Kinetic Energy Calculator - KE = ½mv² & PE = mgh

How to use this tool

1. Select kinetic energy (KE) or potential energy (PE) mode.
2. Choose the quantity to solve for: KE, mass, or speed in KE mode; PE, mass, gravity, or height in PE mode.
3. Enter the remaining known values using kilograms, meters per second, meters, meters per second squared, and joules.
4. Read the solved value and the energy in joules, kilojoules, and kilowatt-hours.

The velocity-squared effect in everyday context

KE = ½mv² means kinetic energy increases with the square of velocity. Practical consequences:

• A car at 60 mph has 4× the kinetic energy of the same car at 30 mph - not 2×
• Stopping distance on wet roads at 60 mph is roughly 4× the stopping distance at 30 mph
• This relationship is why speed limits in school zones and parking lots are so much lower

Unit conversion notes

The SI unit of energy is the joule (J). Conversions:

• 1 J = 0.2389 cal (thermochemical calorie)
• 1 kJ = 0.2778 Wh (watt-hour)
• 1 Wh = 3,600 J
• 1 kWh = 3.6 MJ
• 1 BTU ≈ 1,055 J

Examples on the kinetic energy scale:

• Baseball pitch (90 mph / 40 m/s, 0.145 kg): ~116 J (roughly a 28-calorie bite of food)
• Car at 60 mph (26.8 m/s, 1,500 kg): ~539 kJ (0.15 kWh)
• Jumbo jet at cruise (560 mph / 250.3 m/s, 280,000 kg): ~8.77 GJ (about 2.44 MWh)

Energy Forms

Kinetic energy depends on mass and velocity: KE = ½mv². Doubling the velocity quadruples the kinetic energy (because velocity is squared).

Gravitational potential energy depends on mass, height, and local gravitational acceleration: PE = mgh. On the Moon g ≈ 1.62 m/s².

The velocity-squared effect

Because kinetic energy scales with v², small increases in speed produce large increases in energy - which is why speed is so critical to vehicle safety.

Real-world KE scale

• Baseball pitch (90 mph, 0.145 kg): ≈ 116 J
• Car at highway speed (70 mph, 1,500 kg): ≈ 734 kJ
• Jumbo jet at cruise (560 mph / 250.3 m/s, 280,000 kg): ≈ 8.77 GJ