Energy Calculator
Calculate kinetic, potential, elastic and thermal energy with step-by-step workings
Types of Energy
Energy is the capacity to do work. It exists in many forms and can be converted between them — but the total energy in a closed system is always conserved (First Law of Thermodynamics).
Formulas
Conservation of Energy
At the top of a roller coaster, a car has maximum potential energy and minimum kinetic energy. At the bottom, it has maximum kinetic energy and minimum potential energy. Ignoring friction, the total energy remains the same throughout: GPE + KE = constant.
Energy: One Currency, Many Wallets
Built and verified by Andrius R. · Updated June 2026
Energy is physics' bookkeeping: it changes form constantly — motion, height, heat, chemistry, electricity — but the total never changes. That conservation law, plus a few formulas and one unit-conversion table, explains everything from braking distances to your electricity bill to why stairs feel unfair.
Kinetic energy and the tyranny of the square
KE = ½mv². At 100 km/h (27.8 m/s): ½ × 1,500 × 27.8² ≈ 579 kJ. At 50 km/h: ≈ 145 kJ.
Double the speed, quadruple the energy — and since brakes remove energy at a roughly fixed rate, braking distance quadruples too. This single square is most of road-safety physics: 130 vs 100 km/h isn't "30% faster," it's 69% more energy to shed in an emergency. It's also why wind turbines care so much about wind speed (power goes with v³) and why crashes at highway speed are so unforgiving.
Potential energy and the staircase audit
Lifting against gravity stores PE = mgh. An 80 kg person climbing one 3 m storey stores 80 × 9.81 × 3 ≈ 2,354 J — about 0.56 food calories. That deflating number is honest physics: bodies burn several times the mechanical minimum (muscles are ~20–25% efficient), but the lesson stands — "earning" a chocolate bar (~250 kcal) by stairs alone means roughly a hundred storeys. Exercise is magnificent for health; as an eraser of eating it's badly outgunned, which is the quantitative heart of "you can't outrun your fork."
The unit zoo, translated
| Unit | In joules | Natural habitat |
|---|---|---|
| Joule (J) | 1 | Physics; ~an apple lifted 1 m |
| Food calorie (kcal) | 4,184 | Nutrition labels |
| Watt-hour (Wh) | 3,600 | Batteries (a phone holds ~15–20 Wh) |
| Kilowatt-hour (kWh) | 3,600,000 | Electricity bills |
The kWh is just power × time — a 2 kW heater for 30 minutes is 1 kWh. Worked bill example: boiling a full 1.5 L kettle from 15 °C takes m·c·ΔT = 1.5 × 4,186 × 85 ≈ 534 kJ ≈ 0.148 kWh — under 4 cents at €0.25/kWh. Water's huge specific heat (4,186 J/kg·°C) is why heating it dominates home energy use — and, planet-scale, why oceans buffer the climate.
Energy vs power: the confusion worth killing
Energy is the amount (joules, kWh); power is the rate (watts = joules per second). A 100 W bulb for 10 hours uses the same energy as a 1,000 W heater for 1 hour. Mixing them produces most everyday energy nonsense — "my panel generates 5 kW per day" is a unit error (kW per day isn't a thing; 5 kWh per day is). Electrical power's own family lives in the Ohm's law calculator.
Conservation: the law with no known exceptions
Energy is never created or destroyed, only converted — usually ending as low-grade heat. A braking car turns 579 kJ of motion into hot discs; a bouncing ball loses height to heat and sound each bounce; "energy loss" in any machine is really energy escaping to forms you didn't want. This is also the one-line debunk of every perpetual-motion machine ever proposed: any device claiming more energy out than in isn't clever engineering, it's an accounting fraud against the most tested law in physics.
// Speed Doubles → 4× Energy
Kinetic energy scales with v². Double your speed → four times the energy. This is why car crashes at 60 mph are four times more destructive than at 30 mph.
// Food Calories
Food "Calories" (with capital C) are kilocalories. 1 food Calorie = 1 kcal = 4,184 J. A 2,000 kcal diet = ~8.4 MJ of energy per day.
// kWh vs Joules
Energy bills use kilowatt-hours. 1 kWh = 3,600,000 J = 3.6 MJ. A 100W bulb running for 10 hours uses 1 kWh.
// Work at 90°
If force is perpendicular to motion (θ = 90°), no work is done. cos(90°) = 0. Carrying a box horizontally does no work against gravity.