Find a centrifugal pump’s specific speed (Ns) from flow, head, and rotational speed at the best efficiency point — or solve for any of the four. Shows both US Ns and metric nq and the impeller type they imply.
US + metric
Formula shown
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Pump Specific Speed
gpm
ft
rpm
US Ns
Use best-efficiency-point values
Specific speed is defined at the BEP, and the head is the head PER STAGE — for a multistage pump, divide total head by the number of stages first.
Specific speed1,240(US Ns · Radial flow (centrifugal))
Specific speed — US (Ns)
1,240
Specific speed — metric (nq)
24
Likely impeller type
Radial flow (centrifugal)
Formula & method
Ns = N · √Q / H0.75
Specific speed is an index of impeller shape, taken at the best efficiency point with head per stage. The US form uses N in rpm, Q in gpm, H in ft; the metric nq uses Q in m³/s and H in m, and is about 51.6× smaller (nq ≈ Ns ÷ 51.6). As an approximate guide, US Ns below ~4000 is a radial (centrifugal) impeller, ~4000–9000 is mixed-flow, and above ~9000 is axial (propeller); boundaries vary by source. Use it to check a pump against its type and to compare geometrically similar pumps.
For preliminary and educational use. Impeller-type ranges are approximate and source-dependent; confirm against the manufacturer’s data.
Specific speed is the single number that tells you what shape a pump’s impeller is — whether it is a high-head radial impeller, a low-head axial propeller, or something in between. It falls straight out of the duty at the best efficiency point, and this calculator runs the relationship in any direction: enter any three of specific speed, flow, head, and rotational speed, and it returns the fourth.
The formula
In US units, Ns = N · √Q / H^0.75, with the rotational speed N in rpm, the flow Q in gpm, and the head H in feet — both taken at the best efficiency point, and the head per stage for a multistage pump. It is an index, not a physical speed, so its numeric value depends on the unit convention: the metric nq uses Q in m³/s and H in m and comes out about 51.6 times smaller. This calculator always shows both so there is no ambiguity about which one you are looking at.
What the number tells you
Roughly, and with boundaries that vary by source:
US Ns below ~4000 (metric nq below ~80): a radial-flow impeller — high head, lower flow, the classic centrifugal shape. Very low Ns pumps push a lot of head from little flow and tend to be less efficient.
~4000–9000 (nq ~80–175): a mixed-flow impeller — a blend of radial and axial.
Above ~9000 (nq above ~175): an axial-flow (propeller) impeller — high flow, low head.
Because geometrically similar pumps share a specific speed, it is also the basis of the affinity laws and a companion to suction specific speed (Nss), which does the same job for the suction side and cavitation.
Worked example
A pump running at 1750 rpm that delivers 500 gpm at 100 ft (per stage) at its BEP has Ns = 1750 · √500 / 100^0.75 ≈ 1240 (US), or nq ≈ 24 (metric) — squarely a radial-flow impeller. Solve the other way to find, say, the speed needed to hit a target specific speed, or the head a given geometry implies.
