Free Energy Calculator
Calculate kinetic and potential energy in joules, calories, and kWh. Enter mass, velocity, or height to solve energy equations.
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Kinetic Energy (½mv²)
125.00 J
Calories
0.0299
kWh
0.000035
Formula
Kinetic: KE = ½mv² | Potential: PE = mgh — where m = mass (kg), v = velocity (m/s), g = 9.81 m/s², h = height (m)How to Calculate Kinetic and Potential Energy
Energy is one of the most fundamental concepts in physics. This calculator handles the two most common types: kinetic energy (energy of motion) and potential energy (energy stored by position). Both are measured in joules (J) and are central to mechanics, engineering, and everyday physics problems.
For kinetic energy, you need the object's mass and velocity. The formula KE = ½mv² shows that energy scales with the square of velocity — doubling speed quadruples the energy. For potential energy, you need mass and height. The formula PE = mgh uses gravitational acceleration (9.81 m/s² on Earth).
Understanding Energy Units
- Joules (J) — the SI unit of energy, used in physics and engineering
- Calories (cal) — commonly used in food and nutrition (1 food calorie = 1 kcal = 4,184 J)
- Kilowatt-hours (kWh) — used for electricity billing (1 kWh = 3,600,000 J)
- Electron volts (eV) — used in atomic and particle physics
- BTU — British Thermal Units, common in heating and cooling (1 BTU = 1,055 J)
Real-World Energy Examples
Understanding energy becomes easier with practical comparisons:
- Walking (70 kg, 1.5 m/s): about 79 joules of kinetic energy
- Cycling (70 kg, 6 m/s): about 1,260 joules of kinetic energy
- Car at highway speed (1,500 kg, 30 m/s): about 675,000 joules
- Book on a shelf (0.5 kg, 2 m high): about 9.8 joules of potential energy
- Roller coaster at top (1,000 kg, 40 m): about 392,400 joules of potential energy
Conservation of Energy
One of the most important principles in physics is that energy cannot be created or destroyed — only converted between forms. When you drop a ball, potential energy converts to kinetic energy. At the bottom of its fall, all the PE has become KE (minus a small amount lost to air resistance as heat).
This principle is why roller coasters work without engines on most of the track — the initial height provides all the potential energy needed to complete the ride, converting back and forth between PE and KE through every hill and valley.
Frequently Asked Questions
What is the difference between kinetic and potential energy?
Kinetic energy is the energy of motion — any moving object has it. Potential energy is stored energy due to position, usually height above the ground. A ball held in the air has potential energy; when dropped, that converts to kinetic energy as it falls.
How do you convert joules to calories?
Divide joules by 4,184 to get kilocalories (food calories). One food calorie (kcal) equals 4,184 joules. For example, 10,000 joules equals about 2.39 kcal. This calculator does the conversion automatically.
What is a joule in everyday terms?
A joule is roughly the energy needed to lift a small apple (100g) one meter straight up. One kWh equals 3.6 million joules. A AA battery stores about 9,000 joules. A single food calorie is 4,184 joules.
Why does velocity matter more than mass for kinetic energy?
Because velocity is squared in the formula (KE = ½mv²). Doubling the mass doubles the energy, but doubling the velocity quadruples it. That's why a small bullet has enormous kinetic energy — its velocity is extremely high.
How is energy related to power?
Power is the rate of energy transfer. One watt equals one joule per second. So a 100-watt light bulb uses 100 joules every second, or 360,000 joules (0.1 kWh) per hour.