Kinetic Energy Calculator
Calculate kinetic energy KE = ½mv² and momentum p = mv. Enter mass (kg) and speed (m/s) for instant results in Joules.
How to use this tool
- Enter mass and speed in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your kinetic energy and the full breakdown beneath it.
Kinetic energy is the energy of motion: KE = ½mv², where m is mass in kilograms and v is speed in metres per second. The result is in Joules (J). Momentum is p = mv (kg·m/s).
Formula
Kinetic Energy: KE = ½ × m × v2
Momentum: p = m × v
Where m = mass (kg), v = speed (m/s), KE in Joules, p in kg·m/s.
How it works
This calculator applies the classical (Newtonian) kinetic energy formula KE = ½mv² and the linear momentum formula p = mv. Both formulas are standard results from Newtonian mechanics and are accurate for speeds well below the speed of light. At relativistic speeds (above roughly 10% of the speed of light), the Lorentz factor must be included and these classical formulas underestimate energy significantly.
Worked example
- Mass m = 2 kg, speed v = 3 m/s.
- Kinetic energy KE = ½ × 2 × 3² = ½ × 2 × 9 = 9 J.
- Momentum p = 2 × 3 = 6 kg·m/s.
Kinetic energy: 9.0 J; Momentum: 6.0 kg·m/s.
Common mistakes to avoid
- Squaring only the number and not the unit -- entering speed in km/h instead of m/s understates KE by a factor of roughly 7.7.
- Using weight (force in Newtons) instead of mass (kg) for m, inflating the result by a factor of 9.81.
- Overlooking that KE scales with v squared: doubling speed quadruples KE, so a 10% speed increase gives about 21% more energy.
Key terms
- Kinetic energy (KE)
- The energy an object possesses due to its motion, equal to ½mv². Measured in joules (J). Doubling the speed quadruples the kinetic energy.
- Momentum (p)
- A vector quantity equal to mass × velocity. Measured in kg·m/s. Momentum is conserved in collisions when no external forces act.
- Mass (m)
- The quantity of matter in an object, measured in kilograms. Distinct from weight, which is mass multiplied by gravitational acceleration.
- Joule (J)
- The SI unit of energy. One joule equals the work done by a force of one newton acting through one metre.
- Newtonian mechanics
- The branch of physics based on Newton's laws of motion, valid for objects moving much slower than the speed of light. The formulas KE = ½mv² and p = mv are classical Newtonian results.
Frequently asked questions
- Why does speed have a larger effect than mass?
- Because speed is squared. Doubling mass doubles KE; doubling speed quadruples it.
- How do I convert km/h to m/s?
- Divide by 3.6. For example, 90 km/h = 25 m/s.