Physics calculator
Kinetic Energy Calculator
Calculate the kinetic energy of a moving object in joules from its mass and velocity, in metric or imperial units.
Kinetic energy
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What is kinetic energy?
Kinetic energy is the energy an object has because of its motion. An object with more mass or a higher velocity has more kinetic energy.
Kinetic energy formula
KE is kinetic energy in joules, m is mass in kilograms, and v is velocity in meters per second.
Example
Suppose an object has a mass of 10 kilograms and is moving at 5 meters per second.
The object has 125 joules of kinetic energy.
Why does velocity matter so much?
Velocity is squared in the kinetic energy formula. That means doubling velocity does not merely double kinetic energy — it increases kinetic energy by a factor of four.
Frequently asked questions
What unit is kinetic energy measured in?
The SI unit of kinetic energy is the joule, abbreviated J.
Does Calquo convert pounds to kilograms?
Yes. If you enter mass in pounds, Calquo converts the value to kilograms before calculating kinetic energy.
Does Calquo convert mph to m/s?
Yes. Miles per hour and kilometers per hour are converted to meters per second automatically.
What happens to kinetic energy if velocity doubles?
Kinetic energy becomes four times greater because velocity is squared in the formula.
What happens to kinetic energy if mass doubles?
Kinetic energy doubles because mass appears to the first power in the equation.
How the calculator works
Enter the object's mass and its velocity and the calculator returns its kinetic energy in joules. Mass can be typed in kilograms, grams, or pounds, and velocity in meters per second, kilometers per hour, or miles per hour. Before anything is squared, both values are converted to SI units: pounds are multiplied by 0.45359237 to get kilograms, km/h is divided by 3.6, and mph is multiplied by 0.44704 to get m/s.
The converted mass and velocity are shown under the result so you can check the intermediate numbers or copy them into a written solution. The result is rounded to four decimal places. Both inputs must be zero or greater; because velocity is squared, the direction of travel makes no difference, so only the speed matters.
Kinetic energy formula
KE is kinetic energy in joules, m is mass in kilograms, and v is velocity in meters per second. A joule is one kilogram meter squared per second squared (kg·m²/s²), which is exactly what the formula produces when the inputs are in SI units. The two rearranged forms let you find speed from energy or mass from energy and speed.
Worked example: a 1,500 kg car traveling at 60 mph. First convert the speed: 60 × 0.44704 = 26.8224 m/s. Square it: 26.8224² = 719.44. Then KE = 0.5 × 1,500 × 719.44 = 539,581 J, or about 540 kJ. A simpler case: a 2 kg object moving at 3 m/s has KE = 0.5 × 2 × 3² = 0.5 × 2 × 9 = 9 J.
Why speed matters more than mass
Mass appears in the formula to the first power, so doubling the mass doubles the kinetic energy. Velocity is squared, so doubling the speed quadruples the energy and tripling it multiplies the energy by nine. The same 1,500 kg car at 30 mph has only 134,895 J, a quarter of its energy at 60 mph.
This is why braking distances grow so quickly with speed and why a small increase in velocity has an outsized effect in collisions, sports, and ballistics. The energy has to go somewhere when an object stops, and the work needed to stop it is equal to its kinetic energy.
Units and typical values
Kinetic energy is always reported in joules here, but it helps to know how joules relate to other energy units and what size of number to expect:
- 1 joule (J) = 1 kg·m²/s² = 1 newton meter
- 1 kilojoule (kJ) = 1,000 J; 1 megajoule (MJ) = 1,000,000 J
- 1 calorie = 4.184 J; 1 food Calorie (kcal) = 4,184 J
- 1 kilowatt-hour (kWh) = 3.6 MJ
- 1 foot-pound (ft·lbf) = 1.356 J
- A 145 g baseball at 40 m/s (about 90 mph): 0.5 × 0.145 × 40² = 116 J
- A 70 kg person walking at 1.4 m/s: 0.5 × 70 × 1.4² = 68.6 J
- An 8 g bullet at 400 m/s: 0.5 × 0.008 × 400² = 640 J
What the formula does and does not cover
This is the classical, or Newtonian, kinetic energy of straight-line motion. It is accurate for anything you will meet in everyday life, engineering, and introductory physics. It starts to break down only at speeds approaching the speed of light, where the relativistic formula is needed; below about 1% of light speed (3,000 km/s) the difference is negligible.
The formula also covers translational motion only. A spinning wheel or a rolling ball has additional rotational kinetic energy equal to ½Iω², where I is the moment of inertia and ω the angular velocity. Kinetic energy can never be negative, and it depends on the observer's frame of reference: a passenger sitting in a moving train has zero kinetic energy relative to the train but a great deal relative to the ground.
A common error is mixing units. Entering grams with m/s, or kilograms with mph, without converting gives a number that is not in joules and can be off by a factor of a thousand or more. Pick the matching unit in each dropdown and the calculator handles the conversion.
Frequently asked questions
What is the formula for kinetic energy?
Kinetic energy equals one half times mass times velocity squared: KE = ½mv². With mass in kilograms and velocity in meters per second, the answer is in joules.
What is the kinetic energy of a 10 kg object moving at 5 m/s?
KE = 0.5 × 10 × 5² = 0.5 × 10 × 25 = 125 joules.
What happens to kinetic energy when speed doubles?
It becomes four times larger, because velocity is squared in the formula. Doubling the mass, by contrast, only doubles the kinetic energy.
Can kinetic energy be negative?
No. Mass is always positive and velocity squared is never negative, so kinetic energy is zero for an object at rest and positive for anything that is moving, regardless of direction.
Do I have to use kilograms and meters per second?
To get joules directly, yes. The calculator accepts grams, pounds, km/h, and mph and converts them to kg and m/s for you; 1 lb = 0.45359237 kg and 1 mph = 0.44704 m/s.
How do you find velocity from kinetic energy?
Rearrange the formula to v = √(2 × KE ÷ m). An object with 200 J of kinetic energy and a mass of 4 kg is moving at √(400 ÷ 4) = √100 = 10 m/s.