Aisha K.
Mar 12, 2026
Clean layout and the results update instantly. Exactly what I needed for a quick planning check.
Unit Converters
Angular Velocity: RPM to Radians per Second
rad/s = rpm × 2π / 60 = rpm × π / 30.
ω = rpm × 2π / 60. A 1,800 rpm motor is 188.5 rad/s. Synchronous 60 Hz four-pole machines sit near 1,800 rpm before slip. The shaft does not care about degrees unless you convert again.
Revolutions per minute
rpm → rad/s
188.496 rad/s
60 rpm → 6.283 rad/s (1 rev/s). 1800 rpm → 188.5 rad/s.
- You typed
- 1,800 rpm
- One rad/s is
- 9.549 rpm
- How it’s calculated
- rad/s = rpm × 2π / 60 = rpm × π / 30.
Plain-English guide
Terms & how it works
Confused by a field? Read the short definitions here while you use the tool.
Revolutions per minute
The “Revolutions per minute” value used in this tool’s formula. Adjust it to see results update live.
How this calculator works
ω = rpm × 2π / 60. A 1,800 rpm motor is 188.5 rad/s. Synchronous 60 Hz four-pole machines sit near 1,800 rpm before slip. The shaft does not care about degrees unless you convert again. rad/s = rpm × 2π / 60 = rpm × π / 30. Example: 60 rpm → 6.283 rad/s (1 rev/s). 1800 rpm → 188.5 rad/s.
rad/s = rpm × 2π / 60 = rpm × π / 30.
Example: 60 rpm → 6.283 rad/s (1 rev/s). 1800 rpm → 188.5 rad/s.
When to use this RPM to rad/s
Common use cases
- ω = rpm × 2π / 60. A 1,800 rpm motor is 188.5 rad/s. Synchronous 60 Hz four-pole machines sit near 1,800 rpm before slip. The shaft does not care about degrees unless you convert again.
- Sanity-check with this case: 60 rpm → 6.283 rad/s (1 rev/s). 1800 rpm → 188.5 rad/s.
- The relationship is: rad/s = rpm × 2π / 60 = rpm × π / 30.
Localized examples
- Unit Converters: the example on this page uses the same formula as the widget.
What you get
- Fields: Revolutions per minute
- rad/s = rpm × 2π / 60 = rpm × π / 30.
- Example on the page: 60 rpm → 6.283 rad/s (1 rev/s). 1800 rpm → 188.5 rad/s.
How to Convert RPM to rad/s Step-by-Step
- 1Enter Revolutions per minute. Use the values you have, not a catalog average, unless that is all you know.
- 2rad/s = rpm × 2π / 60 = rpm × π / 30.
- 3Worked case: 60 rpm → 6.283 rad/s (1 rev/s). 1800 rpm → 188.5 rad/s.
- 4Check which dictionary the other person is using — US or UK, decimal or 1,024 — then trust the number.
Governing formula
rad/s = rpm × 2π / 60 = rpm × π / 30.
60 rpm → 6.283 rad/s (1 rev/s). 1800 rpm → 188.5 rad/s.
Example: set Revolutions per minute = 1,800, then read the result.
Variable definitions
- value
Revolutions per minute
The “Revolutions per minute” field. Default 1800; typical range 0–100000.
- The conversion (rad/s = rpm × 2π / 60 = rpm × π / 30.) does not pick US vs UK gallons, SI vs binary megabytes, or Mach at altitude for you. Read the footnote on the page.
- Nothing here is uploaded for the calculation itself.
Frequently Asked Questions
rpm / 60 = revolutions per second. Not rad/s unless you multiply by 2π.
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4.8
out of 5.0
4 reviews
Daniel R.
Feb 28, 2026
Very usable on mobile. Would love a save/export option later, but the math feels solid.
Priya S.
Feb 3, 2026
The FAQ section answered my questions before I even had to search. Smooth dark mode too.
Marcus L.
Jan 19, 2026
Simple inputs, clear outputs. This replaced three bookmarks I used to juggle.
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