Fan-drive reference
HVAC Fan Belt and Sheave Formulas
A compact reference for speed ratio, driver sizing, pitch length, wrap angle, belt speed, and fan-law scaling.
Formula table
| Check | Formula | Output |
|---|---|---|
| Driven fan speed | Nf = NmDm/Df | Fan RPM |
| Required motor sheave | Dm = DfNf/Nm | Driver pitch diameter |
| Open-belt pitch length | L = 2C + 1.57(D + d) + (D-d)²/(4C) | Approximate pitch length |
| Small-sheave wrap | α = 180° - 2 sin-1((D-d)/(2C)) | Degrees of contact |
| Belt speed | S = πdN/12 | ft/min when d is inches |
| Fan airflow | Q2 = Q1(N2/N1) | New airflow |
| Fan pressure | P2 = P1(N2/N1)² | New pressure |
| Fan power | BHP2 = BHP1(N2/N1)³ | New brake power |
Variable and unit reference
| Symbol | Meaning | Unit rule |
|---|---|---|
| Nm, Nf | Motor and fan rotational speed | RPM |
| Dm, Df, D, d | Sheave pitch/effective diameters | Use one length unit |
| C | Shaft center distance | Same unit as diameters |
| L | Approximate belt pitch length | Same unit as geometry |
| Q | Air volume flow | Any consistent flow unit |
| P | Fan static or total pressure | Same pressure type and unit at both points |
| BHP | Fan shaft/brake power | hp or kW consistently |
Quick fan-law factors
| RPM change | Airflow factor | Pressure factor | Power factor |
|---|---|---|---|
| -20% | 0.800 | 0.640 | 0.512 |
| -10% | 0.900 | 0.810 | 0.729 |
| +5% | 1.050 | 1.103 | 1.158 |
| +10% | 1.100 | 1.210 | 1.331 |
| +20% | 1.200 | 1.440 | 1.728 |
| +25% | 1.250 | 1.563 | 1.953 |
How to use the reference
Use the ratio equations to describe shaft speed, the geometry equations to screen a replacement belt, and the fan laws to estimate the consequence of a proposed speed change. Then return to manufacturer data for actual sheave, belt, fan, and motor limits.
Important limits
- Pitch/effective diameter is not automatically the sheave outside diameter.
- The belt equation is for a two-sheave open drive and returns an approximate pitch length.
- Manufacturer belt tables control section, rating, standard length, tension, and minimum sheave details.
- Fan laws assume the same fan, same system curve, similar efficiency, and consistent air density.
- Final work requires lockout/tagout, guards, alignment, tension, motor-current, vibration, and measured performance checks.