Kinetic Energy Calculator
This kinetic energy calculator uses the formula KE = ½mv² to solve for kinetic energy (joules), mass (kg), or velocity (m/s). Choose what you want to find, enter the two known values, and get an instant result with energy unit conversions.
Kinetic Energy Calculator
Use the formula KE = ½mv² to solve for kinetic energy, mass, or velocity. Select what you want to find, enter the two known values, and get instant results.
Frequently Asked Questions
What is kinetic energy?
Kinetic energy is the energy an object has due to its motion. Any object with mass that is moving possesses kinetic energy. It is measured in joules (J) in the SI system. The faster an object moves, or the more massive it is, the greater its kinetic energy.
What is the kinetic energy formula?
The kinetic energy formula is KE = ½mv², where KE is kinetic energy in joules (J), m is mass in kilograms (kg), and v is velocity in metres per second (m/s). For example, a 10 kg object moving at 5 m/s has KE = ½ × 10 × 5² = 125 J.
How do you solve for velocity from kinetic energy?
Rearrange the formula to isolate v: v = √(2KE / m). For example, if KE = 125 J and m = 10 kg, then v = √(2 × 125 / 10) = √25 = 5 m/s. Velocity cannot be negative, so we always take the positive square root.
How do you solve for mass from kinetic energy?
Rearrange the formula: m = 2KE / v². For example, if KE = 125 J and v = 5 m/s, then m = 2 × 125 / 5² = 250 / 25 = 10 kg. The velocity cannot be zero because division by zero is undefined.
Why does velocity have a bigger effect on kinetic energy than mass?
Because kinetic energy is proportional to v² (velocity squared) but only proportional to m (mass) linearly. Doubling the mass doubles KE, but doubling the velocity quadruples KE. This quadratic relationship explains why high-speed collisions are far more destructive than low-speed ones of the same mass.
What units are used for kinetic energy?
The SI unit is the joule (J). One joule equals 1 kg·m²/s². Common conversions: 1 kJ = 1,000 J; 1 cal = 4.184 J; 1 kcal = 4,184 J; 1 Wh = 3,600 J; 1 BTU ≈ 1,055 J. For very large energies (spacecraft, explosions), megajoules (MJ) are used.
What are some real-world examples of kinetic energy?
A 0.145 kg baseball at 42 m/s has about 128 J. A 1,500 kg car at 30 m/s has 675,000 J (675 kJ). An 8 g bullet at 370 m/s has about 548 J. A 70 kg cyclist at 10 m/s has 3,500 J. These examples show that large masses or high velocities store enormous amounts of kinetic energy.
Is kinetic energy conserved in collisions?
Only in perfectly elastic collisions. In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision (like a car crash), some kinetic energy is converted to heat, sound, and deformation. In a perfectly inelastic collision (objects stick together), the maximum possible kinetic energy is lost while momentum is still conserved.
Understanding Kinetic Energy
The KE Formula (½mv²)
Kinetic energy is the energy an object possesses because of its motion. Any object with mass that is moving at a velocity greater than zero has kinetic energy. The standard SI formula is:
Kinetic Energy Formula:
KE = ½ × m × v²
- KE = Kinetic energy (Joules, J)
- m = Mass (kilograms, kg)
- v = Velocity (metres per second, m/s)
The formula can be rearranged to solve for any of its three variables:
Solve for mass:
m = 2KE / v²
Solve for velocity:
v = √(2KE / m)
Kinetic energy is always non-negative because mass is always positive and velocity is squared. Doubling the mass doubles the kinetic energy, but doubling the velocity quadruples it — this quadratic relationship explains why high-speed collisions are disproportionately more destructive than low-speed ones.
Derivation from the Work-Energy Theorem
The kinetic energy formula is derived from Newton's second law and the definition of work. When a net force F is applied over a displacement d, the work done on an object is:
W = F × d
F = m × a (Newton's second law)
v² = u² + 2ad → d = (v² − u²) / 2a
W = m × a × (v² − u²) / 2a = ½m(v² − u²)
Starting from rest (u = 0): W = ½mv²
The work done on an object from rest equals the kinetic energy acquired. This is the work-energy theorem: the net work done on an object equals the change in its kinetic energy.
Real-World Examples
Baseball Pitch
A regulation baseball has a mass of about 0.145 kg. A fastball leaves the pitcher's hand at around 42 m/s (≈ 94 mph). What is its kinetic energy?
KE = ½ × 0.145 × 42² = ½ × 0.145 × 1764 ≈ 127.9 J
About 128 joules — comparable to a 60-watt light bulb running for roughly 2 seconds.
Family Car on the Motorway
A 1,500 kg car travelling at 30 m/s (108 km/h, about 67 mph) has kinetic energy of:
KE = ½ × 1500 × 30² = ½ × 1500 × 900 = 675,000 J = 675 kJ
675 kilojoules — enough to boil roughly 1.6 litres of water from room temperature. This illustrates why braking distances grow so rapidly with speed.
Rifle Bullet
A 9 mm bullet typically has a mass of about 0.008 kg (8 g) and leaves the barrel at approximately 370 m/s:
KE = ½ × 0.008 × 370² = ½ × 0.008 × 136900 ≈ 547.6 J
Over 500 joules from just 8 grams, almost entirely due to its high velocity — showing why speed has a far greater effect on kinetic energy than mass.
Cyclist at Speed
A 70 kg cyclist riding at 10 m/s (36 km/h):
KE = ½ × 70 × 10² = ½ × 70 × 100 = 3,500 J = 3.5 kJ
3.5 kJ, which all needs to be dissipated by brakes or ground friction when stopping.
Energy Unit Conversions
The SI unit for energy is the joule (J). Here are common conversion factors to help you interpret kinetic energy results in practical contexts:
| Unit | Symbol | Equivalent in Joules |
|---|---|---|
| Joule (SI base unit) | J | 1 J |
| Kilojoule | kJ | 1,000 J |
| Megajoule | MJ | 1,000,000 J |
| Calorie (thermochemical) | cal | 4.184 J |
| Kilocalorie (food Calorie) | kcal | 4,184 J |
| Watt-hour | Wh | 3,600 J |
| Kilowatt-hour | kWh | 3,600,000 J |
| British Thermal Unit | BTU | 1,055.06 J |
| Foot-pound | ft·lb | 1.35582 J |
| Electronvolt | eV | 1.60218 × 10⁻¹⁹ J |
To convert from joules: divide by the "Equivalent in Joules" value. For example, 675,000 J ÷ 3,600 = 187.5 Wh = 0.1875 kWh.