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Fan Laws Calculator

See what happens to airflow, static pressure and power when a fan runs faster or slower — or find the speed a target airflow needs — with the fan affinity laws.

Method reviewed October 26, 2026. Version 1.0.0. How it works

Your inputs

Unit system

RPM (or drive frequency in Hz, or % speed — any consistent measure of speed).

I know the new

Result

New fan speed
800
New airflow
1,600CFM
New static pressure
0.32in. w.c.
New fan power
0.512hp

At 80 % speed: 1,600 CFM, 0.32 in. w.c., 0.512 hp (-49 % power).

Change in power
-48.8%
Speed ratio
0.8
Show the working
  1. Speed ratio n₂/n₁
    0.8
  2. Airflow ∝ speed
    2,000 × 0.8 = 1,600 CFM
  3. Pressure ∝ speed²
    0.5 × 0.8² = 0.32 in. w.c.
  4. Power ∝ speed³
    1 × 0.8³ = 0.512 hp

The three fan laws

For the same fan moving air through the same system, changing speed changes everything else in a fixed way:

  • Airflow changes in proportion to speed.
  • Pressure changes with the square of speed.
  • Power changes with the cube of speed.

That cube is why slowing a fan saves so much energy — 20 % less speed needs roughly half the power — and why speeding one up can overload its motor.

When the laws do not apply

The laws assume the duct system does not change, so the fan moves along one system curve. Closing a damper, loading a filter or adding a coil moves the fan to a different curve; compare those cases with the fan’s performance chart instead. The power law also describes the fan shaft; motor and drive efficiency change somewhat with speed.

Worked example

These are the example values the calculator opens with, and the result the engine calculates for them.

Inputs

Current fan speed
1,000
Current airflow
2,000 CFM
Current static pressure
0.5 in. w.c.
Current fan power
1 hp
I know the new
Fan speed
New fan speed
800

Result

New fan speed
800
New airflow
1,600 CFM
New static pressure
0.32 in. w.c.
New fan power
0.512 hp
Change in power
-48.8 %
Speed ratio
0.8

At 80 % speed: 1,600 CFM, 0.32 in. w.c., 0.512 hp (-49 % power).

Assumptions

  • The same fan in the same duct system: airflow changes with speed, pressure with speed squared and power with speed cubed. Air density is unchanged.

Limitations

  • If the system itself changes (dampers, filters, ducts), the operating point moves to a different system curve and the laws do not apply between the two cases.
  • Motor and drive efficiency change with load and speed; the power law describes fan shaft power.

Frequently asked questions

How much power does a variable-speed drive save?

In a system where the affinity laws hold, power falls with the cube of speed: at 80 % speed the fan needs about 51 % of the power. Real savings are smaller because of drive and motor losses and any minimum pressure the system must hold.

Can I use drive frequency instead of RPM?

Yes. Any consistent measure of speed works, because only the ratio between the new and old speed matters.

Do the fan laws work for pumps too?

The same affinity relationships apply to centrifugal pumps; the Pump Power Calculator covers pump power directly.

Sources

  1. Fan System Cheat Sheet (Better Plants) — U.S. DOE Better Buildings Solution Center. Fan brake horsepower = CFM × pressure ÷ (6,356 × fan efficiency); fan affinity laws (flow ∝ speed, head ∝ speed², power ∝ speed³); cites DOE’s Improving Fan System Performance sourcebook.

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