Kinetic & Potential Energy

Computing Energy from Motion or Height

Kinetic energy is the energy an object has because of its motion; gravitational potential energy is the energy it has because of its height above a reference point. Choose which one you’re finding, enter the relevant values, and this calculator computes the result in joules, kilojoules, and kilowatt-hours.

The Formula

Kinetic energy:

$$\vC{\text{KE}} = \frac{1}{2} \times \vA{\text{Mass}} \times \vB{\text{Velocity}}^2$$

Potential energy:

$$\vC{\text{PE}} = \vA{\text{Mass}} \times g \times \vB{\text{Height}}$$

where $g$ is gravitational acceleration — defaulted to Earth’s standard gravity (9.80665 m/s²), a genuine physical constant, not a guess about your specific situation.

Worked Example

Kinetic energy of a 2 kg object moving at 3 m/s:

1. Square the velocity: $\vB{3}^2 = 9$.
2. Apply the formula: $\vC{\text{KE}} = \frac{1}{2} \times \vA{2} \times 9 = \vC{9}$ joules.

Potential energy of a 2 kg object at a height of 10 m:

1. Apply the formula: $\vC{\text{PE}} = \vA{2} \times 9.80665 \times \vB{10} \approx \vC{196.13}$ joules.
2. Convert to kilowatt-hours: $196.13 \div 3,600,000 \approx 0.0000545$ kWh.

Key Factors to Consider

• Kinetic energy grows with the square of velocity, meaning speed matters more than mass for fast-moving objects. Doubling an object’s speed quadruples its kinetic energy, while doubling its mass only doubles it — this is exactly why a small increase in vehicle speed disproportionately increases the energy involved in a collision.
• Potential energy depends on the choice of reference point, which is arbitrary but must stay consistent. “Height” in the potential energy formula is measured relative to whatever reference level you choose (the ground, a table surface, sea level) — the absolute number changes with a different reference point, but the DIFFERENCE in potential energy between two heights stays the same regardless of where zero is set.
• Energy conservation links these two forms directly — falling converts potential energy into kinetic energy. In an idealized system with no air resistance or friction, an object’s total mechanical energy (kinetic plus potential) stays constant as it falls, with potential energy converting into kinetic energy in exact proportion — the Free Fall Calculator explores this same physical scenario from a different angle.
• Real-world energy calculations often need to account for losses this idealized formula ignores. Air resistance, friction, and other non-conservative forces convert some mechanical energy into heat or sound in a real system — these formulas describe the ideal, lossless case.

Common Mistakes

• Forgetting to square the velocity in the kinetic energy formula. KE = ½mv² means doubling speed quadruples the energy, not doubles it — a common error is plugging velocity in linearly instead of squaring it first.
• Mixing units, such as entering mass in pounds or velocity in miles per hour without converting. The classical formulas require SI units (kilograms, meters per second, meters) to produce a result in joules — mixing unit systems without conversion produces a meaningless number.
• Assuming a “height” figure means the same thing across two different reference points. Potential energy is always relative to a chosen zero point — comparing a PE value computed against the ground to one computed against a tabletop is comparing two different baselines, not the same physical quantity.
• Treating the ideal, frictionless result as an exact real-world prediction. A real falling or moving object loses some energy to air resistance and friction, so its actual kinetic energy is typically slightly less than these classical formulas predict.

Useful to Know

• Want to see how potential energy converts into kinetic energy during an actual fall? The Free Fall Calculator calculator works through that same physical scenario in detail.
• Trying to relate energy to the force and distance involved instead? The Force Calculator (F = ma) calculator covers the force side of classical mechanics.
• Working with heat rather than mechanical energy? The Heat Energy Calculator calculator handles thermal energy calculations using the same kind of unit conversions shown here.