FreeHVACCalculators

Start here

Loading calculators…

Menu

Fan System Curve and VFD Speed Calculator

See how much static pressure a duct system needs at a different airflow, or what a variable-frequency drive setting does to motor speed, airflow and fan power.

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

Your inputs

Unit system

Usually 0 for a duct system. Enter a set-point that must be held regardless of airflow (for example a duct static pressure set-point). DOE notes system curves can have such a static component.

Result

Static pressure at the new airflow
1.152in. w.c.
Change in static pressure
44%

Moving 2,400 CFM through the same system takes about 1.152 in. w.c. (44 % more).

  • The curve applies while the system is unchanged. Closing dampers, loading filters or changing ducts makes a new, steeper or flatter curve.
Air power ratio (CFM × pressure)
1.728

Points on this system curve

At 50 % airflow (1,000 CFM)
0.2in. w.c.
At 75 % airflow (1,500 CFM)
0.45in. w.c.
At 100 % airflow (2,000 CFM)
0.8in. w.c.
At 110 % airflow (2,200 CFM)
0.968in. w.c.
At 125 % airflow (2,500 CFM)
1.25in. w.c.
Show the working
  1. System curve: SP = fixed + (SP₁ − fixed) × (CFM ÷ CFM₁)²
    0 + (0.8 − 0) × (2,400 ÷ 2,000)² = 1.152 in. w.c.

The system curve

In a duct system each component loses pressure in proportion to velocity squared, so the system as a whole needs pressure in proportion to airflow squared. DOE’s fan system sourcebook describes this as a parabolic system curve. Twenty percent more airflow needs 44 % more pressure.

Some systems also hold a fixed pressure that does not depend on airflow, such as a duct static pressure set-point. Enter it and the curve becomes fixed part + variable part × (airflow ratio)².

VFD speed

An induction motor’s synchronous speed is 120 × frequency ÷ number of poles: 1,800 rpm for a 4-pole motor on 60 Hz. Under load it runs a little slower (slip). A drive changes the frequency, and the speed follows. The fan laws then give airflow in proportion to speed and power in proportion to speed cubed.

Cautions

  • The cube law holds for a system curve through zero; with a fixed pressure set-point, savings at low speed are smaller
  • Running above the motor’s rated frequency overspeeds the fan; check its limits first
  • The operating point is where the system curve meets the fan curve, which comes from the fan maker

Worked example

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

Inputs

Calculate
System curve: pressure at a new airflow
Known airflow
2,000 CFM
Static pressure at that airflow
0.8 in. w.c.
Fixed pressure that does not change with airflow
0 in. w.c.
New airflow
2,400 CFM

Result

Static pressure at the new airflow
1.152 in. w.c.
Change in static pressure
44 %
Air power ratio (CFM × pressure)
1.728

Moving 2,400 CFM through the same system takes about 1.152 in. w.c. (44 % more).

Assumptions

  • System curve: pressure loss rises with the square of airflow (DOE’s fan sourcebook: Δp = C·ρ·(V/1,097)² for each component), plus any fixed pressure you enter.
  • Synchronous speed = 120 × frequency ÷ poles; a running induction motor turns slower by its slip. Running speed is taken as proportional to frequency.
  • Fan laws: airflow ∝ speed, power ∝ speed³ for the same fan on the same system.

Limitations

  • Slip changes with load, so the running-speed estimate is approximate.
  • Where the system curve and the fan curve cross is the operating point; this tool does not have your fan curve.

Frequently asked questions

How much static pressure will I need for more airflow?

In the same system, pressure rises with the square of airflow: 2,400 CFM through a system that needs 0.8 in. w.c. at 2,000 CFM needs about 1.15 in. w.c.

What speed does a motor run at 45 Hz?

A 4-pole motor’s synchronous speed at 45 Hz is 1,350 rpm; it actually runs a little slower because of slip.

How much power does slowing a fan save?

For a fan on a system curve through zero, power falls with the cube of speed: 75 % speed uses about 42 % of the power.

Sources

  1. Improving Fan System Performance: A Sourcebook for Industry — U.S. DOE (Industrial Technologies Program) with AMCA International. Component pressure loss Δp = C·ρ·(V/1,097)² (in. wg, V in fpm, ρ = 0.075 lb/ft³ standard), giving a parabolic system curve; system curves can have a static component; sheave changes alter fan speed; airflow is linear with speed and power is cubed.
  2. 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.
  3. Speed Control of Motors — An Introduction to Variable-Frequency Drives (S. J. Vidal, Jan/Feb 2013) — IAEI Magazine (International Association of Electrical Inspectors). Synchronous speed S = 120 × F ÷ P; a 4-pole motor on 60 Hz has a synchronous speed of 1,800 rpm and runs slower under load (slip); changing frequency is how a VFD changes speed.
  4. Premium Efficiency Motor Selection and Application Guide — A Handbook for Industry — U.S. DOE Advanced Manufacturing Office (prepared by Washington State University Energy Program). Glossary: slip is the difference between synchronous and actual rotor speed divided by synchronous speed; motor speed is inversely related to the number of poles; an unloaded motor runs close to synchronous speed.

Spotted an error? Report a problem with this calculator — see our corrections policy.