Electrical frequency f
Hz
Electrical frequency corresponding to the calculated synchronous speed.
Electricity · Industrial electricity
VFD frequency, motor speed and slip
Relate electrical frequency, pole count, synchronous speed and shaft speed, with explicit slip for induction-motor operation.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Synchronous speed nₛ
rpm
Rotating-field speed set by electrical frequency and pole count.
Actual shaft speed n
rpm
Estimated shaft speed after accounting for slip.
Slip s
%
Relative difference between synchronous and actual speed in motoring operation.
Relation and numerical substitution
nₛ = 120 · f / p ; n = nₛ · (1 − s)—
p is the motor’s total pole count and must be an even integer of at least 2. nₛ is rotating-field synchronous speed and n is actual shaft speed at steady state. The calculator is limited to motoring operation with 0 ≤ s < 100%. Use s = 0% for an ideal synchronous-speed estimate or a synchronous machine. This relation does not size a VFD or check V/f law, available torque, field weakening, ramps, harmonics, temperature rise, protection or manufacturer limits.
01Formulas and symbols
Formulas used
nₛ
120 · f / pSynchronous speed from frequency and pole countn
nₛ · (1 − s)Actual speed from synchronous speed and slipf
nₛ · p / 120Frequency from synchronous speed and pole counts
(nₛ − n) / nₛSlip from synchronous and actual speed02Assumptions and limits
Scope of validity
- p is the motor’s total pole count and must be an even integer of at least 2.
- nₛ is rotating-field synchronous speed and n is actual shaft speed at steady state.
- The calculator is limited to motoring operation with 0 ≤ s < 100%. Use s = 0% for an ideal synchronous-speed estimate or a synchronous machine.
- This relation does not size a VFD or check V/f law, available torque, field weakening, ramps, harmonics, temperature rise, protection or manufacturer limits.
03Validation example
Reference numerical case
- f = 50 Hz · p = 4 · s = 3 %
- nₛ = 120 × 50 / 4 = 1500 rpm
- n = 1500 × (1 − 0.03) = 1455 rpm
- Inverse check: n = 1455 rpm · p = 4 · s = 3 % → f = 50 Hz
04References
Technical references
- IEC 60034-1 — Rotating electrical machines: rating and performance.
FAQ
What does pole count mean?
p is the total number of magnetic poles in the motor. Common values are 2, 4, 6, 8, and so on.
Why is actual speed below synchronous speed?
An induction motor needs positive slip in motoring operation to develop torque.
Can I use 0% slip?
Yes for an ideal synchronous-speed estimate or a synchronous machine. For a loaded induction motor, enter a realistic slip.
Does this size the VFD?
No. It only relates frequency and speed; VFD selection must also consider voltage, current, torque, overload and operating conditions.