Energy of motion
What is kinetic energy?
Kinetic energy is the energy an object has because it is moving. It depends on the object's mass and on the square of its speed.
Formula
Kinetic energy formula
Kinetic energyKE = ½mv²
- KE is kinetic energy in joules.
- m is mass in kilograms.
- v is speed in meters per second.
Worked example
A 10 kg object moves at 4 m/s
- Write the formula: KE = ½mv².
- Substitute the values: KE = ½ × 10 × 4².
- Calculate the energy: KE = 80 J.
Rearranged equations
Solve for mass or speed
Mass
m = 2KE ÷ v²
Divide twice the kinetic energy by the square of a non-zero speed.
Speed
v = √(2KE ÷ m)
Divide twice the kinetic energy by a positive mass, then take the square root.
Speed squared
Why speed has a large effect
Speed is squared in the kinetic energy formula. Doubling speed therefore makes kinetic energy four times larger when mass stays constant.
Stationary objects
When kinetic energy equals zero
An object with zero speed has zero kinetic energy. The object may still possess other forms of energy, but its kinetic energy is zero while it is stationary.
Units
Standard SI units
Use kilograms for mass and meters per second for speed. Convert grams, kilometers per hour, and other units before entering values.
One joule1 J = 1 kg·m²/s²
Calculation checks
Important input requirements
- Mass must be greater than zero.
- Speed cannot be negative.
- Kinetic energy cannot be negative.
- Speed must be greater than zero when calculating mass.
- The calculator does not automatically convert units.
Related tools
Continue analyzing motion
Use the Momentum Calculator to analyze mass and velocity using p = m × v.
Use the Force Calculator for Newton's second law problems, and use the Acceleration Calculator to calculate velocity change over time.
Questions and answers
Kinetic energy calculator FAQ
What formula does the kinetic energy calculator use?
It uses the classical kinetic energy formula: KE = ½mv², where m is mass and v is speed.
What is the SI unit of kinetic energy?
The SI unit of kinetic energy is the joule, written as J.
Can kinetic energy be negative?
No. Classical kinetic energy cannot be negative because mass is positive and speed is squared.
Can speed be negative?
No. Speed is a magnitude and must be zero or greater. Direction is represented by velocity, not speed.