Kinetic Energy Calculator
KE = ½mv²
Answer
Kinetic energy questions trip people up for a predictable reason: you have mass in kilograms, speed in miles per hour, and the answer needs to be in joules—and somewhere in the middle you must remember to square the velocity and divide by two. I have graded stacks of homework where the algebra was right but the unit conversion was not. This calculator takes that scratchpad work off your plate: pick what you are solving for, enter two known values in whatever units you actually measured, and get the third without redoing KE = ½mv² by hand.
How to Use This Kinetic Energy Calculator
- Choose a calculation mode. Solve for kinetic energy KE, mass m, or velocity v. The output field grays out and shows (calculated) while you enter the other two values.
- Enter your known values. Pick energy, mass, and velocity units from each row’s dropdown. Mixed units on one run are fine—pounds with m/s, or kg with mph—the tool converts internally before the formula runs.
- Set significant figures. Leave auto for full precision, or choose 3–9 sig figs to match a lab report or textbook problem.
- Press Calculate. The missing value appears in the answer panel and in the calculated field, with the rearranged formula shown underneath.
To get started on a typical worksheet row: leave the mode on Calculate KE | Given m, v, type mass and speed, pick units that match the problem statement, and read joules in the answer panel. If the question instead gives energy and asks for speed, switch to Calculate v | Given KE, m—the square root step is handled automatically so you do not have to retype √(2KE / m) into a separate tool.
Kinetic Energy Formulas and Practical Applications
Anything moving carries kinetic energy—think of a baseball leaving the pitcher’s hand or a car rolling down a hill. The heavier it is and the faster it moves, the more energy it has. Speed matters twice as much as you might guess, because velocity is squared in the formula.
KE = ½mv²
KE is kinetic energy (joules by default), m is mass, and v is speed. Rearrange when you know different pairs: m = 2KE / v² and v = √(2KE / m).
Classroom staple: m = 10 kg and v = 5 m/s gives KE = 125 J—half of ten times twenty-five. Double the speed to 10 m/s without changing mass and energy quadruples to 500 J. That squared relationship is why highway crash severity rises so sharply with speed.
Where this shows up in real work
- Intro mechanics homework: find speed from known energy and mass, or energy from mass and velocity.
- Rough safety estimates comparing vehicle kinetic energy at different speeds (same mass, higher v).
- Lab write-ups where measured mass and photogate velocity must become joules for an energy balance.
- Roller-coaster and sports problems where speed at the bottom follows from GPE lost on the way down.
Pair this page with the Gravitational Potential Energy Calculator when a problem drops an object from height h: compute GPE at the top, set that equal to KE at the bottom, then solve for v here.
Standard Units and Conversion Tables
Kinetic energy units
| Unit | Symbol | Notes |
|---|---|---|
| Joule | J | SI default |
| Kilojoule | kJ | 1 kJ = 1,000 J |
| Electronvolt | eV | Common in atomic-scale problems |
| Watt-hour | Wh | 1 Wh = 3,600 J |
| Foot-pound force | ft·lbf | US mechanical energy specs |
| Ton TNT | t TNT | Large energy comparisons; 1 t TNT ≈ 4.184 GJ |
Mass units
Mass accepts kg, g, lb, oz, grains (gr), and troy tons. For shipping-weight confusion, remember kinetic energy uses mass, not weight—convert pounds of mass correctly if your scale reading is actually weight in a gravity field.
Velocity units
Velocity accepts m/s, km/h, km/s, mi/h, ft/s, ft/h, cm/s, in/s, and m/h. Road speeds often arrive in mph; lab carts in m/s—pick the unit that matches your measurement and let the calculator normalize internally. When solving for v, the answer returns in whichever velocity unit you selected on the velocity row, even if you entered energy in kilojoules and mass in grams.
Relativistic speeds
This tool uses classical KE = ½mv². That holds for everyday speeds far below the speed of light. For particles or scenarios approaching relativistic speeds, use specialized relativistic energy relations instead—see our E = mc² Calculator for mass–energy equivalence at high energy.
Frequently Asked Questions
What is the kinetic energy equation?
KE = ½mv²—half the mass times velocity squared. Enter any two variables to find the third.
Why is velocity squared?
In classical mechanics, the work done to accelerate an object from rest depends on the square of its final speed. Doubling v quadruples KE at the same mass.
Which variable can this calculator solve for?
Pick Calculate KE, Calculate m, or Calculate v from the dropdown. Enter the other two known values and press Calculate.
Can I mix unit systems?
Yes. Select units per field; the tool converts to SI before solving, then displays the answer in the unit you chose for the calculated variable.
What if mass or velocity is zero?
You cannot divide by zero. Solving for mass requires non-zero velocity; solving for velocity requires non-zero mass. Kinetic energy must also be non-negative when solving for speed.
For height-based stored energy, use the Gravitational Potential Energy Calculator. For contact forces, try the Friction Calculator or Force Calculator. Browse all physics calculators on RapidRatio.
Disclaimer. Informational only—not professional engineering or laboratory advice. Verify critical results with qualified analysis and calibrated measurements.