Rad/s to RPM
Convert radians per second to RPM for motor specs, machinery datasheets and physics formulas. Multiply by 9.5493 for instant conversion.
Last updated: May 2026
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Radians per second and revolutions per minute: rotational speed
Radians per second (rad/s) is the SI unit of angular velocity, used in physics, control systems, and motor specifications. Revolutions per minute (RPM) is the intuitive measure — how many full rotations occur in 60 seconds. The conversion factor is π × 2 ÷ 60 ≈ 9.549. One full rotation = 2π radians; thus 1 RPM = 2π/60 rad/s.
Engineers and programmers often work in rad/s (it appears in torque, angular acceleration, and feedback control formulas), while technicians and shop equipment use RPM (drill speed, motor nameplates, centrifuge dials). Converting between them is essential when comparing a motor's theoretical control model (rad/s) with its practical nameplate speed (RPM) or when programming a motor controller.
Common reference values
| rad/s | RPM |
|---|---|
| 6.283 | 60 |
| 12.566 | 120 |
| 104.72 | 1000 |
| 314.159 | 3000 |
Frequently Asked Questions
Why does a motor specify both rad/s and RPM?
A motor's nameplate lists RPM because it's intuitive for operators (how many spins per minute). But control systems and torque calculations use rad/s because angular acceleration and angular momentum are defined in rad/s² and kg⋅m²/s. Both describe the same physical rotation, just in different units.
What is the exact conversion formula?
RPM = rad/s × 60 ÷ (2π) = rad/s × 9.54929659. The factor 2π converts radians back to rotations; dividing by 60 converts seconds to minutes. Conversely, rad/s = RPM × (2π) ÷ 60.
When would I need this conversion?
When programming a motor controller with a theoretical speed (rad/s) but the physical motor is rated in RPM. Also when comparing sensor data (often in rad/s) with equipment nameplates or when converting between research papers (physics, rad/s) and practical manuals (RPM).