Fan Power & Fan Affinity Laws Calculator (CFM, Pa, kW)
By Santaji GadepatilinUpdated November 5, 2026
A fan's air power is simply airflow times pressure rise, and its shaft power is that divided by the fan efficiency. This fan affinity laws calculator finds both, then scales flow, pressure and power to a new speed — flow with the speed ratio, pressure with its square and power with its cube — which is how VFD energy savings on fans are estimated.
How to use the fan power calculator
Enter the airflow, the pressure rise across the fan and the fan efficiency to get air and shaft power. Then enter the present and new speeds to see how flow, pressure and power change — for example when a VFD slows the fan.
Fan power and fan law formulas
Pair = Q × Δp · Pshaft = Q × Δp ÷ η · Q₂ = Q₁(N₂/N₁) · Δp₂ = Δp₁(N₂/N₁)² · P₂ = P₁(N₂/N₁)³
Worked example
10,000 m³/h (2.7778 m³/s) against 1,000 Pa, fan efficiency 70%, slowed from 1,450 to 1,160 rpm:
- Air power = 2.7778 × 1,000 = 2.778 kW
- Shaft power = 2.778 ÷ 0.70 = 3.968 kW
- At 1,160 rpm: Q = 8,000 m³/h, Δp = 640 Pa, shaft power = 2.032 kW
Fan speed table (10,000 m³/h, 1,000 Pa, 70% efficiency)
| Speed | Airflow | Pressure | Shaft power |
|---|---|---|---|
| 100% | 10,000 m³/h | 1000 Pa | 3.97 kW |
| 90% | 9,000 m³/h | 810 Pa | 2.89 kW |
| 80% | 8,000 m³/h | 640 Pa | 2.03 kW |
| 70% | 7,000 m³/h | 490 Pa | 1.36 kW |
| 60% | 6,000 m³/h | 360 Pa | 0.86 kW |
| 50% | 5,000 m³/h | 250 Pa | 0.50 kW |
Notes
- Air density matters: pressure and power scale with density, so a fan handling hot air needs less power for the same volume flow.
- Add motor and drive losses to the shaft power when sizing the motor.
Frequently asked questions
How do I calculate fan power?
Air power = Q × Δp (m³/s × Pa = W). Shaft power = air power ÷ fan efficiency. 10,000 m³/h at 1,000 Pa is 2.78 kW of air power, or about 3.97 kW at the shaft with a 70% efficient fan.
What are the fan affinity laws?
At constant air density, Q₂/Q₁ = N₂/N₁, p₂/p₁ = (N₂/N₁)² and P₂/P₁ = (N₂/N₁)³.
What is the fan power formula in imperial units?
Shaft horsepower = CFM × total pressure (in. w.g.) ÷ (6356 × efficiency).
Should I use static or total pressure?
Use fan total pressure with total efficiency, or fan static pressure with static efficiency — do not mix them. Both give the same shaft power.