The kinetic energy formula KE = 1/2 m v squared
What the kinetic energy equation means, how to rearrange it for mass and velocity, and why doubling speed quadruples the energy of motion.
What kinetic energy measures
Kinetic energy is the energy an object has because it is moving. Bring a moving object to rest and that energy has to go somewhere, into brakes heating up, a wall deforming, or sound and light. The formula KE = 1/2 m v^2 ties it to just two things, how heavy the object is and how fast it travels. Because the units are joules, one joule is the energy of a two kilogram mass moving at one metre per second, which this calculator confirms as 1 J.
Reading the equation
The one half is a fixed constant that falls out of the physics, not something you tune. Mass appears once, so doubling the mass doubles the energy. Velocity appears squared, which is the part that surprises people. A car at 20 m/s carries four times the kinetic energy it had at 10 m/s, not twice, which is why stopping distances grow so steeply with speed. Keeping velocity inside the square is the single most important habit when working the formula by hand.
Rearranging for the unknown
When you know the energy and one other quantity, algebra gives you the third. Solving for velocity gives v = sqrt(2 times KE divided by m), and because a square root returns a magnitude the answer is never negative. Solving for mass gives m = 2 times KE divided by v squared, which needs a non zero velocity or the division fails. The calculator picks the right rearrangement automatically based on the value you choose in the Solve for menu.
Worked examples in SI units
Take a 2 kg object at 3 m/s: half of 2 is 1, times 3 squared which is 9, gives 9 J. Reverse it and a 2 kg object with 9 J of energy must be moving at sqrt(9) which is 3 m/s. Scale up to a 1500 kg car at 10 m/s and you get half of 1500, times 100, which is 75000 J or 75 kilojoules. Each of these drops straight into the tool by entering the two known values and reading the highlighted card.