What is the kinetic energy formula?

Kinetic energy (KE) = ½ × m × v², where m is mass in kilograms and v is velocity in meters per second. The result is in joules (J). Because velocity is squared, doubling speed quadruples kinetic energy. A car at 60 mph has 4× the kinetic energy of the same car at 30 mph.

How much kinetic energy does a car have at highway speed?

A 3,500 lb (1,590 kg) car at 60 mph (26.8 m/s) has approximately 571,000 joules (571 kJ) of kinetic energy — enough energy to lift the car about 36 meters straight up. At 30 mph, it has 143 kJ. This energy must be absorbed by brakes or crash structures in a collision, which is why higher speeds are so much more dangerous.

What is the unit of kinetic energy?

In SI units, kinetic energy is measured in joules (J). One joule = 1 kg·m²/s². For larger amounts, kilojoules (kJ) or megajoules (MJ) are used. In US customary units, energy is measured in foot-pounds (ft·lbf) — often used for bullet energy in ballistics. Other units: 1 Wh = 3,600 J; 1 BTU = 1,055 J; 1 food calorie (kcal) = 4,184 J.

Why does kinetic energy depend on velocity squared?

Kinetic energy scales with v² because of the work-energy theorem. Doubling speed requires quadruple the distance to stop (F × d = ΔKE), which is why stopping distances grow so rapidly with speed. Physically, it comes from Newton's second law — the work done to accelerate a mass from 0 to v is ∫mv dv = ½mv².

What is the kinetic energy of a bullet?

Bullet kinetic energies vary widely by caliber. A .22 LR has about 160–200 J. A 9mm Luger has 450–600 J. A .308 Winchester rifle has 3,500–4,000 J. For reference, 1,000 J (1 kJ) is considered the minimum for large-game hunting by many jurisdictions. Kinetic energy determines terminal ballistics and wound channel behavior.

What is the kinetic energy of a person running?

A 160 lb (73 kg) person running at 10 mph (4.47 m/s) has approximately 730 J (0.73 kJ) of kinetic energy — comparable to a rifle bullet. At 6 mph (jogging), about 260 J. This energy must be absorbed by joints and muscles with each footstrike, which is why proper footwear and running form matter for injury prevention.

How does speed affect kinetic energy in a car crash?

Because KE = ½mv², 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, and 9× the energy at 20 mph. This quadratic relationship explains why crash fatality rates rise so steeply with speed: a 60 mph crash requires dissipating 4× the energy compared to 30 mph, overwhelming crumple zones, airbags, and the human body's tolerance limits.

What is the kinetic energy of a 2,000 kg car at 60 mph?

A 2,000 kg car at 60 mph (26.82 m/s) has KE = ½ × 2,000 × 26.82² = 719,000 J (719 kJ). That is enough energy to lift the car to a height of about 36.7 meters (120 feet). At 30 mph (13.41 m/s), the same car has only 179,750 J — exactly one-quarter of the 60 mph value, illustrating the v² effect.

What is the difference between kinetic energy and potential energy?

Kinetic energy (KE = ½mv²) is energy of motion — it depends on mass and velocity. Potential energy (PE = mgh for gravitational) is stored energy of position — it depends on mass, height, and gravitational acceleration. The two convert into each other in a frictionless system: a ball dropped from 10 m converts all its PE (mgh = m × 9.81 × 10) into KE at the moment of impact. This conservation of mechanical energy is fundamental to roller coaster design, pendulums, and hydroelectric power generation.

Kinetic Energy Calculator — Joules & Foot-Pounds

Calculates kinetic energy in joules, foot-pounds, kWh, and BTU from mass and velocity — with real-world comparisons.

The Kinetic Energy Formula — KE = ½mv²

The kinetic energy calculator on this page computes KE in joules, foot-pounds, kWh, and BTU from mass and velocity. Kinetic energy is the energy possessed by any moving object. The formula is:

KE = ½ × m × v²

Where m is mass in kilograms and v is velocity in meters per second. The result is in joules (J). The v² term is critical: kinetic energy scales with the square of velocity. A car at 60 mph has 4× the KE of the same car at 30 mph, and 9× the KE at 20 mph. This is why high-speed collisions are catastrophically more destructive.

Energy Units — Joules, Foot-Pounds, kWh, BTU

This calculator outputs kinetic energy in several units:

Joules (J) — SI unit. 1 J = 1 kg·m²/s² = 1 watt-second. Used in physics and engineering.
Kilojoules (kJ) — 1,000 J. Food energy is measured in kcal (1 food calorie = 4.184 kJ).
Foot-pounds (ft·lbf) — US customary. Used in ballistics, automotive torque specs. 1 ft·lbf = 1.356 J.
Kilowatt-hours (kWh) — utility billing unit. 1 kWh = 3.6 MJ. A typical home uses 30 kWh/day.
BTU (British Thermal Unit) — HVAC and heating. 1 BTU = 1,055 J.

AdvertisementResponsive Ad

Kinetic Energy in Car Crashes

Understanding kinetic energy is essential for road safety. All of a vehicle's kinetic energy must be dissipated during a crash through deformation, heat, and sound. Key data points for a 3,500 lb (1,590 kg) vehicle:

20 mph — 64 kJ. Equivalent to dropping the car from 4 meters (13 feet) high
30 mph — 143 kJ. Survivable in modern vehicles with airbags and crumple zones
60 mph — 571 kJ. 4× the energy of 30 mph. Severe injury/fatality risk
80 mph — 1,015 kJ. Over 7× the energy of 30 mph

Crumple zones extend the stopping distance (time), reducing the peak force on occupants. This is the engineering application of the impulse-momentum theorem.

Kinetic Energy in Ballistics

Firearms and projectile energy is commonly measured in foot-pounds (ft·lbf):

Handguns — 9mm: ~350–400 ft·lbf; .45 ACP: ~350–425 ft·lbf
Rifle cartridges — .223 Rem: ~1,200 ft·lbf; .308 Win: ~2,600 ft·lbf
Large game hunting — typically requires 1,000+ ft·lbf at impact

Note: a bullet's lethality depends on energy, velocity, bullet design, and placement — not energy alone.

Kinetic Energy and Work

By the work-energy theorem, the net work done on an object equals its change in kinetic energy: W = ΔKE = ½mv₂² − ½mv₁². This means stopping a moving car requires doing negative work equal to its kinetic energy. A 3,500 lb car at 60 mph requires 571,000 J of work to stop — provided by brake friction over approximately 150–180 feet of stopping distance at 0.7g deceleration.

AdvertisementResponsive Ad

Kinetic Energy vs. Potential Energy

Kinetic energy is energy of motion; potential energy is stored energy of position. They convert into each other: a ball at the top of a hill has maximum potential energy (mgh) and zero KE; at the bottom, all PE has converted to KE. In a frictionless system, total mechanical energy (KE + PE) is conserved.

For mass-related calculations in other fields, see our density calculator which finds mass from volume and density — useful for estimating the mass of objects whose volume you know. For engine applications, the compression ratio calculator shows how cylinder geometry determines the compression that directly affects the combustion energy delivered to the crankshaft.

Sources & References

NIST: Energy Units and Conversion Factors — National Institute of Standards and Technology
Kinetic Energy — Britannica — Encyclopædia Britannica

Kinetic Energy Calculator