Energy Calculator
Calculate kinetic and potential energy
How It Works
Overview
Mechanical energy comes in two basic flavors. Kinetic energy is the energy of motion — anything with mass and speed has it. Potential energyis stored energy due to position, most commonly gravitational PE for objects raised above a reference point. This calculator handles both, plus their sum (total mechanical energy).
Energy is measured in Joules (J), where 1 J = 1 kg·m²/s² = 1 N·m. A key principle: in a frictionless system, kinetic and potential energy can convert into each other, but their total stays constant. That's the conservation of mechanical energy, and it's why a pendulum keeps swinging or a roller coaster regains nearly all its starting speed at the bottom of a drop.
The Formula
Where:
- m = mass in kilograms (kg)
- v = velocity in meters per second (m/s)
- g = gravitational acceleration, 9.8 m/s² on Earth's surface
- h = height above the chosen reference level in meters (m)
Notice the v² in kinetic energy: doubling speed quadruples KE. The reference height for PE is arbitrary — what matters physically is differences in height, not absolute height.
Worked Example
A 0.145 kg baseball is thrown at 40 m/s (about 90 mph) from a height of 1.5 m above the ground. What is its total mechanical energy?
- Kinetic energy: KE = ½ × 0.145 × 40² = 116 J
- Potential energy: PE = 0.145 × 9.8 × 1.5 ≈ 2.13 J
- Total: E = 116 + 2.13 ≈ 118.1 J
Most of the energy is kinetic — that's typical when speeds are appreciable. By contrast, a 50 kg boulder perched motionless 20 m up a cliff has 0 J of KE but mgh = 50 × 9.8 × 20 = 9,800 J of stored gravitational PE.
When to Use This
- Physics problem solving — finding speed at the bottom of a ramp from PE at the top, or vice versa.
- Roller coaster / pendulum analysis — using conservation to predict speeds without dealing with forces.
- Impact and stopping distance estimates — KE tells you how much work the brakes (or a wall) must absorb.
- Hydropower estimates — water dropping h meters releases mgh joules of PE per kilogram.
- Comparing speeds vs. heights — converting "dropped from 5 m" into an equivalent impact velocity.
Common Mistakes to Avoid
- Forgetting to square the velocity. KE = ½mv² has v squared — a common slip is to use ½mv and underestimate energy by the factor v.
- Mixing units. Always use kg, m, and m/s. Grams or km/h will silently produce wrong answers.
- Choosing an inconsistent reference for height. Pick one ground level and stick with it for every step in a problem.
- Ignoring losses. In real systems, friction and air drag remove energy. Don't expect a falling object's final KE to equal its starting PE exactly.
- Confusing weight (m × g) with mass. PE uses mass times g — if you already have weight in Newtons, just multiply by h directly.
Frequently Asked Questions
Ad Space