Work and Power Calculator
Calculate mechanical work (W = F x d x cos theta), power (P = W / t), or the alternative P = F x v formula. Choose your solve mode, enter any two known quantities, and get the third instantly with a full show-your-work panel. Supports joules, kilowatt-hours, watts, horsepower, and a full set of metric and imperial units.
Formula
Worked example
A worker pushes a box with 200 N of force through 30 m in 40 s. Work = 200 N x 30 m = 6,000 J. Power = 6,000 J / 40 s = 150 W = 0.15 kW = about 0.20 hp.
What is mechanical work?
In physics, work is the energy transferred to an object when a force causes it to move through a displacement. The formula is W = F x d x cos(theta), where F is the applied force in newtons, d is the displacement in metres, and theta is the angle between the force vector and the direction of motion. When the force is perfectly parallel to the displacement (theta = 0 degrees), all of the force goes into moving the object and cos(0) = 1, so the full F x d product is the work done. When the force is perpendicular (theta = 90 degrees), cos(90) = 0 and no work is done in the direction of motion, even though the person may feel tired. The SI unit of work is the joule (J), which equals one newton-metre. One kilowatt-hour (kWh) equals 3,600,000 J, the unit seen on electricity bills.
What is power and how does it relate to work?
Power is the rate at which work is done, or equivalently the rate at which energy is transferred. The defining formula is P = W / t: if 9,000 J of work is completed in 60 seconds, the average power is 150 watts. Power can also be expressed as P = F x v, the product of force and velocity, which is especially useful for engines and vehicles where speed is known but elapsed time is not. The SI unit is the watt (W), equal to one joule per second. One mechanical horsepower equals 745.7 W, while one kilowatt equals 1,000 W.
How to use this calculator
Choose what you want to solve for from the "Solve for" menu. The five modes are: Power from work and time (P = W / t), Work from power and time (W = P x t), Time from work and power (t = W / P), Force from power and velocity (F = P / v), and Velocity from power and force (v = P / F). Enter your known values in any supported unit - the calculator converts automatically. The angle toggle in Power mode applies the cos(theta) factor when the force direction differs from the displacement direction. The show-your-work panel walks through each conversion step with your actual numbers. The chart shows cumulative work over time at constant power, which is useful for energy budgeting.
Practical examples across everyday contexts
A person lifting a 50 kg box vertically by 1.5 m does work of 50 x 9.81 x 1.5 = 735.75 J. If the lift takes 3 seconds, the power output is about 245 W - comparable to a competitive cyclist climbing a hill. A car cruising at 100 km/h (27.8 m/s) against a 300 N aerodynamic drag force requires 300 x 27.8 = 8,340 W = 8.34 kW just to overcome drag, before losses in the drivetrain. A 3 kW electric kettle boiling 1 litre of water (which absorbs about 334 kJ) takes roughly 334,000 J / 3,000 W = 111 seconds.
Typical power outputs - reference values
| Device / activity | Typical power | Notes |
|---|---|---|
| Human at rest | 80 W | Basal metabolic rate (heat equivalent) |
| Cycling (recreational) | 100-200 W | Varies with speed and terrain |
| Elite cyclist (sprint) | 1,000-1,500 W | Peak, sustainable for seconds only |
| Electric car motor | 100-300 kW | Continuous road load is much less |
| Household kettle | 2-3 kW | Electrical power |
| Small gasoline engine | 3-15 kW | Lawnmower, chainsaw range |
| Passenger jet engine | 50-100 MW | Each engine at take-off thrust |
| Large power station | 500 MW - 1.5 GW | Coal, gas, or nuclear plant |
Approximate continuous mechanical or electrical power for common devices and activities.
Frequently asked questions
What is the difference between work and energy?
Work and energy are measured in the same unit (the joule) and are closely related but distinct concepts. Energy is a property a system possesses, while work is the process of transferring energy from one system to another via a force acting over a distance. When you do 500 J of work on an object, you transfer 500 J of energy into it, typically as kinetic or potential energy.
Why does the angle matter in the work formula?
Only the component of force that acts along the direction of motion does mechanical work. If you pull a suitcase at 45 degrees above horizontal, the cos(45) = 0.707 factor means only about 71% of your pulling force moves the suitcase forward; the rest lifts up against gravity without contributing to horizontal work. At 90 degrees, such as pushing down on top of a box moving horizontally, you do zero work on that horizontal motion no matter how hard you push.
How is horsepower related to watts?
One mechanical horsepower equals exactly 745.7 watts. The unit was defined by James Watt in the 18th century to compare steam engine output against the work a draught horse could sustain. Today horsepower is used mainly for engines, motors, and power tools in countries that have not fully adopted SI units. Electrical horsepower (550 ft-lbf/s) is essentially the same value.
Can power ever be negative?
Yes, in the signed-physics sense. When a force acts opposite to the direction of motion, the work done is negative, and so is the power - the classic example is a braking system absorbing energy from a moving vehicle. In regenerative braking the absorbed kinetic energy is converted back to electrical energy. This calculator uses magnitudes and does not handle signed power; for braking or deceleration problems, apply the formulas with sign conventions manually.
What is the difference between average power and instantaneous power?
Average power is total work divided by total elapsed time (P = W / t). Instantaneous power is the limit of that ratio as the time interval shrinks to zero, equivalent to P = F x v at a specific instant. For constant force and speed these are equal. For varying forces or speeds, such as an athlete sprinting or an engine at changing throttle, you need the instantaneous formula or calculus to find the exact value at any moment.