Calculation
ns = 60f/p; s = (ns−n)/ns
In motoring operation the rotor runs below synchronous speed; the relative difference is slip.
Busch 2006, Gleichungen zu Synchrondrehzahl und Schlupf
Induction motor slip
In motoring operation the rotor runs below synchronous speed; the relative difference is slip.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Slip s — Relative speed difference between rotating field and rotor; 0.04 means 4%.
- Stator frequency f₁ — Electrical fundamental frequency of stator voltage, commonly 50 Hz or 60 Hz on mains.
- Pole-pair count p — Number of magnetic pole pairs; a four-pole motor has p=2, not p=4.
- Measured rotor speed n — Mechanical shaft speed at the same steady operating point as the frequency.
Example
At 50 Hz and p=2, ns=1,500 rpm. With n=1,440 rpm, s=0.04 or 4%.
Assumptions and limits
Steady motoring operation with known fundamental frequency and integer pole-pair count; generating operation, harmonic fields and speed fluctuation are excluded.
Understand Induction motor slip
This calculator relates measured motor speed to electrical rotating-field speed. It supports nameplate checks, laboratories and understanding why an induction motor does not run synchronously under load.
What does this quantity describe?
The rotating field runs at ns=60f/p rpm. In motoring operation rotor speed n is lower and s=(ns−n)/ns. Slip provides relative motion needed for rotor induction and torque.
Formula and variables
ns = 60f/p; s = (ns−n)/ns
ns = 60f/ps = (ns−n)/nsf₂ = s·f₁
| Symbol / input | Meaning |
|---|---|
| Slip s | Relative speed difference between rotating field and rotor; 0.04 means 4%. |
| Stator frequency f₁ | Electrical fundamental frequency of stator voltage, commonly 50 Hz or 60 Hz on mains. |
| Pole-pair count p | Number of magnetic pole pairs; a four-pole motor has p=2, not p=4. |
| Measured rotor speed n | Mechanical shaft speed at the same steady operating point as the frequency. |
Choose the inputs correctly
f is the stator fundamental frequency, i.e. actual inverter output when applicable. p counts pole pairs: 2 poles mean p=1, 4 poles p=2. n is simultaneous mechanical shaft speed.
How to use the calculator
Obtain frequency and pole count from supply/drive and motor data, convert poles to pole pairs, and measure n at steady load. Compare s with nameplate and operating load.
Worked example
50 Hz and p=2 give ns=1,500 rpm. At 1,440 rpm the difference is 60 rpm and s=60/1,500=0.04=4%.
Understand the result and units
Greater positive slip usually indicates higher load for the same motor, but is not a direct torque measurement without a characteristic curve. s=1 is standstill and s=0 ideal synchronism.
f in Hz, n in rpm or rad/s, p a whole dimensionless number. Slip is returned as a decimal; multiply by 100 for percent.
Typical applications
Understanding induction-motor nameplates, assessing load change, checking variable-frequency operation and preparing rotor-frequency f₂=s·f₁ calculations.
Assumptions, limits and common mistakes
Restricted to steady motoring operation 0≤s≤1. Generating with negative slip, harmonic fields, pole changing and dynamic speed variation are excluded.
Common mistake: Do not confuse poles with pole pairs: a four-pole motor has p=2. Do not use mains frequency when an inverter supplies another fundamental frequency.
Frequently asked questions
What is “Induction motor slip” used for?
Understanding induction-motor nameplates, assessing load change, checking variable-frequency operation and preparing rotor-frequency f₂=s·f₁ calculations.
Where do the input values come from?
f is the stator fundamental frequency, i.e. actual inverter output when applicable. p counts pole pairs: 2 poles mean p=1, 4 poles p=2. n is simultaneous mechanical shaft speed.
What does the result not cover?
Restricted to steady motoring operation 0≤s≤1. Generating with negative slip, harmonic fields, pole changing and dynamic speed variation are excluded.