Kinetic Energy Calculator (KE = ½mv²)

Calculate kinetic energy, mass, or velocity instantly using KE = ½mv². Explore the non-linear squared speed effect, convert between Joules, ft-lbf, and Watt-hours, and inspect real-world energy benchmarks.

Target Parameter

Live calculation
Quick Sample Presets
kg
m/s
Calculated Ke
300.00 kJvia KE = ½ m v²
Foot-Pounds Force221,268.6 ft-lbf

Joules (Total)

300,000 J

Velocity (mph)

44.7 mph

Velocity (km/h)

72.0 km/h

Watt-Hours

83.33 Wh

Explosive & Thermal Equivalence

TNT Explosive Equivalent

71.70 grams of TNT

Linear Momentum (p = mv)

30000.00 kg·m/s

A 1500.0 kg body at 20.0 m/s (44.7 mph) possesses 300.00 kJ of kinetic energy.

If velocity doubles to 40.0 m/s (89.5 mph), the kinetic energy will quadruple to 1200.00 kJ.

The Physics of Kinetic Energy & The Quadratic Speed Effect

Kinetic energy ($KE$) is the scalar mechanical energy possessed by an object due to its motion. Derived by integrating Newton's Second Law across a displacement vector, kinetic energy is mathematically expressed as $KE = \frac12 m v^2$.

Kinetic Energy Kinematic Equations
1. Solve Kinetic Energy (KE)
KE =
12
m · v²

Joules = 0.5 × kg × (m/s)²

2. Solve Mass (m)
m =
2 · KEv²

kg = (2 × Joules) ÷ (m/s)²

3. Solve Velocity (v)
v =√
2 · KEm

m/s = √(2 × Joules ÷ kg)

The Velocity Doubling Impact Law
Speed v × 2 ⇒ Energy KE × 4|Speed v × 3 ⇒ Energy KE × 9|1 Joule = 0.73756 ft·lbf
Step-by-Step Calculation Breakdown
Example 1: 1,500 kg Passenger Sedan Traveling at 20 m/s (~45 mph)
1. Parameters: Mass m = 1,500.00 kg, Velocity v = 20.00 m/s
2. Square velocity: v² = 20.00² = 400.00 m²/s²
3. Compute energy: KE = ½ × 1,500.00 × 400.00 = 300,000.00 Joules (300.00 kJ)
4. Imperial work: 300,000.00 × 0.737562 = 221,268.60 ft-lbf
Example 2: 9mm Bullet (8g / 0.008 kg at 350 m/s Muzzle Velocity)
1. Parameters: Mass m = 0.008 kg, Velocity v = 350.00 m/s
2. Square velocity: v² = 350² = 122,500.00 m²/s²
3. Compute muzzle energy: KE = 0.5 × 0.008 × 122,500 = 490.00 Joules (361.41 ft-lbf)

Real-World Kinetic Energy Comparison Benchmarks

Moving System / ObjectEnergy (Joules)Foot-Pounds (ft-lbf)Engineering Significance
Dropping a coin from hand height (0.1 J)0.1 J0.1 ft-lbfHuman & sports scale
Baseball pitch impact on glove (10-150 J)10 J7.4 ft-lbfHuman & sports scale
9mm handgun bullet muzzle energy (~500 J)500 J368.8 ft-lbfHuman & sports scale
5.56mm NATO rifle bullet muzzle energy (~1.8 kJ)1.8 kJ1,327.6 ft-lbfAutomotive impact safety scale
Compact sedan (1,200 kg) driving at 30 mph (~135 kJ)135.0 kJ99,570.9 ft-lbfAutomotive impact safety scale
Compact sedan (1,200 kg) driving at 60 mph (~540 kJ - 4× higher!)540.0 kJ398,283.5 ft-lbfAutomotive impact safety scale
Heavy SUV (2,400 kg) cruising at 65 mph (1.08 MJ)1.08 MJ796,567 ft-lbfAutomotive impact safety scale
Boeing 737 passenger airliner upon touchdown (~140 MJ)140.00 MJ103,258,680 ft-lbfAviation & heavy transport

Frequently Asked Questions

What is kinetic energy and why is velocity squared?
Kinetic energy is the mechanical work required to accelerate a body of a given mass from rest to its current velocity: KE = ½mv². Because velocity is squared, kinetic energy does NOT scale linearly with speed: doubling your speed quadruples (4×) the kinetic energy, and tripling your speed increases kinetic energy ninefold (9×).
How does kinetic energy differ from linear momentum?
Linear momentum (p = mv) is a vector quantity proportional to velocity to the first power and is conserved in all collisions. Kinetic energy (KE = ½mv²) is a scalar quantity proportional to velocity squared and is only conserved in perfectly elastic collisions; in inelastic collisions, kinetic energy is dissipated into thermal heat, acoustic shockwaves, and metal deformation.
How do you convert Joules to Foot-Pounds (ft-lbf) and Watt-hours?
1 Joule (J) = 0.737562 foot-pounds force (ft-lbf) = 0.000277778 Watt-hours (Wh) = 0.239006 calories = 2.39006 × 10⁻⁴ kilocalories (dietary Calories). 1 kilojoule (kJ) = 1,000 Joules.
Why are high-speed vehicle crashes disproportionately lethal?
Vehicle crash severity is governed directly by kinetic energy dissipation. When a vehicle stops suddenly, all its kinetic energy must be absorbed by crumple zones and occupants. A crash at 60 mph involves four times (400%) the destructive energy of a crash at 30 mph, despite speed only increasing by 100%.

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