Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity, or find velocity from kinetic energy. Enter any two values — get results in Joules, kJ, and other energy units.
kg
m/s
Enter your values above to see the results.
Tips & Notes
- ✓Kinetic energy scales with the square of velocity — doubling speed quadruples KE. A car at 60 mph has 4× the kinetic energy of the same car at 30 mph, which is why highway crashes are so much more severe than low-speed impacts.
- ✓The SI unit is the Joule (J = kg·m²/s²). For large energies: 1 kJ = 1,000 J. A 1,500 kg car at 27.8 m/s (100 km/h) has KE = ½ × 1,500 × 27.8² = 579,510 J ≈ 580 kJ.
- ✓Stopping distance is proportional to KE — all braking force must do work equal to the initial kinetic energy. Double the speed → 4× the kinetic energy → 4× the stopping distance (assuming constant braking force).
- ✓In collisions, total kinetic energy is conserved only in perfectly elastic collisions. Most real collisions are inelastic — some KE converts to heat, sound, and deformation. Momentum is always conserved regardless.
- ✓The work-energy theorem states: Net work done = Change in KE. If a 500 N force acts over 10 m: Work = 5,000 J. If the object started from rest, it gains 5,000 J of KE.
Common Mistakes
- ✗Forgetting the ½ factor — KE = ½mv², not mv². A common error gives twice the correct answer. The ½ comes from integrating force over distance during constant acceleration.
- ✗Using mass in grams or pounds without converting to kilograms first — KE in Joules requires mass in kg and velocity in m/s. A 2,000 lb car = 907 kg; 60 mph = 26.8 m/s.
- ✗Squaring only the number but forgetting to square the unit — (m/s)² appears in the dimensional analysis. If velocity is in km/h, convert to m/s first: 1 km/h = 0.2778 m/s.
- ✗Treating kinetic energy as a vector — KE is a scalar (no direction). Two objects moving in opposite directions at the same speed have the same KE, even though their momenta cancel.
- ✗Confusing KE with momentum (p = mv) — momentum is proportional to velocity (not v²), is a vector, and is conserved in all collisions. KE is proportional to v², is scalar, and is only conserved in elastic collisions.
Kinetic Energy Calculator Overview
Kinetic energy is the energy of motion — it quantifies how much work an object can do by virtue of its speed and mass. The v² dependence makes it one of the most important safety-critical quantities in transportation, structural engineering, and impact mechanics.
Kinetic energy formula:
KE = ½ × m × v² | Units: Joules (J) = kg·m²/s²
EX: 1,500 kg car at 100 km/h (27.78 m/s) → KE = ½ × 1,500 × 27.78² = ½ × 1,500 × 771.7 = 578,775 J ≈ 579 kJ. At 50 km/h (13.89 m/s) → KE = ½ × 1,500 × 193 = 144,694 J ≈ 145 kJ (exactly ¼ the KE at 100 km/h)Work-energy theorem — force, distance, and KE:
Work = F × d = ΔKE | Stopping distance: d = KE / F_braking = mv² / (2F)
EX: Car 1,500 kg at 25 m/s, braking force 9,000 N → KE = ½ × 1,500 × 625 = 468,750 J → Stopping distance = 468,750 / 9,000 = 52.1 m. At 50 m/s (double speed) → KE = 1,875,000 J → d = 208.3 m (4× longer)Kinetic energy by scenario — reference:
| Object | Mass | Speed | Kinetic Energy |
|---|---|---|---|
| Walking person | 70 kg | 1.4 m/s (5 km/h) | 69 J |
| Cyclist | 80 kg total | 8 m/s (29 km/h) | 2,560 J |
| Car (city speed) | 1,500 kg | 13.9 m/s (50 km/h) | 144,675 J |
| Car (highway) | 1,500 kg | 27.8 m/s (100 km/h) | 578,700 J |
| Truck (highway) | 40,000 kg | 27.8 m/s | 15,448,800 J |
| 9mm bullet | 0.008 kg | 370 m/s | 548 J |
| Boeing 747 (cruise) | 300,000 kg | 250 m/s | 9,375,000,000 J = 9.375 GJ |
| Unit | Conversion from J | Example (579 kJ car) |
|---|---|---|
| Kilojoule (kJ) | ÷ 1,000 | 579 kJ |
| Watt-hour (Wh) | ÷ 3,600 | 160.8 Wh |
| BTU | ÷ 1,055 | 548.8 BTU |
| Foot-pound (ft·lb) | × 0.7376 | 427,160 ft·lb |
| Calorie (kcal) | ÷ 4,184 | 138.4 kcal |
Frequently Asked Questions
Use the formula KE = ½ × m × v², where m is mass in kilograms and v is velocity in meters per second. The result is in Joules. Example: a 70 kg runner at 8 m/s → KE = ½ × 70 × 8² = ½ × 70 × 64 = 2,240 J. A 1,200 kg car at 30 m/s (108 km/h) → KE = ½ × 1,200 × 30² = ½ × 1,200 × 900 = 540,000 J = 540 kJ. The v² relationship means velocity has a disproportionate impact on kinetic energy.
The v² relationship comes from the work-energy theorem. A constant force F accelerates a mass m from rest. Using kinematics: d = v²/(2a) and F = ma, so Work = F × d = ma × v²/(2a) = ½mv². Physically, going twice as fast requires stopping over four times the distance (at the same braking force), means four times the crash impact energy, and requires four times the energy to reach that speed from rest. This nonlinear relationship is why speed limits matter disproportionately for safety.
Stopping distance is directly proportional to kinetic energy. If braking force F is constant, Work = F × d must equal KE = ½mv². So d = mv²/(2F) = KE/F. At 30 mph (13.4 m/s), a 1,500 kg car with 8,000 N braking force: KE = 134,670 J, d = 16.8 m. At 60 mph (26.8 m/s): KE = 538,680 J, d = 67.3 m — exactly 4× farther despite only 2× the speed. This is why the Highway Code warns that stopping distance quadruples when speed doubles.
From Joules: 1 kJ = 1,000 J; 1 MJ = 1,000,000 J; 1 Wh = 3,600 J; 1 kWh = 3,600,000 J; 1 BTU = 1,055 J; 1 foot-pound = 1.356 J; 1 calorie = 4.184 J. Example: a 1,500 kg car at 27.8 m/s has KE = 579,510 J = 579.5 kJ = 0.161 kWh = 549 BTU. In EV battery terms: a 50 kWh battery stores 50,000 Wh = 180,000,000 J — about 311 times the kinetic energy of a car at highway speed.
Kinetic energy (KE = ½mv²) and momentum (p = mv) both involve mass and velocity but differ in key ways. KE is scalar (no direction), proportional to v², measured in Joules. Momentum is vector (has direction), proportional to v, measured in kg·m/s. In collisions: momentum is always conserved; KE is only conserved in elastic collisions. Practical difference: two 1,000 kg cars each moving at 20 m/s in opposite directions have the same KE (400 kJ each) but their momenta cancel (net = 0). Understanding which quantity applies changes the analysis completely.
Kinetic energy calculations appear throughout engineering. Flywheel energy storage: a 100 kg flywheel rotating at 3,000 RPM (314 rad/s) stores KE = ½Iω² where I is moment of inertia. Vehicle crash testing: regulatory standards require cars to absorb specific KE amounts (frontal crash at 56 km/h into a rigid barrier = ½ × 1,500 × 15.6² ≈ 182 kJ). Impact mechanics: pile driver energy = ½mv² determines penetration depth. Ballistics: bullet energy = ½mv² determines armor penetration. Hydroelectric power: water KE converts to electrical energy via turbines.