VFD Frequency ↔ Motor RPM Calculator

Synchronous speed from drive Hz and poles, slip from the nameplate, approximate actual and gearbox output speed, and the Hz needed for a target rpm.

Nameplate rated frequency (Hz)Nameplate rated speed (r/min)Poles

Output frequency (Hz)Gear ratio (1 = direct)

Results
Synchronous speed
Rated slip (nameplate)
Speed (approx., same slip rpm)
Gearbox output speed (approx.)

Target output shaft speed (r/min)

The defaults (60 Hz, 4 poles, 1750 r/min, 30 Hz, ratio 10) are an example. Take the poles and rated speed from the motor nameplate.

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Formulas

4-pole motor at 60 Hz: synchronous 1800 r/min, rated 1750 r/min, the 50 r/min difference is slip. At 30 Hz: synchronous 900 r/min, about 850 r/min with the same slip — Synchronous speed scales with frequency; the actual speed is lower by the slip.

Synchronous speed ns (r/min) = 120 × f ÷ poles
Slip s = (ns − n) ÷ ns, slip speed = ns − n
Rated slip (Hz) = rated frequency − rated speed × poles ÷ 120
Speed at f ≈ 120 × f ÷ poles − rated slip speed (approximation)
Required frequency ≈ (target rpm × gear ratio + slip speed) × poles ÷ 120

An induction motor runs slightly slower than synchronous speed (slip). A 4-pole motor at 60 Hz has a synchronous speed of 1800 r/min, but its nameplate says something like 1750 r/min — the 50 r/min difference is the slip at rated load. Expressed in hertz (60 − 1750 × 4 ÷ 120 ≈ 1.67 Hz) it has the same form as a drive's «rated slip» parameter (e.g. YASKAWA A1000 E2-02).

Why «approximate»

Below base frequency with constant V/f, the slip speed at a given torque is taken as nearly unchanged. So 30 Hz on a 4-pole motor gives a 900 r/min synchronous speed minus 50 r/min, about 850 r/min.
Real slip changes with load torque: closer to synchronous speed when lightly loaded, slower when heavily loaded.
With slip compensation or vector control, the drive raises the frequency by the slip to hold the commanded speed, so the synchronous figure is closer to reality.
Nameplate speed has a tolerance too. ABB's Motor guide gives, after IEC 60034-1, a slip tolerance of ±20 % (1 kW and above) and ±30 % (below 1 kW).

Synchronous speed by poles (r/min)

Poles	50 Hz	60 Hz	10 Hz	30 Hz	90 Hz
2	3000	3600	600	1800	5400
4	1500	1800	300	900	2700
6	1000	1200	200	600	1800
8	750	900	150	450	1350
10	600	720	120	360	1080
12	500	600	100	300	900

The rpm shown on the drive

Drives can display output frequency converted to rpm using the pole setting. On the LS S300, DRV-32 (Hz/rpm Select) = 1 switches to rpm, and the value depends on the pole number setting (MOT1, 2-25; 4-pole basis). On the YASKAWA A1000, o1-03 = 2 shows r/min calculated from the maximum output frequency and the number of motor poles (E2-04). If the pole setting does not match the motor, the rpm display is wrong.

FAQ

What rpm is a 4-pole motor at 60 Hz?

Synchronous speed is 120 × 60 ÷ 4 = 1800 r/min; the actual rated speed is lower by the slip, so the nameplate shows a smaller figure (e.g. 1750 r/min). At 50 Hz the synchronous speed is 1500 r/min.

Does 30 Hz halve the speed?

The synchronous speed is exactly half (900 r/min for 4 poles). The real speed is lower by the slip speed, so at rated load it is a little under half (about 850 r/min for a 1750 r/min nameplate).

What frequency gives the rpm I want?

Enter the rpm in «Target output shaft speed»; gear ratio and slip are added to give the frequency. With slip compensation, set it from synchronous speed without the slip.

What if I do not know the number of poles?

Estimate it from the nameplate rated frequency and speed: find the synchronous speed just above the rated speed (at 60 Hz, 3500s → 2 poles, 1700s → 4 poles, 1100s → 6 poles).

For the motor's rated current and torque, use the Motor Current Calculator.

To measure the real speed with an encoder, use the Encoder Pulses ↔ RPM Calculator. For the motor speed and torque a ball screw axis needs, use the Ball Screw Torque & Motor Sizing Calculator.