Conversion Formulas

From	To rad/s	To RPM
1 RPM	π/30 ≈ 0.10472	1
1 rad/s	1	30/π ≈ 9.5493
1 deg/s	π/180 ≈ 0.01745	1/6 ≈ 0.1667
1 rev/s	2π ≈ 6.2832	60
1 Hz	2π ≈ 6.2832	60

Common Motor Speeds

Poles	50 Hz Sync	50 Hz Typical	60 Hz Sync	rad/s (50 Hz)
2	3000	2940	3600	314.2
4	1500	1460	1800	157.1
6	1000	970	1200	104.7
8	750	720	900	78.5

Angular Velocity in Engineering

Angular velocity is fundamental in rotating machinery calculations:

• Centripetal acceleration: a = ω² × r
• Unbalance force: F = m × e × ω²
• Torque-power relation: P = T × ω (where P in watts, T in Nm, ω in rad/s)
• Angular momentum: L = I × ω
• Kinetic energy: KE = ½ × I × ω²
• Frequency: f = ω / (2π)

Quick Mental Conversions

RPM	rad/s (approx)	Hz	Typical Use
60	6.28	1	Slow agitators
300	31.4	5	Slow pumps
750	78.5	12.5	8-pole motors (50 Hz)
1000	104.7	16.7	6-pole motors (50 Hz)
1500	157.1	25	4-pole motors (50 Hz)
3000	314.2	50	2-pole motors (50 Hz)
3600	377.0	60	2-pole motors (60 Hz)
10000	1047	166.7	Turbochargers
50000	5236	833	Dental drills, micro turbines

Tip: Memorize π/30

The conversion factor from RPM to rad/s is π/30 ≈ 0.10472. So:

• 1000 RPM × 0.10472 ≈ 104.7 rad/s
• 1500 RPM × 0.10472 ≈ 157.1 rad/s
• 3000 RPM × 0.10472 ≈ 314.2 rad/s (≈ 100π)