Power from Work
Power is the rate at which work is done. Given the total work (or energy) and the time taken, this equation yields power in watts. One watt equals one joule per second.
P = W / t
Power from Force and Velocity
When a constant force moves an object at a constant velocity, the power delivered equals force times velocity. Useful for engines, motors, and conveyor systems.
P = F × v
Electrical Power
Electrical power equals voltage multiplied by current. This is the fundamental equation for sizing circuits, selecting wire gauges, and calculating energy consumption.
P = V × I
Power from Displacement
When force acts over a displacement in a given time, power equals force times displacement divided by time. This combines the work and rate concepts into one formula.
P = F × d / t
How It Works
Power measures how fast energy is transferred or work is done. This calculator supports four formulas: P = W/t (work over time), P = F·v (force times velocity), P = V·I (voltage times current), and P = Fd/t (force times displacement over time). The SI unit is the watt (W), equal to one joule per second.
Example Problem
An engine exerts 200 N of force on a car moving at 15 m/s. What power does it deliver?
- P = F × v = 200 × 15 = 3,000 W (3 kW)
In electrical terms, a 120 V outlet supplying 10 A delivers 120 × 10 = 1,200 W.
When to Use Each Variable
- Solve for Power (Work) — when you know the total work or energy and the time taken, e.g., calculating the power output of an engine from dynamometer data.
- Solve for Power (Force × Velocity) — when a constant force moves an object at a steady speed, e.g., determining motor power for a conveyor belt.
- Solve for Electrical Power — when you know voltage and current, e.g., sizing a circuit breaker or calculating appliance energy consumption.
- Solve for Power (Displacement) — when force acts over a distance in a given time, e.g., calculating the power needed to push a piston a certain stroke length.
Key Concepts
Power is the rate of doing work or transferring energy, measured in watts (1 W = 1 J/s). It can be expressed as work over time (P = W/t), force times velocity (P = Fv), voltage times current (P = VI), or force times displacement over time (P = Fd/t). These are all equivalent — they just use different known quantities.
Applications
- Electrical systems: sizing circuit breakers and wiring based on P = VI for appliance loads
- Automotive engineering: calculating engine power output from dynamometer force and roller speed measurements
- Manufacturing: determining motor power requirements for conveyor belts moving loads at constant speed
- Fitness science: measuring human power output during cycling or weightlifting exercises
Common Mistakes
- Confusing power and energy — power is a rate (joules per second), energy is the total (joules); running a 100 W bulb for 10 hours uses 1,000 Wh of energy
- Forgetting efficiency losses in P = VI — the electrical power input is always higher than mechanical output due to motor and friction losses
- Using inconsistent units — mixing feet with newtons or pounds with meters gives nonsensical results; verify all values are in the same unit system before calculating
Frequently Asked Questions
What is the difference between power and energy?
Energy is the total amount of work done or heat transferred (measured in joules). Power is the rate at which that energy is used (joules per second, or watts). A 100 W bulb uses 100 J every second.
How do you convert watts to horsepower?
One mechanical horsepower equals about 745.7 W. Divide watts by 745.7 to get HP. For example, 3,000 W ÷ 745.7 ≈ 4.02 HP.
What is a kilowatt-hour?
A kilowatt-hour (kWh) is a unit of energy, not power. It equals the energy consumed by a 1 kW device running for one hour: 1 kWh = 3.6 MJ.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.
Related Calculators
- Work Calculator — calculate work from force and displacement.
- Kinetic Energy Calculator — find the energy of a moving object.
- Force Equation Calculator — determine the force component of P = Fv.
- Horsepower Calculator — convert between horsepower and watts for engines and motors.
- Ohm's Law Calculator — compute electrical power from voltage and current.
- Power Unit Converter — convert between watts, kilowatts, and horsepower.
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Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.