Power Calculator

Power describes the rate at which work is done or energy is transferred. This power tool allows calculations in four different ways: using work and time, force and velocity, force times distance divided by time, or torque and rotational speed. Select the method that matches your known conditions, enter the corresponding values, and leave the field for the value you want to calculate blank. The tool will then determine the result.

What is power?

Power is the rate at which work is done, or the rate at which energy is transferred from one form to another. If two people carry identical boxes up an identical number of stairs, they do the same amount of work. However, the person who runs up the stairs faster has a higher power because he took less time to do the work.

The SI unit of power is the watt (W). The name was given to it by Scottish engineer James Watt. One watt equals one joule per second. Since power is a scalar quantity, it has only magnitude and no direction. A 1500-watt kettle, a 100-watt light bulb, and an automobile engine whose rated power is in kilowatts are all measured by the same unit of measure.

Calculate average power from work and time

The most common definition of power is the division of work done by time taken.

W is work in joules, t is time in seconds and the result of P has the unit watt. Suppose a small motor does 2450 Joule of work in 8 seconds. In this case average power is the value obtained by dividing 2450 by 8 which is approximately 306 watts. By rearranging the same relationship, one can calculate work when power and time are known or calculate time when work and power are known.

Calculation of instantaneous power from force and speed:

If a constant force acts on a moving object, the instantaneous power is the product of the force and the velocity along the direction of the force.

This can be directly derived from the definition of work. Work is force times distance and speed is distance over time. So if a car has a driving force of 500 newtons and it's going at a speed of 20 meters per second, then it must be putting out 10,000 watts or 10 kilowatts to maintain that motion.

Calculation of power from force, distance and time:

Sometimes the force and distance are known instead of the velocity. Since work is the product of force and distance, these two concepts can be combined to get a corresponding formula.

Suppose it takes 15 seconds to lift a load of 850 newtons by 10 meters. The work is 8,500 joules, which is the product of 850 and 10. Dividing this by 15 seconds gives about 567 watts. Because this method also shows the work done and average speed, you can check these values with two other formulas. Conversely: What force is required to move an object with a motor of 50 watts over a distance of 25 meters in 6 seconds? The answer is 12 newtons.

Calculation of rotational power from torque and speed

Since motors, turbines and other rotating devices deliver power through a rotational axis, this power is not dependent on linear force but rather the torque and speed.

where τ is the torque in newton metres and ω is the angular velocity in radians per second. Since rotational speed is usually quoted in revolutions per minute (rpm), a calculation tool will first convert this to radians per second before multiplying. If an engine produces 100 Nm of torque at 3,000 rpm, then it will produce about 31,400 watts of power, which is roughly 31.4 kW or 42 mechanical horsepower.

Watts, kilowatts, horsepower

Since the range of power we use on a daily basis is so large it can be useful to change units. A kilowatt is 1000 watts and a megawatt is one million watts. The horsepower is an older unit but still commonly used for motors. One mechanical horsepower is approximately equal to 745.7 watts. In the results you can directly change the unit of the answer to either watts, kilowatts, megawatts or horsepower.

This is how this calculation tool works:

Select a method from the top. Each method will only show the fields that are required, so for example the torque value won't be shown next to a stopwatch. Enter known values and leave unknown fields blank. The calculator will then calculate the result for that field and display it both in the field itself and in a separate results area.

Each field has a units menu. Time can be entered in seconds, minutes or hours, distance in centimeters or feet and speed in kilometers per hour. Power is shown in either watts or horsepower. The calculator will convert between the units so you can mix different units as appropriate for your problem.