Kinetic energy
Calculate translational kinetic energy, mass, or speed using the classical relationship between mass and motion.
Ek = 1/2 × m × v² Calculated quantities
Ek - kinetic energy · m - mass · v - speed
Physics formulas
Work, energy and power
Calculate mechanical work, energy changes, power, and the quantities connected with energy transfer.
Formulas and calculators
Open formula
Mechanical work
Calculate work, force, or displacement when a constant force acts in the direction of motion.
W = F × s Calculated quantities
W - mechanical work · F - force · s - displacement
Power, work and time
Calculate average power, work, or elapsed time from the relation between transferred energy and time.
P = W / t Calculated quantities
P - average power · W - work or energy · t - elapsed time
Gravitational potential energy
Calculate gravitational potential energy, mass, gravitational acceleration, or height near a planet surface.
Ep = m × g × h Calculated quantities
Ep - gravitational potential energy · m - mass · g - gravitational acceleration · h - height difference
How to choose the right formula
Kinetic energy
Ek = 1/2 × m × v² - When to use it
- Translational kinetic energy equals one half of the mass multiplied by the square of speed.
- Calculated quantities
- Ek - kinetic energy (J) · m - mass (kg) · v - speed (m/s)
- Worked example: Kinetic energy of a car
- A car with a mass of 1500 kg travels at 20 m/s. Calculate its kinetic energy.
Mechanical work
W = F × s - When to use it
- For a constant force parallel to displacement, mechanical work equals force multiplied by displacement.
- Calculated quantities
- W - mechanical work (J) · F - force (N) · s - displacement (m)
- Worked example: Work done while pulling a load
- A constant 250 N force moves a load 12 m in the same direction. Calculate the work.
Power, work and time
P = W / t - When to use it
- Average power is the work done, or energy transferred, per unit of time.
- Calculated quantities
- P - average power (W) · W - work or energy (J) · t - elapsed time (s)
- Worked example: Average power of a lifting machine
- A machine performs 3600 J of work in 30 seconds. Calculate its average power.
Gravitational potential energy
Ep = m × g × h - When to use it
- In a uniform gravitational field, the change in potential energy equals mass times gravitational acceleration times the vertical height change.
- Calculated quantities
- Ep - gravitational potential energy (J) · m - mass (kg) · g - gravitational acceleration (m/s²) · h - height difference (m)
- Worked example: Energy of a box on a platform
- A 12 kg box is lifted 5 m. Use g = 9.81 m/s² and calculate the energy increase.
What to check before calculating
Assumptions and conditions
- This is the classical formula for translational motion. Relativistic effects are neglected.
- Mass must be greater than zero and speed is treated as a non-negative scalar.
- Energy depends on the selected frame of reference because the measured speed depends on that frame.
- Rotational, vibrational, and internal energy are not included.
- The force is constant and parallel to the displacement.
- The formula uses the component of force along the path; perpendicular force does no work in this model.
- Force and displacement must use compatible units.
- Displacement and force used as divisors must be greater than zero.
Common mistakes
- Forgetting to square the speed.
- Using grams with joules without first converting mass to kilograms.
- Using velocity in km/h as though it were already expressed in m/s.
- Adding rotational energy to this result without using the separate rotational-energy formula.
- Using the full force when it is not parallel to the displacement.
- Treating holding an object still as mechanical work despite zero displacement.
- Mixing kilojoules with joules or kilometres with metres.
- Confusing work measured in joules with power measured in watts.