Convert angular velocity between radian per second (rad/s) and revolutions per minute (RPM). 1 RPM = 0.10472 rad/s. Formula and table free.
Angular velocity measures how fast an object rotates around an axis — that is, the rate of change of an angle over time. The SI unit is the radian per second (rad/s), while revolutions per minute (RPM) is the more familiar everyday unit, used to describe engines, fans, hard drives, and power drills. The relationship between the two units comes from the very definition of the radian: one full turn equals 2π radians (approximately 6.2832 rad). Since 1 minute has 60 seconds, 1 RPM corresponds to 2π ÷ 60 rad/s, that is, approximately 0.10472 rad/s. Inverting, 1 rad/s equals 60 ÷ (2π), approximately 9.5493 RPM. This conversion is essential for mechanical and electrical engineers specifying motors and gearboxes, maintenance technicians comparing catalogs in different units, control systems and robotics designers (where rotation math works in rad/s, but sensors and manuals often use RPM), and physics students who need to move from everyday language (RPM) to the language of angular calculations (rad/s).
1 RPM equals approximately 0.10472 rad/s (2π ÷ 60).
1 rad/s equals approximately 9.5493 RPM (60 ÷ 2π).
Multiply the value in RPM by 2π and divide by 60 (or multiply by 0.10472).
Because the radian is defined by the arc whose length equals the radius; the circle perimeter is 2π times the radius.
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