Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity, or solve for speed or mass when energy is known. Useful for motion and impact energy checks.
Kinetic Energy Calculator
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What the kinetic energy calculator does
Anything that moves carries energy because it is moving, and that is its kinetic energy. This calculator works it out from the mass and the speed, and it can run the other way too, solving for the speed that a given energy implies, or the mass.
Below is what kinetic energy means, the equation behind it, why speed matters so much more than mass, and a worked example.
How to use it
- Choose what to find: kinetic energy, mass, or velocity.
- Enter the other two, each with its own unit. Mass ranges from micrograms to the mass of the Earth, and energy can be read in joules, calories, foot-pounds, even tons of TNT.
- Press Calculate for the answer across the energy units, or Reset to clear it.
What kinetic energy is
Kinetic energy is the energy of motion. To get an object moving you have to do work on it, pushing it up to speed, and that work is stored in the motion itself. Bring the object back to rest and it gives that energy back, doing work on whatever stops it. This is the link between energy and force: the kinetic energy an object has is exactly the work needed to bring it from rest to its speed, a statement known as the work-energy theorem.
It explains why a moving thing can do damage. A hammer head swung up to speed carries kinetic energy, and when it stops against a nail, that energy drives the nail in. The same idea connects a car's speed to how hard it hits, and a falling object's speed to the dent it makes.
The equation it solves
Kinetic energy, written KE, depends on the mass m and the speed v:
KE = ½ m v²
Rearranged, the same relationship gives the other two quantities the calculator can find: the speed an energy implies for a given mass, v = √(2·KE ÷ m), and the mass implied by an energy and a speed, m = 2·KE ÷ v².
Why speed counts double
The most important feature of the formula is that the speed is squared while the mass is not. That makes speed the dominant influence by far. Double the mass and you double the kinetic energy, fair enough. But double the speed and the energy goes up four times, since two squared is four. Triple the speed and it is nine times.
This is why a small rise in speed matters so much for safety and impact. A car at 60 km/h carries four times the kinetic energy it had at 30, not twice, which is why the faster crash is so much worse and why braking distances grow so steeply with speed. The same squaring is why a light but fast bullet carries so much energy.
Units and precision
The SI unit of energy is the joule, and the calculator converts your mass to kilograms and speed to metres per second before computing, then shows the result across a wide range of energy units, from joules and kilojoules up to kilowatt-hours, alongside calories, foot-pounds, electronvolts, and tons of TNT for very large energies. Mass and speed each carry their own unit selector. Some results are shown with many digits; the precision lives in the arithmetic, and you can read off whichever unit and rounding suits your need.
A worked example
How much kinetic energy does a 1,000 kg car have at 20 m/s, about 72 km/h?
From the formula, KE = ½ × 1,000 × 20² = ½ × 1,000 × 400 = 200,000 J, or 200 kJ. Now speed it up to 40 m/s and the energy is ½ × 1,000 × 1,600 = 800 kJ, four times as much for twice the speed, the squaring at work.
Questions people ask
What is the formula for kinetic energy?
Kinetic energy equals one-half the mass times the square of the speed, KE = ½mv². Knowing any two of energy, mass, and speed fixes the third.
What are the units of kinetic energy?
The SI unit is the joule (J), the same unit as all energy. One joule is one kilogram-metre squared per second squared.
What happens to kinetic energy if I double the speed?
It quadruples. Because the speed is squared, doubling it multiplies the energy by four, and tripling it multiplies by nine. Mass only scales the energy in direct proportion.
How is kinetic energy different from potential energy?
Kinetic energy is the energy of motion, set by speed. Potential energy is stored energy of position, such as height or a stretched spring. One can convert into the other, as when a falling object trades height for speed.
References
A quick note on where the physics comes from. Kinetic energy as ½mv² and the work-energy theorem that defines it are standard mechanics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The joule and the other SI units follow the US National Institute of Standards and Technology.
- OpenStax, University Physics Volume 1, Section 7.2, Kinetic Energy. https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy
- HyperPhysics, Georgia State University, Kinetic Energy. http://hyperphysics.phy-astr.gsu.edu/hbase/ke.html
- National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811
Bibek Lal Karna is a PhD student and graduate teaching assistant at the University of Mississippi, with deep interests in theoretical and gravitational physics. He is also the founder of NRCC and is strongly engaged in scientific teaching and communication. At Eon Tools, he reviews physics tools.