💨 Kinetic Energy Calculator (KE = ½mv²)
Find kinetic energy from mass and speed (KE = ½mv²), or solve for mass or speed.
Kinetic energy KE
100 J
Kinetic energy KE = ½·m·v². Rearranged, v = √(2·KE/m). 🔒 Computed in your browser.
How the kinetic energy calculator (ke = ½mv²) works
Kinetic energy is the energy of motion: KE = ½mv². Enter any two of kinetic energy, mass and speed and the tool solves for the third; solving for speed uses v = √(2·KE/m).
Kinetic energy grows with the square of speed, so doubling speed quadruples the energy, the reason stopping distances rise so steeply with speed.
Frequently asked questions
How do I calculate kinetic energy?
KE = ½mv². A 2 kg object at 10 m/s has KE = ½ × 2 × 10² = 100 J. Enter mass and speed to compute it.
How do I find speed from kinetic energy?
Rearrange to v = √(2·KE/m). This square root is where careless algebra (and chatbots) slip; the tool does it exactly.
Why does kinetic energy depend on speed squared?
Because work done to accelerate scales with v². Doubling speed quadruples KE, a car at 60 mph has four times the energy of the same car at 30 mph.
What are the units of kinetic energy?
Joules (J), with mass in kg and speed in m/s. 1 J = 1 kg·m²/s².
What is the difference between kinetic and potential energy?
Kinetic energy is energy of motion (½mv²); potential energy is stored energy of position (e.g. mgh for gravity). They convert into each other as an object moves.
Worked example: a moving car
A 1200 kg car at 20 m/s has KE = ½ × 1200 × 20² = 240,000 J = 240 kJ. Doubling the speed to 40 m/s quadruples it to 960 kJ.
How does kinetic energy relate to stopping distance?
The brakes must do work equal to the kinetic energy to stop the car. Because KE scales with v², stopping distance rises with the square of speed, a car at twice the speed needs roughly four times the distance to stop.
How does kinetic energy relate to momentum?
Both use mass and velocity, and they connect through KE = p²/(2m), where p = mv is the momentum. Momentum is a vector conserved in every collision; kinetic energy is a scalar conserved only in elastic ones.
Does kinetic energy depend on the reference frame?
Yes, speed is measured relative to an observer, so KE differs between frames. A seated passenger has zero KE in the train’s frame but a large KE in the ground frame. Pick one consistent frame for a problem.