How the Pump Sizing & Power Calculator Works

This page documents exactly what the calculator does with your inputs, in the order it does it: it turns a duty point (flowrate and head) into hydraulic power, shaft power, the electrical power the motor draws, and a recommended standard motor frame. Each step lists the formula used and links to a published engineering reference for that method.

If you already know the differential head the pump must develop, enter it in metres of liquid, kPa or bar. A pressure entry is converted to metres of liquid with the hydrostatic relationship pressure = density × gravity × height:

When the head is unknown, the calculator assembles it from the system components below, each computed in kPa and then summed. Velocity head is assumed negligible (taken as zero), as this is a preliminary sizing calculation.^[4] The conceptual basis is the total dynamic head — the static lift, the pressure difference between the two ends, and the friction losses, added together.^[2]

The difference between destination and source pressure, expressed as an equivalent head — one of the head terms in TDH.^[2]

The vertical lift between source and destination liquid levels, converted from metres to kPa using density and gravity (the static-lift term of TDH).^[2]

Fixed pressure drops across in-line equipment (heat exchangers, filters, and anything else), entered directly because their drop is a known equipment characteristic. If you want to reserve a control-valve allowance, you can add it here under “Other”.

The total is converted back to metres of liquid with the same hydrostatic relationship used in Option A, giving the head H the rest of the calculation uses.

Method 1 (preferred): Darcy–Weisbach. If you provide the internal pipe diameter, pipe material and fluid viscosity, friction loss is computed rigorously for the suction and discharge runs and summed:^[5]

The fluid velocity comes from flow and bore, v = Q / (πD²/4); the Reynolds number is Re = ρvD/μ. The Darcy friction factor f is taken as 64/Re in laminar flow (Re < 2300) and from the explicit Swamee–Jain approximation to the Colebrook–White equation in turbulent flow:^[6]

The absolute roughness ε is set by the selected material — for example commercial steel 0.045 mm, stainless 0.015 mm, cast iron 0.26 mm, PVC/plastic 0.0015 mm.^[5] You can also enter an optional number of 90° elbows; each is added as a minor loss ΔP = K × (ρ × v² / 2) with K ≈ 0.9, at the pipe size provided (defaults to zero).^[14] This is the route to use whenever the pipe data is available.

Method 2 (fallback): simplified gradient. If detailed pipe data isn’t available, the tool estimates friction from length alone using published liquid-line rules of thumb — roughly 0.4 psi per 100 ft on the suction line and 2 psi per 100 ft on the discharge line,^[7] which work out to about:

Hydraulic power (water power) is the useful power delivered to the fluid — what an ideal 100 %-efficient pump would need for this flow and head.^[1][3] It is the product of flow, head, density and gravity:

This is the SI form of the standard pump-power equation P = ρ·g·Q·H, with flow converted from m³/h to m³/s (divide by 3600) and density written as 1000 × SG.^[1][3] A denser liquid needs proportionally more power for the same flow and head.^[1]

No real pump is 100 % efficient. If you know the efficiency at the duty point, enter it. If you leave it blank, the calculator estimates it from the Branan correlation published in Rules of Thumb for Chemical Engineers, which gives pump efficiency as a function of developed head F (ft) and flow G (US gpm):^[8]

The correlation is valid for F = 50–300 ft and G = 100–1000 gpm (about 23–227 m³/h) and reproduces typical pump curves to within roughly 7 %.^[8] The values it returns over that range (rising with capacity, because clearance and surface-friction losses are proportionally larger in small casings):

Both limits are enforced. If either the head is outside 50–300 ft (15–91 m) or the flow is outside 100–1000 gpm (23–227 m³/h), the correlation no longer applies, so the tool falls back to published typical figures — about 55 % for small pumps (below ~23 m³/h) and 75–85 % for larger units (above ~227 m³/h, where field data reaches ~87 % near 1135 m³/h) — and flags the result as estimated outside the valid range.^[9]

The shaft power — also called brake or absorbed power — is the mechanical power the driver must deliver to the pump shaft. It is the hydraulic power divided by the pump efficiency:^[1][3]

Because efficiency is below 100 %, shaft power always exceeds hydraulic power; the difference is the energy lost inside the pump.^[1]

The motor also has losses, so it draws more electrical power than it delivers to the shaft. Enter a motor efficiency if you have it; otherwise the calculator reads a full-load efficiency from a standard-frame table, indexed by the shaft power. The values used are the NEMA Premium full-load efficiencies from NEMA MG-1 (4-pole),^[10][11] which rise with rating. A representative subset:

Full ladder continues to 500 hp in MG-1; the calculator holds the top value for larger frames.

The motor input power required is the shaft power divided by the motor efficiency — the actual power demand the motor must meet:

This is the figure used to pick a frame in the next step.

Motors come in a fixed ladder of standard ratings (NEMA integral horsepower: 1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50… hp, converted to the kW frames used here).^[12] The calculator selects the smallest standard frame whose rating is at least the required motor power — it rounds up to the next size.

This ensures the motor is never run above its nameplate rating in normal operation. As extra margin, standard induction motors carry a service factor — commonly 1.15 for general-purpose designs — meaning brief overloads up to 15 % above nameplate are tolerable, though continuous operation in that band shortens life.^[13] The result panel reports the reference service factor for the selected frame.

Water (SG = 1.0) at 200 m³/h from a source at 100 kPag, 4.3 m, to a destination at 2500 kPag, 100 m. Suction run 25 m, discharge run 1000 m, with a heat exchanger (70 kPa) and a filter (150 kPa). Piping by the simplified method.

This tool is for preliminary sizing of centrifugal pumps on liquid service. Velocity head is assumed zero, and efficiencies default to representative values when not supplied. Use the Darcy–Weisbach option for friction whenever pipe data is available; the simplified gradient is a rough fallback only.^[7] For detailed design, confirm pump efficiency against the vendor curve at the duty point^[9] and the motor against the supplier’s nameplate.

1. The Engineering ToolBox — Pumps – Power Calculator (hydraulic and shaft power).
2. Wikipedia — Total dynamic head (static lift + pressure head + velocity head + friction loss).
3. Wikipedia — Specific pump power (power, head and system efficiency).
4. Pumps & Systems — How to Quickly Calculate a Centrifugal Pump’s Total Dynamic Head (velocity head balances out for centrifugal duty).
5. The Engineering ToolBox — Darcy–Weisbach equation; pipe roughness values per FluidFlow.
6. Swamee–Jain explicit friction-factor approximation to Colebrook–White — Darcy–Weisbach calculator (FIRGELLI).
7. Liquid-line pressure-drop rules of thumb (≈0.4 psi/100 ft suction, ≈2 psi/100 ft discharge) — Engineersfield: Piping Design Rules of Thumb; The Chemical Engineer: Rules of Thumb — Flow Parameters.
8. C. R. Branan, Rules of Thumb for Chemical Engineers — pump-efficiency correlation, reproduced and discussed at Eng-Tips: Centrifugal Pump Efficiency vs. Flow Rate.
9. Typical centrifugal-pump efficiency ranges — Linquip (small ~50–70 %, medium/large ~75–93 %); Mislier (~50 % small to ~88 % large).
10. NEMA — NEMA Premium full-load efficiencies (MG-1 Table 12-12).
11. The Engineering ToolBox — NEMA electrical motor efficiency ratings.
12. U.S. DOE / EERE — Premium Efficiency Motors (standard ratings, 1–500 hp).
13. ABB — How to read a NEMA motor nameplate (service factor 1.15).
14. Minor (fitting) losses, ΔP = K·ρv²/2 with K ≈ 0.9 for a standard 90° elbow — MechSimulator: Fluid Flow in Pipes.

Results are estimates for preliminary engineering and screening. Final equipment selection should be confirmed with vendor data and a detailed hydraulic analysis. This material is not a substitute for review by a qualified engineer.