Work and Power Calculator
Calculate power from work and time, force and speed, lifting and acceleration, and turn watts into kilowatt-hours and cost.
🏋️ What is a Work and Power Calculator?
Power is the rate at which work is done or energy is transferred. If work W is done in a time t, the average power is P = W / t, measured in watts, where one watt is one joule per second. This work and power calculator solves that equation for whichever of the three quantities you do not know, and it reports the power in watts, kilowatts and horsepower so that it fits an engine rating, a motor label or a gym machine display. It is built around the questions people ask about power in practice, which is why it has separate modes for force and speed, for a constant force acting from rest, for lifting and stair climbing, and for the cost of electrical energy.
The page is deliberately different from the general work, energy and power calculator, which links work to kinetic and potential energy in four short modes. Here the focus is on power itself. The force-and-speed mode uses the instantaneous form P = F v cos(theta), which tells you how much power a car needs to hold a speed against drag. The constant-force mode shows the often surprising result that the average power from rest is half the instantaneous power at the end. The lifting mode takes efficiency into account so that you can see input power and food Calories as well as useful output. The cost mode turns watts into kilowatt-hours and into money. For the work side of the story alone, use the work calculator.
A few distinctions matter. Power is not energy: a kilowatt is a rate, a kilowatt-hour is an amount. Power is not force either, although they are linked through speed. A strong person lifting slowly and a weaker person lifting quickly can produce the same power. And horsepower is not one number. Mechanical horsepower is 745.6999 W and metric horsepower is 735.49875 W, so the unit you choose changes the figure by about 1.4 percent. Use the watt converter when you need to move between many power units, including BTU per hour and dBm.
Typical uses include sizing a motor or winch for a given lift, estimating the power of a sprint up a staircase, checking an engine rating against the drag on a vehicle, and comparing the running cost of heaters, kettles and computers. Because every result is shown with its working, the page doubles as a way to check homework steps.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Power from Work and Time
A hoist does 4500 J of work in 30 seconds
Example 2 — Time for a Given Work
A 1500 W heater must supply 90000 J. How long does it take?
Example 3 — A Car Against Drag
A car holds 25 m/s against 600 N of total resistance
Example 4 — Average vs Instantaneous Power
A 1000 kg car feels a constant net force of 3000 N for 8 seconds from rest
Example 5 — Climbing a Staircase
A 70 kg person climbs 3 m in 4 seconds, with muscles that are 25 percent efficient
Example 6 — Running a Heater
A 1500 W heater runs 6 hours a day for 30 days at 0.15 per kWh
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for power in physics?
Average power is P = W / t, work divided by the time taken, in watts. For a force acting on a moving object the instantaneous power is P = F v cos(theta). One watt is one joule per second.
How do you calculate power from work and time?
Divide the work in joules by the time in seconds. 4500 J done in 30 s is 150 W. To get horsepower divide the watts by 745.7.
What is the difference between work and power?
Work is the energy transferred, in joules. Power is how fast the energy is transferred, in watts. Lifting a crate 3 m takes the same work whether it takes 2 s or 20 s, but the quick lift needs ten times the power.
What is the difference between average and instantaneous power?
Average power is total work over total time. Instantaneous power is F v at one moment. For a constant force from rest the final instantaneous power is exactly twice the average, because the speed rises linearly.
How many watts is one horsepower?
One mechanical horsepower is 745.6999 W, or 550 foot-pounds per second. Metric horsepower is 735.49875 W. A 15 kW engine output is about 20.1 mechanical hp.
How do you find the power needed to lift something?
Work is m g h and power is that work divided by the time. Lifting 70 kg by 3 m in 4 s needs 70 x 9.80665 x 3 / 4 = 514.85 W, about 0.69 hp.
How do you convert watts to kilowatt-hours?
Multiply the power in kilowatts by the time in hours. A 1500 W (1.5 kW) heater running for 6 hours uses 9 kWh. One kWh is 3.6 million joules.
How do you calculate the cost of running an appliance?
Energy in kWh is the power in kW times the hours used. Multiply by the price per kWh. 1.5 kW for 6 hours a day for 30 days is 270 kWh, and at 0.15 per kWh the cost is 40.50.
How is power related to force and speed?
P = F v. A car holding 25 m/s against 600 N of drag must deliver 15 000 W, or 15 kW. At twice the speed the drag is larger and the power needed rises even faster.
Why does efficiency matter for power?
Efficiency is useful output over total input. If the climber's muscles are 25 percent efficient, the 514.85 W of useful power is produced from 2059.40 W of input power.