Calculate the work done by a force over a distance at an angle, and the average power when the time is known, in joules, watts and horsepower.
N
m
°
s
Enter the values to see the result here.
Formula
W=FdcosθP=tW
where F is the force in newtons, d the distance in metres, θ the angle between the force and the direction of motion and t the time in seconds. One horsepower is 745.7 W.
Worked example
A person pulls a crate 20 m with a rope at 30° above the horizontal, with a force of 100 N, in 40 s.
Work: 100×20×cos30°=1732 J.
Power: 1732/40=43.3 W.
In horsepower: 43.3/745.7=0.058 hp.
Common mistakes
Using the angle between the force and the vertical instead of the direction of motion.
Entering minutes or hours for the time. It must be in seconds.
Counting work for a force that does not move anything, such as pushing on a wall.
Confusing watts (power) with watt-hours (energy) on a bill.
Frequently asked questions
Why is there an angle?
Only the part of the force that points along the motion does work. Pulling a sled with a rope at 30 degrees above the ground uses cos 30° = 0.87 of the force to move it forward; the rest lifts it.
What is the difference between work and power?
Work is the energy transferred, in joules. Power is how fast it is transferred, in watts (joules per second). Lifting the same box takes the same work whether you do it in one second or ten, but needs ten times the power in one second.
How many watts is a horsepower?
One mechanical horsepower is about 745.7 W. Metric horsepower (PS) is 735.5 W, so car power figures in hp and PS differ by about 1.4 percent.