Fan Laws (Affinity) Calculator
Change a fan’s speed or impeller size and the affinity laws tell you the new airflow, pressure and power. The headline: power follows the cube of speed, so a small slowdown saves a lot of energy.
What the Fan Laws Say
The fan affinity laws predict how a fan’s performance shifts when you change its speed or impeller diameter. For a speed change at fixed diameter: airflow moves in direct proportion to speed, static pressure with the square of speed, and shaft power with the cube of speed. They let you take one known operating point and project a new one without a fresh fan curve.
The Cube Rule and Energy
The power-cubed relationship is the reason variable-speed drives save so much. Slow a fan to 80% speed and it still moves 80% of the air, but draws only 0.8 cubed — about 51% — of the power, a 49% saving. Drop to half speed and power falls to one eighth. This is why throttling a damper (which wastes energy) is far less efficient than simply slowing the fan.
Trimming the Impeller
Changing impeller diameter at constant speed follows a related set: airflow scales with diameter cubed, pressure with diameter squared, and power with diameter to the fifth. Impeller trims are common for permanent capacity reductions, though the laws are less exact for large trims because the blade geometry no longer scales cleanly.
When They Break Down
The affinity laws assume the same fan operating at a similar point on its curve with unchanged efficiency. In reality efficiency drifts, motor and belt losses do not scale perfectly, and system effects intrude. They are excellent for quick projections and energy estimates, but a manufacturer’s fan curve is the final word for selection.
Frequently Asked Questions
What are the fan affinity laws?
Rules that scale a fan’s flow, pressure and power with speed or diameter: flow with speed, pressure with speed squared, power with speed cubed at constant diameter.
How much energy does slowing a fan save?
Power drops with the cube of speed, so running at 80% speed uses about 51% of the power – roughly a 49% saving – while still delivering 80% of the airflow.
Do the fan laws apply to pumps?
Yes. Centrifugal pumps follow the same affinity laws, which is why variable-speed pumping saves energy the same way.
Why is reducing fan speed better than closing a damper?
A damper wastes energy as pressure loss while the fan keeps spinning at full power. Slowing the fan cuts the power draw itself, following the cube law.
Related calculators
- CFM & Air Changes Calculator — the airflow a space needs.
- Duct Static Pressure Calculator — the pressure the fan must develop.
- Pump Horsepower Calculator — pumps follow the same affinity laws.
- Pipe Flow Calculator — flow and velocity in a duct or pipe.