Kinetic Energy Calculator
Compute kinetic energy from mass and speed, or solve for mass or velocity using the classical formula \( KE = \tfrac12 m v^2 \). Supports SI and imperial units plus convenient energy conversions.
Kinetic Energy Calculator
What is kinetic energy?
Kinetic energy is the energy an object has because it is moving. In classical mechanics, the translational kinetic energy of a point mass is
Kinetic energy formula
\( KE = \frac{1}{2} m v^2 \)
- \( KE \) – kinetic energy (joules, J)
- \( m \) – mass of the object (kilograms, kg)
- \( v \) – speed of the object (meters per second, m/s)
The faster an object moves, the more kinetic energy it has. Because speed is squared, doubling the speed increases kinetic energy by a factor of four.
Rearranging the kinetic energy formula
You can solve the same equation for any of the three quantities:
Solve for velocity (speed)
\( v = \sqrt{\dfrac{2\,KE}{m}} \)
Solve for mass
\( m = \dfrac{2\,KE}{v^2} \)
Worked examples
Example 1 – Running person
A person of mass \( m = 70\,\text{kg} \) runs at \( v = 5\,\text{m/s} \). Their kinetic energy is
\( KE = \tfrac12 m v^2 = \tfrac12 \times 70 \times 5^2 = 0.5 \times 70 \times 25 = 875\,\text{J} \)
That is about \( 0.875\,\text{kJ} \), or roughly \( 0.21\,\text{kcal} \).
Example 2 – Car at highway speed
A car of mass \( 1{,}200\,\text{kg} \) travels at \( 90\,\text{km/h} \). First convert to m/s:
\( 90\,\text{km/h} = 25\,\text{m/s} \)
\( KE = \tfrac12 \times 1{,}200 \times 25^2 = 600 \times 625 = 375{,}000\,\text{J} = 375\,\text{kJ} \)
Units used in this calculator
- Mass: kg, g, metric tonnes, pounds (lb), slugs
- Velocity: m/s, km/h, mph, ft/s, knots
- Energy: J, kJ, MJ, cal, kcal, kWh, eV
All inputs are converted internally to SI units (kg, m/s, J) to keep the physics consistent.
Common questions
Can kinetic energy be negative?
No. Mass is non‑negative and speed squared is always non‑negative, so \( KE = \tfrac12 m v^2 \ge 0 \). A negative result usually means a sign or unit error.
What about rotational kinetic energy?
This tool focuses on translational kinetic energy. For rotating bodies, the rotational kinetic energy is
\( KE_\text{rot} = \tfrac12 I \omega^2 \)
where \( I \) is the moment of inertia and \( \omega \) is the angular speed in rad/s.
Kinetic Energy FAQ
What is the formula for kinetic energy?
The translational kinetic energy of an object is \( KE = \tfrac12 m v^2 \), where \( m \) is mass in kilograms and \( v \) is speed in meters per second. The result is in joules.
What units does this calculator support?
You can enter mass in kg, g, tonnes, lb, or slugs and velocity in m/s, km/h, mph, ft/s, or knots. The calculator converts everything to SI units and outputs energy in your chosen unit (J, kJ, MJ, cal, kcal, kWh, or eV).
How do I calculate speed from kinetic energy?
Rearrange the formula to \( v = \sqrt{2 KE / m} \). In the calculator, choose “Solve for velocity (v)”, enter mass and kinetic energy, and it will compute the speed for you.
How is kinetic energy different from momentum?
Momentum is \( p = m v \) and is a vector (direction matters). Kinetic energy is \( KE = \tfrac12 m v^2 \) and is a scalar (no direction). Two objects with equal and opposite velocities can have total momentum zero but still have positive total kinetic energy.
Does this calculator handle relativistic speeds?
No. This tool uses the classical kinetic energy formula, which is accurate when speeds are much less than the speed of light. For relativistic speeds, the correct expression is \( KE = (\gamma - 1) m c^2 \), where \( \gamma \) is the Lorentz factor.