Resources · Education
Kinetic Energy Formula
Kinetic energy is the energy of motion. Any moving object, whether it is a tennis ball, a car, or a planet, carries kinetic energy. Understanding the kinetic energy formula is a key requirement in physics and engineering. For a fast calculation, use the velocity calculator or the force calculator to solve for motion and force variables in physics equations.
7 min read
What is kinetic energy?
Kinetic energy is the quantitative measurement of energy that an object possesses because it is moving. In classical mechanics, kinetic energy is directly proportional to the mass of the object and to the square of its speed.
An object keeps its kinetic energy unless its speed changes. To slow down or speed up an object, work must be applied.
The kinetic energy formula
The mathematical formula for kinetic energy is:
The formula
KE = ½mv²
The variables
- KE = kinetic energy
- m = mass of the object
- v = velocity (or speed) of the object
Understanding Kinetic Energy Units
To compute kinetic energy correctly, you must use standard International System of Units (SI) values:
- Mass must be in kilograms (kg).
- Velocity must be in meters per second (m/s).
When these units are multiplied in the formula (kg × (m/s)²), the resulting unit is the Joule (J).
1 Joule = 1 kg·m²/s²
Worked Example: Calculating Kinetic Energy
Let's calculate the kinetic energy of a 0.15-kilogram baseball thrown at a speed of 40 meters per second.
- Identify the mass: m = 0.15 kg.
- Identify the velocity: v = 40 m/s.
- Set up the equation: KE = ½ × 0.15 × 40².
- Square the velocity first: 40² = 1600.
- Multiply by the mass: 0.15 × 1600 = 240.
- Multiply by ½: KE = ½ × 240 = 120 J.
The kinetic energy of the baseball is exactly 120 Joules.
Common Kinetic Energy Mistakes
- Forgetting to square the velocity. It is common to calculate ½ × m × v instead of ½ × m × v². Make sure you square the velocity first before multiplying the other factors.
- Mixing up mass and weight. Mass is a measure of the amount of matter in kilograms, whereas weight is a force measured in Newtons (or pounds) due to gravity. If you are given weight in pounds or Newtons, you must convert it to mass (kg) before using the formula.
- Using non-SI units. If you have mass in grams or velocity in kilometers per hour or miles per hour, you must convert them to kilograms and meters per second first, or your result will not be in Joules.
Run the numbers
Explore physics calculators to check your homework and motion dynamics:
Frequently asked questions
Kinetic energy is the energy an object possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
The standard International System (SI) unit for energy, including kinetic energy, is the Joule (J). One Joule is equal to 1 kg·m²/s².
Because velocity is squared in the kinetic energy formula (KE = ½mv²), doubling the velocity increases the kinetic energy by a factor of four (2² = 4).
No. Mass is always positive, and any velocity (whether positive or negative) becomes positive when squared. Therefore, kinetic energy is always zero or positive.
The kinetic energy calculator solves for kinetic energy, mass, or velocity given the other two parameters, automatically performing the unit conversions for speeds and masses.