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.
| Poles | Synchronous RPM | Full-Load RPM | Sync Angular Speed (rad/s) | Full-Load rad/s | Frequency (Hz) |
|---|---|---|---|---|---|
| 2 Poles | 3,600 RPM | 3,450 RPM | 120π ≈ 376.991 | 115π ≈ 361.283 | 60 Hz |
| 4 Poles | 1,800 RPM | 1,750 RPM | 60π ≈ 188.496 | 58.33π ≈ 183.260 | 30 Hz |
| 6 Poles | 1,200 RPM | 1,150 RPM | 40π ≈ 125.664 | 38.33π ≈ 120.428 | 20 Hz |
| 8 Poles | 900 RPM | 850 RPM | 30π ≈ 94.248 | 28.33π ≈ 89.012 | 15 Hz |
| 10 Poles | 720 RPM | 680 RPM | 24π ≈ 75.398 | 22.67π ≈ 71.209 | 12 Hz |
| 12 Poles | 600 RPM | 560 RPM | 20π ≈ 62.832 | 18.67π ≈ 58.643 | 10 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.
| Poles | Synchronous RPM | Full-Load RPM | Sync Angular Speed (rad/s) | Full-Load rad/s | Frequency (Hz) |
|---|---|---|---|---|---|
| 2 Poles | 3,000 RPM | 2,850 RPM | 100π ≈ 314.159 | 95π ≈ 298.451 | 50 Hz |
| 4 Poles | 1,500 RPM | 1,450 RPM | 50π ≈ 157.080 | 48.33π ≈ 151.844 | 25 Hz |
| 6 Poles | 1,000 RPM | 950 RPM | 33.33π ≈ 104.720 | 31.67π ≈ 99.484 | 16.67 Hz |
| 8 Poles | 750 RPM | 700 RPM | 25π ≈ 78.540 | 23.33π ≈ 73.304 | 12.5 Hz |
| 10 Poles | 600 RPM | 560 RPM | 20π ≈ 62.832 | 18.67π ≈ 58.643 | 10 Hz |
| 12 Poles | 500 RPM | 460 RPM | 16.67π ≈ 52.360 | 15.33π ≈ 48.171 | 8.33 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.