Fan affinity laws

A little slower saves a lot of fan power

For the same fan at a corresponding operating point, 20% less speed means 20% less airflow — but 48.8% less predicted shaft power. The difference is the cube hiding in the fan laws.

Q2/Q1 = N2/N1
Δp2/Δp1 = (N2/N1)2
P2/P1 = (N2/N1)3

Same fan, corresponding operating points

What changes as speed changes

airflow Q ∝ N pressure Δp ∝ N² power P ∝ N³
Fan speed N2relative to the 100% design point
design
30%slower ← speed → faster120%
Predicted fan shaft power
The vertical mark is the original 100% design point. Bar scale runs to 180%.
Try

These are the fan affinity laws for changing the speed of the same fan at corresponding operating points: Q2/Q1 = N2/N1, Δp2/Δp1 = (N2/N1)², and P2/P1 = (N2/N1)³. The page holds fan diameter, air density and efficiency constant. It predicts power delivered at the fan shaft, not electrical input: motor, variable-speed drive, bearing and transmission losses do not follow the cube law. A system with a significant fixed static-pressure requirement may not produce airflow in direct proportion to speed. Similarity also becomes less reliable at very low speed. Never exceed a fan or motor’s manufacturer-rated speed; the 120% setting is a mathematical comparison, not an operating recommendation. Measured fan and system curves remain the authority. The U.S. Department of Energy gives the same 20%-speed-reduction example; Wikipedia’s affinity-laws article gives an accessible derivation; and ANSI/AMCA 210-25, Annex E defines the similarity relationships and their limits.