information:extraction, structural:reformatting, stylistic:style_transfer, stylistic:tone
Conversion to other units

A conversion factor may be necessary when using different units of power or torque. For example, if rotational speed (unit: revolution per minute or second) is used in place of angular speed (unit: radian per second), we must multiply by 2 π radians per revolution. In the following formulas, P is power, τ is torque, and ν (Greek letter nu) is rotational speed.

P = τ ⋅ 2 π ⋅ ν {\displaystyle P=\tau \cdot 2\pi \cdot \nu }

Showing units:

P W = τ N ⋅ m ⋅ 2 π r a d / r e v ⋅ ν r e v / s {\displaystyle P_{\rm {W}}=\tau _{\rm {N{\cdot }m}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/s}}}

Dividing by 60 seconds per minute gives us the following.

P W = τ N ⋅ m ⋅ 2 π r a d / r e v ⋅ ν r e v / m i n 60 s / m i n {\displaystyle P_{\rm {W}}={\frac {\tau _{\rm {N{\cdot }m}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/min}}}{\rm {60~s/min}}}}

where rotational speed is in revolutions per minute (rpm, rev/min).

Some people (e.g., American automotive engineers) use horsepower (mechanical) for power, foot-pounds (lbf⋅ft) for torque and rpm for rotational speed. This results in the formula changing to:

P h p = τ l b f ⋅ f t ⋅ 2 π r a d / r e v ⋅ ν r e v / m i n 33, 000. {\displaystyle P_{\rm {hp}}={\frac {\tau _{\rm {lbf{\cdot }ft}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/min}}}{33,000}}.}

The constant below (in foot-pounds per minute) changes with the definition of the horsepower; for example, using metric horsepower, it becomes approximately 32,550.

The use of other units (e.g., BTU per hour for power) would require a different custom conversion factor.