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RPM to rad/s

Reviewed08·2026

One revolution is 2 pi radians and one minute is sixty seconds; put together they give the exact factor 2 pi over 60. The tool below converts both directions, and the page shows why the radian version is the one physics equations demand.

By Oliver Wakefield-Smith. Written by Oliver Wakefield-Smith, who maintains the reference tables on this site against manufacturer and standards-body documents.

↔ ×2π/60

3,000 rpm × 2π/60 = 314.16 rad/s

Both directions, worked

exact factor: 2π ÷ 60 = π/30 ≈ 0.104720
3,000 rpm × π/30 = 314.16 rad/s
1,500 rpm × π/30 = 157.08 rad/s
reverse: 100 rad/s × 30/π = 954.9 rpm

The radian is the SI's angle unit and rad/s its angular velocity, per the SI Brochure BIPM SI Brochure2026-08; revolution-based units sit alongside as accepted non-SI forms NIST2026-08. The distinction between rotational frequency (rev/min, Hz) and angular velocity (rad/s) is drawn carefully on the unit page.

Why physics insists on rad/s

Because the calculus does. Angular kinematics (θ = ωt), centripetal acceleration (a = ω²r) and rotational power all assume angles in radians; feed them revolutions and every answer is off by powers of 2π. The paying example:

P = τω
engine: 250 N·m at 3,000 rpm → ω = 314.16 rad/s
P = 250 × 314.16 = 78,540 W ≈ 78.5 kW

Industry quotes the dial number and physics quotes the equation-ready one; the factor π/30 is the entire treaty between them. Frequency proper, the third representation, converts on RPM to Hz.