Velocity Angular / rpm → rad/s
Convert Revolutions per minute to Radians per second
Convert angular speeds between radians, degrees, and revolutions per unit time. Convert Revolutions per minute (rpm) to Radians per second (rad/s). Find the formula, worked examples, unit definitions, and practical guidance below.
Reverse: Radians per second to Revolutions per minute →
How to convert revolutions per minute to radians per second
Angular speed measures rotation, not linear speed. To find tangential speed you also need the radius. Revolutions per minute are divided by 60 when converted to revolutions per second.
Use x for the value in rpm, b for the intermediate value in rad/s, and y for the result in rad/s.
rad/s = rpm × 0.10471975511965977
Worked examples
10 rpm ≈ 1.0471975512 rad/s
Step 1: (10 × 0.10471975512) ≈ 1.0471975512 rad/s.
Step 2: 1.0471975512 ÷ 1 ≈ 1.0471975512 rad/s.20 rpm ≈ 2.09439510239 rad/s
Step 1: (20 × 0.10471975512) ≈ 2.09439510239 rad/s.
Step 2: 2.09439510239 ÷ 1 ≈ 2.09439510239 rad/s.
Results are rounded to 12 significant digits. Converting units does not increase the precision of the original measurement. Very large or small values outside JavaScript’s finite numeric range are rejected.
About Revolutions per minute
Revolutions per minute (rpm) measures velocity angular under the conventions above. The base value in rad/s is (x × 0.10471975512), where x is the numerical value in rpm. Factors shown here are rounded for display; calculations use the stored factor.
About Radians per second
Radians per second (rad/s) measures velocity angular under the conventions above. The base value in rad/s is (x × 1), where x is the numerical value in rad/s. Factors shown here are rounded for display; calculations use the stored factor.
Definitions and sources
Carry the same physical assumptions into subsequent physics calculations.
Revolutions per minute to radians per second reference table
| Revolutions per minute (rpm) | Radians per second (rad/s) |
|---|---|
| 1 | 0.10471975512 |
| 5 | 0.523598775598 |
| 10 | 1.0471975512 |
| 25 | 2.61799387799 |
| 50 | 5.23598775598 |
| 100 | 10.471975512 |
| 1000 | 104.71975512 |
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