadratic in velocity. Doubling mass doubles KE. Doubling speed quadruples KE. Speed is more "expensive" energetically.
What happens to KE when an object stops?
KE converts to other forms: heat (friction), sound, deformation (crashes), or potential energy (climbing a hill). Energy is conserved, just transformed.
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