Calculate synchronous, shaft, driven, and angular speeds. Add poles, slip, and gear ratios for accuracy. Export clean results and learn each conversion step clearly.
Synchronous RPM = (120 × Frequency in Hz) ÷ Poles
Shaft RPM = Synchronous RPM × (1 − Slip ÷ 100)
Driven RPM = Shaft RPM ÷ Gear Ratio
Angular Speed = (2 × π × Shaft RPM) ÷ 60
Period in milliseconds = (1 ÷ Frequency) × 1000
Cycles per minute = Frequency × 60
| Frequency (Hz) | Poles | Slip (%) | Gear Ratio | Synchronous RPM | Shaft RPM | Driven RPM |
|---|---|---|---|---|---|---|
| 50 | 4 | 2 | 1 | 1500 | 1470 | 1470 |
| 60 | 6 | 3 | 2 | 1200 | 1164 | 582 |
| 25 | 8 | 1.5 | 1.5 | 375 | 369.38 | 246.25 |
Hertz and RPM are closely linked in electrical systems. Hertz measures electrical cycles each second. RPM measures mechanical rotation each minute. A convert hertz to RPM calculator helps technicians, students, and engineers move between both values with fewer manual mistakes. It is useful for motors, generators, variable frequency drives, and machine troubleshooting. It also helps during commissioning, maintenance checks, classroom exercises, and speed verification tasks.
The core relation comes from synchronous motor speed. Electrical frequency and motor pole count determine the theoretical RPM. A four pole motor at 50 hertz runs at 1500 synchronous RPM. A four pole motor at 60 hertz runs at 1800 synchronous RPM. This makes the tool useful for comparing regional power standards, drive settings, and equipment nameplate expectations. It also supports quick checks when a machine must match a target operating speed.
Real machines also have slip. Induction motors usually run slightly below synchronous speed. That difference affects shaft RPM, fan speed, conveyor movement, and pump performance. A good calculator includes slip so users can estimate real operating speed, not just ideal speed. This matters when sizing belts, matching driven equipment, and checking expected output under load. It also helps explain why measured speed can differ from catalog speed.
Gear ratio adds another practical layer. Many electrical systems drive reducers, pulleys, or gearboxes. Even if the motor shaft speed is correct, the final driven RPM can be much lower. By including gear ratio, the calculator becomes more useful for design reviews, maintenance planning, and production settings where output speed matters most. This reduces guesswork and supports clearer documentation for teams. It also simplifies handover notes between electrical and mechanical staff.
This page also shows angular velocity, period, and cycles per minute. Those extra values help when linking electrical frequency with mechanical motion, sensor timing, and control logic. Students can learn the concept faster. Professionals can document results clearly and export them for reports or field records. Use this calculator when selecting motors, checking VFD settings, estimating machine speed, or preparing electrical training material. The formulas, example table, downloads, and FAQ section make the tool practical for daily electrical work. Clear output tables also support audits, inspections, and preventive maintenance planning.
Use synchronous RPM = 120 × hertz ÷ poles. This gives theoretical motor speed before slip. Real shaft speed is slightly lower for most induction motors.
Pole count changes the synchronous speed. More poles mean lower RPM at the same frequency. That is why 50 hertz does not create the same speed for every motor.
Slip is the percentage difference between synchronous speed and actual rotor speed. It appears in induction motors under load and reduces the final shaft RPM.
Driven RPM equals shaft RPM divided by gear ratio. In this calculator, gear ratio means motor RPM divided by output RPM. A ratio above one lowers output speed.
Yes. Enter the VFD output frequency instead of supply frequency. The calculator then estimates synchronous speed, shaft speed, and driven speed for that operating point.
Angular speed in radians per second helps when connecting motor rotation to control systems, motion equations, sensor timing, and mechanical design calculations.
Yes. Add a comma separated batch list of frequencies. The calculator creates a table for all values, which is helpful for testing ranges and export tasks.
Not always. Synchronous RPM is the ideal magnetic field speed. Actual shaft RPM is lower when slip exists, especially in loaded induction motors.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.