How to convert RPM to radians

Written by stephen byron cooper | 13/05/2017
How to convert RPM to radians
RPM and radians measure different properties of circles. (Jupiterimages/Comstock/Getty Images)

RPM measures the number of times a circle turns on its access in a minute. It is “revolutions per minute.” A radian is an angle created by mapping the radius of a circle to its perimeter. This shows that RPM and radians are units of measure for two quite different things. RPM is a unit with respect to time, but radians are not. There is a common unit of measure that expresses radian with respect to time and that is radians per second, or rad/s. It is possible to convert RPM to rad/s.

Translate your RPM figure into radians per minute. To get the most accurate calculation use a calculator that has a “pi” button. Pi is represented by the symbol “π” and has a very large numbers of decimal places. The more decimal places you go to with π the more accurate your results will be. Multiply the RPM by 2 and then multiply that by π ( 3.14159).

Convert the radians per minute into rad/s. There are 60 seconds in a minute so divide the radians per minute number by 60.

Obtain a figure for radians by setting a specific time for your measurement. For example, if you want to convert 100 RPM to radians, and you want to know how many radians that gives you in an hour, get the radians per second through (100 x 2 x π)/60, which gives 10.47197 rad/s. Multiply this out to an hour through 10.47197 x 60 x 60 which gives 37,699.08 radians.

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