How to calculate kinetic energy, mass and velocity
Kinetic energy is the energy an object has because of its motion. It is tied to mass and speed by one simple equation: KE = ½ × m × v². Here KE is the kinetic energy, measured in joules (J); m is the object's mass in kilograms (kg); and v is its speed in metres per second (m/s). Because the three are linked by a single relationship, knowing any two of them lets you rearrange the formula and find the third.
To solve for one quantity, rearrange the equation: KE = ½mv² for energy, m = 2 × KE / v² for mass, and v = √(2 × KE / m) for velocity. This calculator detects which field you leave blank and applies the matching form automatically, guarding against division by zero and against negative values under the square root.
Units do not have to be SI. Energy may be entered in joules (J), kilojoules (kJ) or calories (cal); mass in kilograms (kg), grams (g) or pounds (lb); and velocity in m/s, km/h, mph or ft/s. The calculator converts every input to joules, kilograms and m/s, computes with KE = ½mv², then converts the answer back into the unit you selected. Because velocity is squared, doubling the speed quadruples the kinetic energy.
Common units and SI conversions
| Quantity | Unit | SI conversion |
|---|---|---|
| Energy (KE) | kJ | 1 kJ = 1,000 J |
| Energy (KE) | cal | 1 cal ≈ 4.184 J |
| Mass (m) | g | 1 g = 0.001 kg |
| Mass (m) | lb | 1 lb ≈ 0.45359237 kg |
| Velocity (v) | km/h | 1 km/h ≈ 0.2777778 m/s |
| Velocity (v) | mph | 1 mph ≈ 0.44704 m/s |
| Velocity (v) | ft/s | 1 ft/s = 0.3048 m/s |
Reference note: this is a neutral physics math tool. KE = ½mv² gives the translational kinetic energy of an object of mass m moving at speed v, valid at everyday (non-relativistic) speeds. The calorie used here is the thermochemical calorie, 1 cal = 4.184 J. The pound-mass conversion uses the international avoirdupois pound.
Frequently asked questions
- What is the kinetic energy formula?
- The kinetic energy formula is KE = ½ × m × v², where KE is the energy in joules, m is the mass in kilograms and v is the speed in m/s. Rearranged, mass is m = 2 × KE / v² and velocity is v = √(2 × KE / m), so any two of the three quantities give the third.
- What is a joule?
- A joule (J) is the SI unit of energy. One joule is the energy when a force of one newton acts over one metre, so 1 J = 1 kg·m²/s². A 2 kg object moving at 1 m/s carries 1 joule, and a kilojoule (kJ) is 1,000 joules.
- How do I find velocity from kinetic energy?
- Rearrange KE = ½mv² to v = √(2 × KE / m): multiply the energy by two, divide by the mass, then take the square root. For example, 9 J on a 2 kg mass gives v = √(2 × 9 / 2) = √9 = 3 m/s. Enter the energy and mass, leave velocity blank, and the calculator solves for it.
- Does doubling speed quadruple kinetic energy?
- Yes. Kinetic energy is proportional to the square of speed, so doubling the velocity multiplies the energy by four and tripling it multiplies the energy by nine. For a fixed mass, going from 10 m/s to 20 m/s raises kinetic energy by a factor of 400/100 = 4.
- What is the difference between mass and weight here?
- Kinetic energy depends on mass, not weight. Mass is the amount of matter in an object, in kilograms, and does not change with location. Weight is the force of gravity on that mass, in newtons. KE = ½mv² uses mass in kilograms, so enter mass values, not weight.
- What units does this calculator use?
- Enter energy in joules (J), kilojoules (kJ) or calories (cal); mass in kilograms (kg), grams (g) or pounds (lb); and velocity in m/s, km/h, mph or ft/s. The tool converts inputs to SI units, computes with KE = ½mv², then shows the answer in your chosen unit.