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

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)
• Boeing 747 at cruise (250 m/s, 280,000 kg): ~8.75 GJ (enough to power an average home for ~800 days)

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): ≈ 700 kJ
• Jumbo jet at cruise (560 mph, 280,000 kg): ≈ 7 GJ