Have you ever looked at the specs of an engine in a magazine and
seen something like "this engine makes 300 pound-feet of torque
at 4,000 RPM," and wondered how much power that was? How much
horsepower are we talking about here? You can calculate how many
foot-pounds of horsepower this engine produces using a common
equation:

**(Torque x Engine speed) / 5,252 = Horsepower**
The engine that makes 300 pound-feet of torque at 4,000 RPM
produces [(300 x 4,000) / 5,252] 228 horsepower at 4,000 RPM. But
where does the number 5,252 come from?

To get from pound-feet of torque to horsepower, you need to go
through a few conversions. The number 5,252 is the result of
lumping several different conversion factors together into one
number.

First, 1 horsepower is defined as 550 foot-pounds per second
The units of torque are pound-feet. So to get from torque to
horsepower, you need the "per second" term. You get that by
multiplying the torque by the engine speed.

But engine speed is normally referred to in revolutions per
minute (RPM). Since we want a "per second," we need to convert
RPMs to "something per second." The seconds are easy -- we just
divide by 60 to get from minutes to seconds. Now what we need is a
dimensionless unit for revolutions: a radian. A radian is actually
a ratio of the length of an arc divided by the length of a radius,
so the units of length cancel out and you're left with a
dimensionless measure.

You can think of a revolution as a measurement of an angle. One
revolution is 360 degrees of a circle. Since the circumference of
a circle is (2 x pi x radius), there are 2-pi radians in a
revolution. To convert revolutions per minute to radians per
second, you multiply RPM by (2-pi/60), which equals 0.10472
radians per second. This gives us the "per second" we need to
calculate horsepower.

Let's put this all together. We need to get to horsepower,
which is 550 foot-pounds per second, using torque (pound-feet) and
engine speed (RPM). If we divide the 550 foot-pounds by the
0.10472 radians per second (engine speed), we get 550/0.10472,
which equals 5,252.

So if you multiply torque (in pound-feet) by engine speed (in
RPM) and divide the product by 5,252, RPM is converted to "radians
per second" and you can get from torque to horsepower -- from
"pound-feet" to "foot-pounds per second."