Conveyor Speed ↔ VFD Frequency Calculator
Conveyor line speed (m/min) from drive frequency, roller diameter, gear ratio, motor poles and slip, and the frequency (Hz) needed for a target speed.
Formulas
- Synchronous speed ns = 120 × f ÷ poles [r/min]
- Motor speed n ≈ ns − rated slip speed (rated slip = synchronous − nameplate speed)
- Roller speed = n ÷ gear ratio
- Line speed v = π × D × roller speed [m/min, D in m]
- Required frequency f = (v ÷ (π × D) × ratio + slip speed) × poles ÷ 120
Example: 4 poles, 1/30 gearbox, 100 mm roller (slip ignored)
| Frequency | Motor r/min | Roller r/min | Line m/min |
|---|---|---|---|
| 10 Hz | 300 | 10 | 3.14 |
| 20 Hz | 600 | 20 | 6.28 |
| 30 Hz | 900 | 30 | 9.42 |
| 40 Hz | 1200 | 40 | 12.57 |
| 50 Hz | 1500 | 50 | 15.71 |
| 60 Hz | 1800 | 60 | 18.85 |
Ignoring slip, line speed is proportional to frequency (0.314 m/min per Hz in this example). In practice slip under load makes it a little slower at the same frequency.
Things to check
- Belt thickness and slipping are not in this formula, so the real speed can differ a little. Measure once (e.g. seconds for 10 m) and compare with the calculation.
- For an extra chain or pulley stage, multiply the ratios (1/30 gearbox × 2:1 sprockets → 60).
- Keeping the slip speed constant is an approximation. With slip compensation or vector control on, the speed gets closer to synchronous.
- If the drive can display in m/min (a display coefficient), «line speed per Hz» is that coefficient; see the drive manual for how to set it.
Where it is used
- Setting the drive frequency and maximum frequency for a line speed spec in m/min.
- Recalculating the frequency for the same speed after changing a gearbox or roller.
- The speed ↔ Hz factor for a PLC that sends frequency commands over Modbus.
FAQ
How do I calculate conveyor speed?
Motor speed ÷ gear ratio = roller speed; multiply by the roller circumference (π × diameter). At 60 Hz, 4 poles (1800 r/min), a 1/30 gearbox and a 100 mm roller: 60 r/min × 0.314 m = 18.85 m/min (slip ignored).
What frequency gives a target m/min?
Speed ÷ (π × diameter) gives the roller speed, × ratio the motor speed; add the slip and multiply by poles ÷ 120. In the example, 15 m/min needs about 47.7 Hz (slip ignored).
Does doubling the frequency double the speed?
Nearly, below base frequency (apart from slip). Above base frequency the torque drops, so check the motor and gearbox ratings.
For speed from poles, slip and ratio alone, use the Motor Speed Calculator. For belt and pulley dimensions, use the Timing Belt Calculator.
Basis
Line speed follows from the definition that one revolution moves one circumference (π × diameter). Synchronous speed = frequency × 120 ÷ poles is from ABB «Low voltage motors — Motor guide» (2019) §9.3; keeping the rated slip (synchronous − nameplate speed) constant at other frequencies follows the definition of motor rated slip in the YASKAWA A1000 manual (E2-02), the same as the motor speed calculator. ABB Motor guide (PDF).