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.^[2] 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.

In system mode the tool also draws a pie chart of where the head goes — the share contributed by static pressure, elevation, equipment and piping & fittings. Because pump power is proportional to head, that breakdown is also where the energy (and operating cost) goes, which makes it easy to see whether friction, lift or back-pressure dominates the duty.

In system mode you also choose how the pump’s flow is controlled, because that decision changes both the head and the running cost:

Not controlled — nothing is added; the operating point simply sits wherever the pump curve crosses the system curve.

Control valve — the valve sets the flow by burning surplus head. Enter its design pressure drop, or leave it blank and the tool applies the published rule of thumb: about 50 % of the piping & fitting friction loss, or 10 psi (≈ 69 kPa), whichever is greater.^[16] That drop is added to the head and shown as its own slice in the pie.

VFD (variable speed) — the drive trims pump speed to deliver the required flow, so no throttling head is added.

Because a control valve dissipates its pressure drop as heat, the tool estimates what that throttling costs per year and what a VFD could save — roughly the operating-cost share of the valve’s head, since pump power tracks head.^[17] Static head and the drive’s own small losses mean the real VFD saving is a little less, so read it as an upper-bound screening figure.

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:^[3]

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:^[4]

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.^[3] 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).^[11] The tool also reports the resulting suction and discharge velocities and checks them against recommended ranges — about 1.2–2.1 m/s on the suction line and 1.2–3 m/s on the discharge line (Crane TP-410).^[12] Velocity drives friction loss (and thus energy cost), so if a line runs faster than its recommended ceiling the tool flags it: a larger bore lowers velocity, pressure drop, power and operating cost. 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,^[5] 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] 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] 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):^[6]

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 %.^[6] 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 together. The Branan equation is used only when the head is within 50–300 ft (15–91 m) and the flow is within 100–1000 gpm (23–227 m³/h). If either one falls outside its range — even when the other is comfortably inside — the equation no longer applies and the estimate falls back to a typical hydraulic efficiency by pump size, keyed on the duty’s hydraulic power (converted to hp at 0.7457 kW/hp). The low end of each published band is used, as a conservative screening value:^[18]

Worked through explicitly: a duty with low flow and high head together (e.g. 10 m³/h at 150 m) has Branan dropped because both limits are exceeded; its hydraulic power is about 4 kW (~5 hp), so it returns 50 %. The worked example below (200 m³/h at 409 m) has flow inside the band but head far above it, so Branan is dropped; its hydraulic power is about 223 kW (~299 hp), above 200 hp, giving 78 %. Whenever a value is produced outside the Branan box the tool flags it as estimated, and a known (vendor) efficiency should be entered for anything beyond screening.

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]

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

Motors come in a fixed ladder of standard NEMA ratings (1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50… hp, converted to the kW frames used here).^[10] The calculator picks the smallest standard frame whose rated output is at least 10 % above the shaft (brake) power — it rounds up to the next size, building in a 10 % design margin.

This frame-selection approach is intended for preliminary estimation in this calculator; confirm the final motor rating against the pump curve and vendor data.

Each motor has losses, so it draws more electrical power than it delivers to the shaft. The calculator uses the selected frame’s full-load efficiency (enter your own if you have it). The values are the NEMA Premium full-load efficiencies from NEMA MG-1 Table 12-12, taking the conservative 2-pole, totally-enclosed (TEFC) minimum column,^[8][9] which rise with rating. (2-pole runs slightly below 4-pole, and the minimum column is the guaranteed floor, so this under-states efficiency a touch and keeps the power and cost estimates on the safe side.) A representative subset:

The electrical power the motor draws from the supply is the shaft power divided by the motor efficiency:

This is the figure the operating cost (Step 8) is based on. It is larger than the shaft power because of motor losses, and it can sit slightly above the chosen frame’s nameplate number — the nameplate is a mechanical-output rating while this is electrical input, so the two are different quantities and aren’t directly comparable.

The electricity a pump consumes is its dominant lifetime cost. The motor draws the duty-point input power (the motor required power from Step 6), so the annual energy and cost are:

Continuous operation is 8760 h/yr (you can change the hours). The electricity price defaults to the BC Hydro tier-2 energy charge of about $0.14/kWh (CAD)^[15] — enter your own regional price to localise the result.

If you chose a control valve for flow control (Step 1), the calculator also reports the slice of that annual cost spent burning head across the valve, and flags it as the saving a VFD could capture — throttling wastes energy that variable-speed control simply never spends.^[17]

The purchase cost is estimated from a published correlation for centrifugal pumps (regression of QUE$TOR cost data), which gives the cost as a function of the pump’s working power Ẇₚ (the operating-point shaft power, in kW — not the dead-head/shut-off value):^[13]

That cost is on a 2020 basis (the source’s cost database). The tool reports it as-is, then escalates it to the present (~2026) with the Chemical Engineering Plant Cost Index (CEPCI ≈ 596 in 2020 vs ≈ 800 now)^[14] and converts to Canadian dollars (≈ 1.37 CAD/USD):

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.^[5] For detailed design, confirm pump efficiency against the vendor curve at the duty point^[7] and the motor against the supplier’s nameplate.

1. The Engineering ToolBox — Pumps – Power Calculator (hydraulic and shaft power).
2. Pumps & Systems — How to Quickly Calculate a Centrifugal Pump’s Total Dynamic Head (velocity head balances out for centrifugal duty).
3. The Engineering ToolBox — Darcy–Weisbach equation; pipe roughness values per FluidFlow.
4. Swamee–Jain explicit friction-factor approximation to Colebrook–White — Darcy–Weisbach calculator (FIRGELLI).
5. 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.
6. C. R. Branan, Rules of Thumb for Chemical Engineers — pump-efficiency correlation, reproduced and discussed at Eng-Tips: Centrifugal Pump Efficiency vs. Flow Rate.
7. Typical centrifugal-pump efficiency ranges — Linquip (small ~50–70 %, medium/large ~75–93 %); Mislier (~50 % small to ~88 % large).
8. NEMA — NEMA Premium full-load efficiencies (MG-1 Table 12-12).
9. The Engineering ToolBox — NEMA electrical motor efficiency ratings.
10. U.S. DOE / EERE — Premium Efficiency Motors (standard ratings, 1–500 hp).
11. Minor (fitting) losses, ΔP = K·ρv²/2 with K ≈ 0.9 for a standard 90° elbow — MechSimulator: Fluid Flow in Pipes.
12. Recommended pump-line velocities (suction ~1.2–2.1 m/s, discharge ~1.2–3 m/s) — Crane Co., Technical Paper No. 410 (Flow of Fluids Through Valves, Fittings, and Pipe).
13. Centrifugal-pump purchase-cost correlation (QUE$TOR regression, 2020 basis, valid 20–3500 kW) — Shamoushaki et al., open-access: Energies 2021, 14, 2665 (Eq. 5, Table 4); benchmarked there against the Turton correlation (CAPCOST, Appendix A).
14. Cost escalation — Chemical Engineering Plant Cost Index (CEPCI).
15. Default electricity price — BC Hydro electricity rates (tier-2 energy charge ~14 ¢/kWh).
16. Control-valve pressure-drop rule of thumb (≈50–60 % of piping friction loss, or ~10 psi minimum) — Instrumentation Toolbox; ControlGlobal.
17. VFD vs. throttling-valve energy savings (affinity laws) — DOE / Hydraulic Institute: Variable Speed Pumping; ISA.
18. Typical hydraulic efficiency by pump size — small end-suction (< 50 hp) 50–70 %, mid-size (50–200 hp) 65–80 %, large double-suction (> 200 hp) 78–88 %; consistent with the ranges in Linquip and Mislier. The low end of each band is used as the out-of-range estimate.

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.