RPM to Radians Per SecondRPM to rad/s
Metrology & Kinematics Quick Reference Cheatsheet

Rotational Velocity & Motor Speeds Reference Chart

Standard induction motor synchronous speeds, full-load slip estimations, and exact SI angular velocities (BIPM / NIST / DIN 1301)

Key Analytical Conversion Formulas

RPM to Angular Velocity (rad/s):ω = RPM × (π / 30)
Angular Velocity to RPM:RPM = ω × (30 / π)
Tangential Linear Speed (m/s):v = ω · r
Centripetal Acceleration (m/s²):a_c = ω² · r = v² / r

1. 60 Hz Grid Motor Speeds (NEMA Standard — US / Canada / Latin America)

Calculated for 3-phase induction motors with typical 2.5%–3% full-load slip.

PolesSynchronous RPMFull-Load RPMSync Angular Speed (rad/s)Full-Load rad/sFrequency (Hz)
2 Poles3,600 RPM3,450 RPM120π ≈ 376.991115π ≈ 361.28360 Hz
4 Poles1,800 RPM1,750 RPM60π ≈ 188.49658.33π ≈ 183.26030 Hz
6 Poles1,200 RPM1,150 RPM40π ≈ 125.66438.33π ≈ 120.42820 Hz
8 Poles900 RPM850 RPM30π ≈ 94.24828.33π ≈ 89.01215 Hz
10 Poles720 RPM680 RPM24π ≈ 75.39822.67π ≈ 71.20912 Hz
12 Poles600 RPM560 RPM20π ≈ 62.83218.67π ≈ 58.64310 Hz

2. 50 Hz Grid Motor Speeds (IEC / DIN Standard — Europe / Asia / Africa)

Calculated for standard industrial motors operating on European and international 50 Hz AC supply networks.

PolesSynchronous RPMFull-Load RPMSync Angular Speed (rad/s)Full-Load rad/sFrequency (Hz)
2 Poles3,000 RPM2,850 RPM100π ≈ 314.15995π ≈ 298.45150 Hz
4 Poles1,500 RPM1,450 RPM50π ≈ 157.08048.33π ≈ 151.84425 Hz
6 Poles1,000 RPM950 RPM33.33π ≈ 104.72031.67π ≈ 99.48416.67 Hz
8 Poles750 RPM700 RPM25π ≈ 78.54023.33π ≈ 73.30412.5 Hz
10 Poles600 RPM560 RPM20π ≈ 62.83218.67π ≈ 58.64310 Hz
12 Poles500 RPM460 RPM16.67π ≈ 52.36015.33π ≈ 48.1718.33 Hz
Academic Benchmark Note: In college physics homework (Halliday & Resnick, Serway & Jewett), the frequently assigned problem value of 5.36 rad/s converts to exactly 51.18423 RPM (reciprocal calculation: $5.36 \times 30/\pi$). See the full textbook solution in our 5.36 rad/s guide.