Kinetic & Potential Energy Calculator

Understanding the kinetic and potential energy calculator — concept and principle

Mechanical energy comes in two everyday forms: kinetic energy, the energy of motion, and gravitational potential energy, the energy stored by height. This calculator gives both for a chosen mass, speed and height, their total, and the speed an object would reach if all of its potential energy turned into motion. It is used for vehicle safety intuition, roller coasters and falling objects, hydro storage and physics homework.

Speed counts squared: 100 km/h holds about four times the energy of 10 m of height.

How it is calculated

Kinetic energy: KE = ½ m v², with m in kg and v in m/s, giving joules (J).
Potential energy: PE = m g h, with g = 9.80665 m/s² and h the height in metres above your chosen reference level.
Total: (KE + PE) ÷ 1,000, in kilojoules.
Speed if PE → KE: v = √(2 g h), independent of mass.

The principle

Work done by a force changes energy. Accelerating a mass from rest with force F over distance d does work F·d, and using v² = 2ad with F = ma gives exactly ½mv². Lifting a mass at constant speed against its weight mg through height h stores mgh. Without friction or air resistance, mechanical energy is conserved, so falling from h converts mgh into ½mv², and mass cancels to give √(2gh). Only differences in PE matter, so h is measured from whatever level you choose as zero.

Worked example

Inputs: m = 1,000 kg, v = 27.8 m/s (about 100 km/h), h = 10 m.
KE = ½ × 1,000 × 27.8² = 500 × 772.84 = 386,420 J.
PE = 1,000 × 9.80665 × 10 = 98,066.5 J.
Total = (386,420 + 98,066.5) ÷ 1,000 = 484.4865 kJ.
Speed from 10 m: √(2 × 9.80665 × 10) = √196.133 ≈ 14.005 m/s.

Each point is the calculator re-run with only “Speed (m/s)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Speed (m/s)	Kinetic energy (J)
6.95	24,151.25
13.9	96,605
20.9	217,361.25
27.8	386,420
34.8	603,781.25
41.7	869,445
55.6	1,545,680

How to read the result

Kinetic energy grows with the square of speed: a car at 100 km/h carries four times the energy it has at 50 km/h, which is why stopping distance and crash severity rise so steeply. A useful comparison is the height that gives the same energy, h = v² ÷ 2g; for 27.8 m/s that is about 39.4 m, roughly a 13-storey fall. For scale, 1 kWh = 3.6 MJ, so the total here is about 0.13 kWh.

Common mistakes

Entering speed in km/h; divide by 3.6 first.
Forgetting to square the speed, or squaring the mass.
Treating PE as absolute; it depends on the reference level.
Applying √(2gh) when friction or drag is significant.

Keep in mind: These are ideal values that ignore friction, air resistance and rotation of wheels or other parts. They are for understanding, not for safety-critical or engineering design.

Frequently asked questions

Why does kinetic energy depend on v² but momentum only on v?

Momentum relates force to time, while energy relates force to distance; at higher speed you cover more distance while braking, so the energy grows faster.

Does a heavier object reach a higher speed from the same drop?

Not in a vacuum: √(2gh) has no mass in it. In air, heavier compact objects lose relatively less to drag.

How do I convert joules to calories?

1 kcal = 4,184 J (thermochemical calorie), so 484.5 kJ is about 116 kcal.

Sources: Halliday, Resnick and Walker, Fundamentals of Physics, Wiley · BIPM, The International System of Units (SI Brochure), 9th edition, 2019

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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