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    Air systems / fans

    Fan curve calculator

    A fan does not deliver its catalogue flow; it delivers the flow where its curve meets the system curve. This calculator finds that intersection, then applies the affinity laws so you can see why a variable-speed drive at 80% speed uses about half the power.

    Speed ratio0.80Power ratio0.51System K100
    Operating flow
    1.63 m³/s
    82% of free delivery
    Operating pressure
    267 Pa
    Where the fan and system curves cross
    Shaft power
    0.62 kW
    At 70% total fan efficiency
    At new speed
    1.31 m³/s
    0.32 kW at 800 rpm
    Affinity laws
    What happens to the duty point when the speed changes.
    800 rpm
    Affinity laws
    QuantityDesignAt new speed
    Flow (m³/s)1.631.31
    Pressure (Pa)267171
    Power (kW)0.620.32
    Speed (rpm)1000800

    Flow scales linearly, pressure with the square, power with the cube of speed.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Fan and system curves
    The intersection is the operating point; there is no other stable one.
    Fan and system curves0.000179.20358.40537.60716.80896.000.00.00.20.20.40.40.70.70.90.91.11.11.31.31.51.51.81.82.02.02.22.2FanSystem
    Power against speed
    The cube law is why variable-speed drives save so much energy.
    Power against speed0.00022.4044.8067.2089.60112.0060%60%70%70%80%80%90%90%100%100%Power %
    Canonical equations
    The exact relationships implemented by this engine.

    Δp = a − bQ² · Backward-curved centrifugal approximation.

    Δp = KQ² · K rises with dampers, filters and duct resistance.

    Q∝n, Δp∝n², P∝n³ · Holds for geometrically similar conditions.

    engineering methodology

    A clear path from inputs to results.

    A fan does not deliver its catalogue flow; it delivers the flow where its curve meets the system curve. This calculator finds that intersection, then applies the affinity laws so you can see why a variable-speed drive at 80% speed uses about half the power.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the shut-off pressure and free delivery.
    2. Set the system resistance coefficient.
    3. Read the operating flow and pressure.
    4. Change the speed to see the affinity-law effect.

    The formula

    Q=a/(K+b),Q∝n,  Δp∝n2,  P∝n3Q = \sqrt{a/(K + b)}, \qquad Q \propto n, \; \Delta p \propto n^2, \; P \propto n^3

    Reference: Fan affinity laws; backward-curved centrifugal curve approximation.

    Worked example

    800 Pa shut-off, 2 m³/s free delivery, K = 100

    Inputs
    • Shut-off 800 Pa, free delivery 2 m³/s.
    • System K = 100 Pa/(m³/s)².
    • Design 1,000 rpm, new speed 800 rpm.
    Calculation path
    1. 1

      Fan curve b = 800/2² = 200.

    2. 2

      Operating flow: √(800/(100+200)) = 1.633 m³/s.

    3. 3

      Operating pressure: 100 × 1.633² = 267 Pa.

    4. 4

      Shaft power: 1.633 × 267 / 0.7 = 0.62 kW.

    5. 5

      At 800 rpm: flow 1.31 m³/s, power 0.32 kW — half, for 80% of the speed.

    Result

    1.633 m³/s at 267 Pa · 0.62 kW · 0.32 kW at 80% speed.

    Interpreting the result

    The cube law is the most valuable fact in air systems. Dropping to 80% speed halves the power, and to 60% takes it to about a fifth. That is why variable-speed drives pay back so quickly on systems that run part-loaded — which is almost all of them.

    Assumptions & limitations

    • Single fan with a smooth, non-stalling curve.
    • System curve of the form Δp = KQ².
    • Affinity laws hold (geometrically similar conditions).
    • No system effect or duct leakage.

    Frequently asked questions

    Why does my measured flow differ?

    System effect, duct leakage and actual damper positions move the system curve.

    What is the stall region?

    The left-hand part of an unstable fan curve where flow can reverse — avoid operating there.

    Can I use this for a pump?

    The laws are the same; the curve shapes and efficiency islands differ.

    Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.