Fan Affinity Calculator Formula
Understand the math behind the fan affinity calculator. Each variable explained with a worked example.
Formulas Used
New Airflow (Q2)
cfm2 = cfm1 * ratioNew Static Pressure (SP2)
sp2 = sp1 * pow(ratio, 2)New Brake Horsepower (BHP2)
bhp2 = bhp1 * pow(ratio, 3)Variables
| Variable | Description | Default |
|---|---|---|
cfm1 | Original Airflow (Q1)(CFM) | 10000 |
sp1 | Original Static Pressure (SP1)(in. w.g.) | 2 |
bhp1 | Original Brake Horsepower (BHP1)(HP) | 5 |
rpm1 | Original Speed (N1)(RPM) | 1200 |
rpm2 | New Speed (N2)(RPM) | 1500 |
ratio | Derived value= rpm2 / rpm1 | calculated |
How It Works
Fan Laws (Affinity Laws for Fans)
The fan laws are identical in form to the pump affinity laws. They predict how fan performance changes with rotational speed.
Fan Laws for Speed Change
Q2/Q1 = N2/N1 (airflow scales linearly)
SP2/SP1 = (N2/N1)² (pressure scales with speed squared)
BHP2/BHP1 = (N2/N1)³ (power scales with speed cubed)
A small 10% speed reduction cuts power by 27%, making variable-speed fans highly efficient for part-load operation.
Worked Example
A fan at 1200 RPM moves 10,000 CFM at 2.0" w.g. using 5 HP. Speed increased to 1500 RPM.
cfm1 = 10000sp1 = 2bhp1 = 5rpm1 = 1200rpm2 = 1500
- 01Speed ratio = 1500 / 1200 = 1.25
- 02Q2 = 10000 × 1.25 = 12,500 CFM
- 03SP2 = 2.0 × 1.25² = 2.0 × 1.5625 = 3.13 in. w.g.
- 04BHP2 = 5 × 1.25³ = 5 × 1.9531 = 9.77 HP
Ready to run the numbers?
Open Fan Affinity Calculator