Fit a manufacturer pump curve, build the system curve (static head plus friction), and find the operating point where they cross — with parallel-pump support. Runs entirely offline; inputs persist in this browser via localStorage.
Use limits: The operating point is only as good as the two curves. The pump curve is the manufacturer's, at a stated speed and impeller trim; the system curve moves as valves throttle, tanks fill, and pipe roughens with age. This finds where today's curves intersect — run the aged/dirty case too. Verify suction conditions separately with the NPSH available calculator.
Operating point
Operating flow
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Operating head
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Shutoff head (per pump, flow 0)
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System static head
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Flow per pump
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How the Numbers Are Derived
Fitting the pump curve
A centrifugal pump's head-capacity curve is well approximated by a quadratic, H = a + bQ + cQ². The tool least-squares fits that through your entered points (at least three; shutoff and a far-right point pin it down). a is the shutoff head. For N pumps in parallel, the combined curve carries total flow Q at the head one pump makes at Q/N — parallel pumps add flow at equal head.
The system curve and the operating point
The system curve is Hsys = Hstatic + K·Qn: a fixed lift plus friction that grows with flow (n = 2 for Darcy, ~1.85 for Hazen-Williams). K comes from one design point, K = Hf / Qdesignn, or is entered directly. The operating point is the single flow where the pump curve and system curve cross — found here by bisection, since the pump head falls and the system head rises, giving exactly one intersection when the pump can overcome the static head.
Field notes
The manufacturer curve is at a specific speed and impeller diameter. A trimmed impeller or a VFD shifts it — scale it with the affinity laws first, then intersect.
Run two system curves: clean/new (low K) and aged/fouled (high K, valves throttled). The operating point walks left up the pump curve as the system stiffens — often into a worse-efficiency, higher-vibration zone.
Parallel pumps never double the flow. Because the system curve steepens with flow, two pumps might deliver only ~1.4× one pump's flow — the plot shows exactly how much you actually gain.
An operating point far right of best-efficiency (flat system, oversized pump) risks cavitation and motor overload; far left risks recirculation and low flow. Check it lands near BEP, and confirm NPSH margin separately.
References
Hydraulic Institute / pump handbooks — head-capacity and system-head curves, parallel operation.