Power Calculator

Calculate mechanical power using two methods: P = W/t (work per time) or P = F*v (force times velocity). Choose your method and enter the values.

Power Formulas: Method 1 - Work and Time: P = W / t Where: ? P = Power (Watts, W) ? W = Work done (Joules, J) ? t = Time interval (seconds, s) Method 2 - Force and Velocity: P = F * v Where: ? P = Power (Watts, W) ? F = Force applied (Newtons, N) ? v = Velocity (meters/second, m/s) Unit Conversions: ? 1 W = 1 J/s = 1 N*m/s ? 1 kW = 1000 W ? 1 hp = 745.7 W = 0.7457 kW ? 1 kW = 1.341 hp ? 1 MW = 1,000,000 W Related Concepts: ? Energy = Power * Time (E = P*t) ? Efficiency = (P_out / P_in) * 100% ? Average power = Total work / Total time
Example 1 - Lifting (Work/Time): Work = 2000 J, Time = 5 seconds P = 2000 / 5 = 400 W = 0.4 kW = 0.536 hp Average power: 400 Watts Example 2 - Car Engine (Force/Velocity): Force = 1500 N (drag + resistance), Velocity = 25 m/s (90 km/h) P = 1500 * 25 = 37,500 W = 37.5 kW = 50.3 hp Engine power needed: 37.5 kW Example 3 - Running Uphill: Work = 15,000 J (climbing), Time = 30 seconds P = 15,000 / 30 = 500 W = 0.5 kW = 0.67 hp Human power output: 500 W Example 4 - Electric Motor: Work = 50,000 J, Time = 25 seconds P = 50,000 / 25 = 2000 W = 2 kW = 2.68 hp Motor power rating: 2 kW Example 5 - Cyclist (Force/Velocity): Force = 150 N (pedaling), Velocity = 10 m/s (36 km/h) P = 150 * 10 = 1500 W = 1.5 kW = 2.01 hp Cyclist power: 1500 W (high performance) Example 6 - Pumping Water: Work = 100,000 J, Time = 50 seconds P = 100,000 / 50 = 2000 W = 2 kW Pump power: 2 kilowatts

What is power in physics?

Power is the rate at which work is done or energy is transferred. It measures how quickly energy changes form or moves. Formula: P = W/t (work per time) or P = F*v (force times velocity). Power is measured in Watts (W), where 1 W = 1 J/s.

What is the difference between work and power?

Work is total energy transferred (Joules). Power is the rate of doing work (Joules per second = Watts). Example: lifting 100 kg 2 m does 1960 J of work. If done in 2 seconds, power is 980 W. If in 10 seconds, power is 196 W. Same work, different power.

What are common units for power?

SI unit: Watt (W) = J/s. Other units: kilowatt (kW) = 1000 W, megawatt (MW) = 1,000,000 W, horsepower (hp), where 1 hp = 745.7 W. Conversions: 1 kW = 1.341 hp, 1 hp = 0.746 kW. Electric bills use kWh (kilowatt-hours) for energy.

How do I convert between Watts and horsepower?

Conversions: 1 hp = 745.7 W = 0.7457 kW, and 1 kW = 1.341 hp. To convert: multiply hp by 745.7 to get Watts, or divide Watts by 745.7 to get hp. Example: a 100 hp car engine = 74,570 W = 74.57 kW.

What is mechanical power vs electrical power?

Mechanical power: P = F*v (force times velocity) or P = W/t (work per time), used for engines, motors, mechanical systems. Electrical power: P = V*I (voltage times current), used for circuits. Both measured in Watts. This calculator handles mechanical power.

How does power relate to force and velocity?

For constant force and velocity: P = F*v. This shows power needed to maintain velocity v against force F. Example: car at constant 30 m/s against 500 N air resistance needs P = 500*30 = 15,000 W = 15 kW = 20 hp to maintain speed.

What is average power vs instantaneous power?

Average power is total work divided by total time: P_avg = W_total/t_total. Instantaneous power is power at a specific moment: P = dW/dt (calculus) or P = F*v at that instant. This calculator computes average power from work/time or instantaneous from force/velocity.

What is power efficiency?

Efficiency = (useful power output / power input) * 100%. No machine is 100% efficient due to friction, heat loss, etc. Example: electric motor with 1000 W input and 850 W output has 85% efficiency. The other 150 W becomes waste heat.

What are real-world examples of power calculations?

Examples: car engine power (hp or kW), electric appliance consumption (W or kW), human athletic power (cycling, running), solar panel output, wind turbine generation, electric motor ratings, and industrial machinery power requirements.

How much power does a human produce?

Average human: ~100 W sustained (walking). Athletic: 200-400 W sustained (cycling, rowing). Peak: up to 2000 W for seconds (sprinting, jumping). Professional cyclists: 300-400 W for hours. Elite sprinters: >2000 W briefly. Compare to a 1500 W hair dryer.

What is the difference between power and energy?

Energy is the capacity to do work (Joules). Power is the rate of using energy (Watts = Joules/second). Example: a 100 W light bulb uses 100 J every second. Run for 10 seconds = 1000 J total energy. Power = rate, Energy = total amount.

How do I calculate power if I know work and time?

Use P = W/t, where W is work (Joules) and t is time (seconds). Example: if you do 5000 J of work in 10 seconds, P = 5000/10 = 500 W. Or if lifting requires 2000 J and takes 4 s, P = 2000/4 = 500 W average power.