Kinetic Energy Calculator
Solve KE = ½mv² for energy, mass or speed, in joules, kilojoules or calories.
What is Kinetic Energy?
Kinetic energy is the energy of motion: KE = ½mv². Because velocity is squared, speed matters far more than mass — doubling the mass doubles the energy, but doubling the speed quadruples it, which is why stopping distances grow so steeply with speed.
How it works
The formula is rearranged for whichever field is blank, including for speed, which needs a square root. Units for mass and speed are converted to kilograms and metres per second first, and the energy can be displayed in joules, kilojoules, calories or kilowatt-hours, since the same number appears in very different guises across physics and nutrition.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
What is the kinetic energy of a 2 kg mass at 3 m/s?
9 J. KE = ½ × 2 × 3² = ½ × 2 × 9 — load the example and the substituted formula appears underneath the answer.
Why is velocity squared?
Because the work done to accelerate an object is force times distance, and accelerating to twice the speed takes four times the distance at the same force. The square falls out of that relationship rather than being an extra assumption.
How does kinetic energy relate to work?
The work-energy theorem: the net work done on an object equals its change in kinetic energy. Braking a car from 30 m/s to rest removes the same energy the engine had to supply.