Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity (KE=½mv²). Find the energy of moving objects and convert between units like joules and calories.
Kinetic Energy
125.0000 J
Kinetic Energy
125.0000 J
Mass
10.0000 kg
Velocity
5.0000 m/s
Momentum
50.0000 kg·m/s
Energy Conversions
Joules: 125.0000 J
Kilojoules: 0.125000 kJ
Calories: 29.8757 cal
Kilocalories: 0.029876 kcal
BTU: 0.118477 BTU
ft·lbf: 92.1951
Energy Reference
- • Walking person (70kg, 1.4m/s): ~69 J
- • Running person (70kg, 5m/s): ~875 J
- • Car (1500kg, 30m/s): ~675,000 J
- • Bullet (0.01kg, 500m/s): ~1,250 J
About This Calculator
Kinetic energy is the energy an object possesses due to its motion. Any moving object—from a rolling ball to a speeding car to a orbiting planet—has kinetic energy. This calculator helps you find the kinetic energy of moving objects and understand the relationship between mass, velocity, and energy.
What is Kinetic Energy? Kinetic energy (KE) is the energy of motion, calculated as half the mass times velocity squared: KE = ½mv². The faster an object moves and the more massive it is, the more kinetic energy it has. The unit of energy is the Joule (J).
The Formula: KE = ½mv²
- KE = Kinetic energy (Joules)
- m = Mass (kilograms)
- v = Velocity (meters per second)
Why Kinetic Energy Matters:
- Understanding crash impacts and safety
- Designing braking systems
- Calculating work and power
- Energy conservation problems
- Engineering and physics applications
This calculator handles kinetic energy calculations and unit conversions. For gravitational energy, see our Potential Energy Calculator. For momentum analysis, see our Momentum Calculator.
How to Use the Kinetic Energy Calculator
- 1Select what you want to calculate: energy, mass, or velocity.
- 2For kinetic energy: Enter mass and velocity.
- 3For mass: Enter kinetic energy and velocity.
- 4For velocity: Enter kinetic energy and mass.
- 5Choose your preferred units for input.
- 6Review the calculated result in SI units.
- 7Check the energy conversions for other units.
- 8Compare with reference values for context.
- 9Note the related momentum calculation.
- 10Apply to real-world problems.
The Kinetic Energy Formula
Understanding energy of motion.
The Basic Formula
KE = ½mv²
Where:
- KE = kinetic energy (Joules, J)
- m = mass (kilograms, kg)
- v = velocity (meters per second, m/s)
Why ½ and v²?
The ½ comes from the work-energy theorem integration. The v² means doubling speed quadruples energy!
Rearranged Forms
For mass: m = 2KE/v² For velocity: v = √(2KE/m)
Example
Car: m = 1500 kg, v = 30 m/s (108 km/h)
KE = ½ × 1500 × 30² KE = ½ × 1500 × 900 KE = 675,000 J (675 kJ)
The Velocity Factor
Since energy ∝ v², small velocity changes have big energy effects:
| Speed | Energy Factor |
|---|---|
| 30 km/h | 1× |
| 60 km/h | 4× |
| 90 km/h | 9× |
| 120 km/h | 16× |
Work-Energy Theorem
Connecting force, distance, and energy.
The Theorem
Work done on an object = Change in kinetic energy
W = ΔKE = KE_final - KE_initial
Calculating Work
W = F × d × cos(θ)
Where θ is the angle between force and motion.
From Rest
If starting from rest (KE_initial = 0): W = KE_final = ½mv²
The work done equals the final kinetic energy.
Example: Acceleration
Car accelerates from 0 to 30 m/s:
- Mass = 1500 kg
- Work needed = ½ × 1500 × 30² = 675,000 J
If this happens over 200 m with constant force: F = W/d = 675,000/200 = 3,375 N
Negative Work
When force opposes motion (like braking):
- Work is negative
- Kinetic energy decreases
- Energy transfers to heat in brakes
Kinetic Energy vs. Momentum
Two related but different quantities.
The Formulas
Kinetic Energy: KE = ½mv² Momentum: p = mv
Key Differences
| Property | Kinetic Energy | Momentum |
|---|---|---|
| Type | Scalar (magnitude only) | Vector (direction matters) |
| Depends on | v² | v |
| Units | Joules (J) | kg·m/s |
| In collisions | May not be conserved | Always conserved |
Relationship
KE = p²/(2m) p = √(2m × KE)
Example
Object: m = 10 kg, v = 5 m/s
Momentum: p = 10 × 5 = 50 kg·m/s Kinetic Energy: KE = ½ × 10 × 25 = 125 J
Check: KE = p²/(2m) = 2500/20 = 125 J ✓
Why Both Matter
- Momentum determines collision outcomes
- Kinetic energy determines damage/deformation
- Same momentum can have different energies
Real-World Examples
Kinetic energy in everyday situations.
Transportation
| Object | Mass | Speed | KE |
|---|---|---|---|
| Walking person | 70 kg | 1.4 m/s | 69 J |
| Running person | 70 kg | 5 m/s | 875 J |
| Bicycle | 85 kg | 8 m/s | 2,720 J |
| Car (city) | 1500 kg | 14 m/s | 147 kJ |
| Car (highway) | 1500 kg | 30 m/s | 675 kJ |
| Truck | 10,000 kg | 25 m/s | 3,125 kJ |
| Train | 500,000 kg | 40 m/s | 400 MJ |
| Airplane | 300,000 kg | 250 m/s | 9,375 MJ |
Sports
Tennis serve (ball): m = 0.057 kg, v = 60 m/s KE = ½ × 0.057 × 3600 = 103 J
Baseball pitch: m = 0.145 kg, v = 45 m/s KE = ½ × 0.145 × 2025 = 147 J
Golf drive: m = 0.046 kg, v = 70 m/s KE = ½ × 0.046 × 4900 = 113 J
Bullets
9mm bullet: m = 0.008 kg, v = 360 m/s KE = ½ × 0.008 × 129,600 = 518 J
This is why bullets are dangerous despite low mass.
Energy Conversions
Converting between energy units.
Common Energy Units
| Unit | Symbol | Joules |
|---|---|---|
| Joule | J | 1 |
| Kilojoule | kJ | 1,000 |
| Calorie | cal | 4.184 |
| Kilocalorie | kcal | 4,184 |
| BTU | BTU | 1,055.06 |
| Kilowatt-hour | kWh | 3,600,000 |
| Foot-pound | ft·lbf | 1.356 |
| Electron-volt | eV | 1.602×10⁻¹⁹ |
Quick Conversions
Joules to Calories: divide by 4.184 Joules to kWh: divide by 3,600,000 Joules to BTU: divide by 1,055
Food Energy Comparison
1 food Calorie = 1 kcal = 4,184 J
A 100 kcal snack = 418,400 J
This could theoretically:
- Lift a 70 kg person 610 meters
- Accelerate a car from 0 to 75 km/h
(In practice, bodies are only ~25% efficient)
Power Context
Energy per time = Power
1 kWh = 3.6 MJ (energy used by 1 kW device for 1 hour)
Rotational Kinetic Energy
Energy of spinning objects.
Rotational Formula
KE_rot = ½Iω²
Where:
- I = moment of inertia (kg·m²)
- ω = angular velocity (rad/s)
Moment of Inertia
Depends on mass distribution:
| Shape | Moment of Inertia |
|---|---|
| Point mass | mr² |
| Solid sphere | (2/5)mr² |
| Hollow sphere | (2/3)mr² |
| Solid cylinder | (1/2)mr² |
| Hollow cylinder | mr² |
| Rod (center) | (1/12)mL² |
Rolling Objects
Rolling = Translation + Rotation
KE_total = ½mv² + ½Iω²
For rolling without slipping: v = rω
Solid sphere: KE = (7/10)mv² Hollow sphere: KE = (5/6)mv² Solid cylinder: KE = (3/4)mv²
Example: Bowling Ball
m = 7 kg, r = 0.11 m, v = 8 m/s
Translational: ½ × 7 × 64 = 224 J Rotational: ½ × (2/5) × 7 × 0.11² × (8/0.11)² = 89.6 J Total: 313.6 J
Pro Tips
- 💡KE = ½mv² — energy scales with velocity squared.
- 💡Double the speed = four times the kinetic energy.
- 💡Kinetic energy is always positive (scalar quantity).
- 💡Work done = change in kinetic energy.
- 💡Same momentum can have different kinetic energies.
- 💡Stopping distance is proportional to speed squared.
- 💡Energy units: 1 J = 1 kg·m²/s².
- 💡Food Calories are actually kilocalories (1 kcal = 4,184 J).
- 💡Rotational KE uses moment of inertia: KE = ½Iω².
- 💡At very high speeds, use relativistic equations.
- 💡In collisions, momentum is always conserved; KE may not be.
- 💡Temperature is average molecular kinetic energy.
Frequently Asked Questions
This comes from the work-energy theorem. Work = force × distance. For constant acceleration, both force (F = ma) and distance (d = ½at²) depend on time, and when combined, the time factors give v² dependency. Physically, it means doubling speed requires four times the work.
