Work, Energy and Power Calculator
Compute work, kinetic energy, gravitational potential energy and power in a single tool.
Work (W = F·d·cos θ)
Kinetic & Potential Energy
Formulas
Kinetic energy: KE = ½ · m · v²
Potential energy:PE = m · g · h
Power: P = W / t
How to use
- Enter force, distance and the angle between them for work.
- Enter mass, velocity and height for KE and PE.
- Time is used to compute power from the work you just calculated.
Physics explanation
Work is the mechanical transfer of energy. When a force acts on an object and the object moves, work equals force times the component of displacement along the force direction. The 'cos θ' accounts for forces that aren't perfectly aligned with the motion. Kinetic energy is the energy of motion; potential energy is stored by position in a gravitational field. Power is how quickly energy is transferred — it's what your electricity meter measures.
Worked example
F = 50 N, d = 10 m, θ = 0°, t = 5 s, m = 2 kg, v = 3 m/s, h = 4 m
W = 50·10·cos 0° = 500 J KE = ½·2·3² = 9 J PE = 2·9.80665·4 ≈ 78.45 J P = 500 / 5 = 100 W
Related tools
FAQs
How do I use work energy power calculator?
Different formulas for different quantities. Work: W = Fd cos(θ), in joules. Kinetic energy: KE = ½mv², in joules. Potential energy: PE = mgh, in joules. Power: P = W/t = Fv, in watts. The calculator picks the right formula based on what you input. So lifting a 5 kg crate 2 m straight up requires W = mgh = 5 × 9.81 × 2 ≈ 98 J of work. If done in 4 s, the power needed is P = 98/4 = 24.5 W. Combining all four lets you analyse almost any energy-related mechanics problem.
How to calculate work from force and distance?
Work equals force times distance times the cosine of the angle between them: W = Fd cos(θ). With force in newtons, distance in metres, you get joules. If you push a 100 N crate 5 m horizontally with the force aligned along the motion (θ = 0°), W = 100 × 5 × 1 = 500 J. If the same force is at 60° to the motion, W = 100 × 5 × 0.5 = 250 J — only half because only half the force points along the motion. Forces perpendicular to motion (θ = 90°) do no work, even if huge.
How do I use kinetic energy calculator mass velocity?
Kinetic energy is KE = ½mv², measured in joules. Mass in kilograms, velocity in m/s. So a 70 kg sprinter at 10 m/s has KE = 0.5 × 70 × 100 = 3500 J. A 1500 kg car at 20 m/s has KE = 300,000 J — and at 40 m/s, four times that, since velocity enters squared. This v² scaling is why crashes at higher speed are vastly more dangerous: doubling speed quadruples kinetic energy that has to be dissipated on impact. The calculator just runs the multiplication, but the implication is sobering.
How do I use potential energy calculator mass height gravity?
Gravitational potential energy is PE = mgh: mass in kilograms, gravity (9.81 m/s² on Earth), height in metres above the reference point. So a 2 kg book on a 1.5 m shelf has PE = 2 × 9.81 × 1.5 ≈ 29.4 J relative to the floor. The reference point is arbitrary — you can measure height from any surface — but consistency within a problem is essential. PE converts cleanly into KE if the object falls freely: at the floor, KE = 29.4 J as well, giving v = √(2 × 29.4/2) ≈ 5.42 m/s. Energy conservation makes these problems neat.
How do I use power from work and time calculator?
Power is the rate of doing work: P = W/t, in watts (J/s). So lifting a 50 kg load 10 m up takes W = mgh = 50 × 9.81 × 10 ≈ 4905 J. Done in 5 seconds, that's P ≈ 981 W. Done in 30 seconds, only 163.5 W. Same total work, vastly different power demand. This is why elevators with strong motors can lift the same load faster than a person. Engines and motors are rated by their power capability (kW or hp), which limits the rate at which they can convert energy. 1 horsepower ≈ 745.7 W.
How do I use work done at an angle calculator?
When force isn't aligned with motion, only the component along the displacement does work: W = Fd cos(θ). So pulling a sled with a rope at 30° above horizontal, applying 80 N over 10 m, does W = 80 × 10 × cos(30°) ≈ 692.8 J of useful work along the direction of motion. The vertical component (80 sin(30°) = 40 N upward) does no work since there's no vertical displacement. Calculators handle the cosine automatically. Always specify θ as the angle between the force vector and the displacement vector, not from any other reference like the ground or the normal.
How do I use work energy theorem calculator?
The work-energy theorem says net work equals change in kinetic energy: W_net = ΔKE = ½mv_f² − ½mv_i². So if a 5 kg block speeds up from 2 m/s to 8 m/s, the net work done on it equals 0.5 × 5 × (64 − 4) = 150 J. This connects forces directly to speed changes without needing to track time or acceleration explicitly. It's especially handy when forces vary along the path or when you only care about start and end states. The theorem applies regardless of the specific shape of the force-distance graph — only the total area under it matters.