Derive the square-law system curve from one duty point and predict the fan/pump operating point at a new speed: plus the speed a target flow needs.
ΔP = ΔPstatic + k·Q². Air (Pa) or water (m head). The maths is identical, only the units differ.
For design guidance only. Always verify against the manufacturer fan/pump curve.
About this system curve calculator
This free system curve & operating point calculator derives the square-law resistance curve of a duct or pipe system from a single duty point, then predicts where a fan or pump will operate at a changed speed and what speed a target flow needs. It is aimed at M&E and building-services engineers sizing VSD setpoints, checking flow turndown, or estimating the effect of a speed change on an air or water system. The maths is identical for air (pressure in Pa) and water (head in m), only the units differ. Everything runs in your browser. Nothing is uploaded.
How the system curve is calculated
The system curve is ΔP = ΔPstatic + k·Q², with the constant k = (ΔP₁ − ΔPstatic) ÷ Q₁² found from the duty point. Friction loss rises with the square of flow. The speed change uses the affinity laws (ratio r = N₂ ÷ N₁): with no static term the operating point tracks them exactly, Q ∝ r and ΔP ∝ r². With a static term present, the new point is estimated by intersecting the system curve with an affinity-scaled flat machine curve, Q₂ = Q₁·√((ΔP₁r² − ΔPstatic) ÷ ΔPfriction). The required speed for a target flow reverses the same relation. The affinity relations stay reliable within roughly ±30% of the reference speed (AMCA 201).
Frequently asked questions
What is the static pressure term for?
It is the flow-independent share of the duty pressure or head, a lift height or a fixed back-pressure that exists even at zero flow. Enter 0 for a closed, friction-only circuit so the system curve is a pure parabola through the origin; enter the static value for an open system, which flattens the low-flow end of the curve and changes how the operating point moves with speed.
Why is the result advisory when there is a static term?
With no static term the operating point follows the affinity laws exactly. With one, the true point depends on the real, sloping fan or pump curve, which this tool approximates with an affinity-scaled flat curve through the duty point. The genuine flow lies between that estimate and the pure-affinity figure, so verify against the manufacturer’s curve.
What does “deadhead” mean?
If the affinity-scaled pressure at the new speed cannot exceed the static term, the machine can no longer overcome the lift and delivers no flow, a deadhead condition. The calculator flags it rather than returning a misleading number. Treat all figures as indicative and confirm them against the manufacturer fan or pump curve.