Hydraulic Horsepower Calculator
The water's own bill: pure ρgQH power delivered to the fluid at 100% — in watts, kilowatts and the exact-mechanical horsepower translation.
Hydraulic Horsepower Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Fluid side at 100% — no efficiency applied
- Metric computation; US 3,960 convention quoted
In short: Lifting 50 L/s through 30 m of head delivers 14,715.000000 W to the water — ρgQH = 1,000 × 9.81 × 0.050000 × 30 — which is 14.715000 kW or 19.733140 hp on the exact 745.699872 W definition. This is the fluid-side figure at a hundred percent: no pump is this good, every real motor pays more, but every honest pump conversation starts from the water's own arithmetic.
Formula
P = ρ·g·Q·H ··· hp = W/745.699872
Water horsepower is gravitational work per second — the flow's weight times the height it climbs, priced at a perfect 100%. It is the pump conversation's ground zero: the American convention divides GPM×feet by the famous 3,960, which is the same arithmetic in less metric clothing. Every efficiency ever quoted is a fraction of THIS number.
Worked Example
- Enter the flow.
- Enter the total dynamic head.
- Enter the fluid density.
- Read the water's watts — then the hp translation.
Defaults: 50 L/s, 30 m, water → 14,715.000000 W = 19.733140 hp. The seawater check: ρ 1,025 → 15,082.875000 W — 2.5% heavier fluid, 2.5% bigger bill, same pump head.
Strengths & Limits Of This Model
Where this engine is strong
- Exact hp definition applied
- The baseline every η needs
Where it stops
- No shaft or motor stage
- No turbine-direction model
Practical Use Cases
Pump comparisons
the fluid-side baseline
Turbine quotes
what the water gives up
Teaching
the 100% that pumps chase
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Hydraulic Horsepower Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why compute a power no pump achieves?
Because it is the reference: hydraulic power is what the fluid receives, and every efficiency figure in the industry is a ratio against it. A pump quoted at 75% is being measured against this page's arithmetic. Without the 100% baseline, efficiency numbers have no denominator and sales brochures have no referee.
What is the 3,960 in the American formula?
It is unit-conversion gravity: water horsepower = GPM × feet ÷ 3,960 collapses the gallon's weight and the foot-pound per minute definition of a horse into one constant. This page computes the same arithmetic in SI — ρgQH watts — and converts by the EXACT 745.699872 W definition instead, because conventions drift but definitions do not. The two roads agree to the third decimal and the metric road keeps its receipts.
How does this relate to the pump power page?
They are two ends of one coupling: this page prices what the WATER receives; the pump power page divides by efficiency to price what the SHAFT must deliver. Water horsepower times its own reciprocal (1/η) is the shaft figure. If the two pages ever disagree on ρgQH, one of them has a typo — the arithmetic is deliberately identical so the pair cross-checks.
Does head or flow matter more to the watts?
Equally — the formula MULTIPLIES them, so doubling either doubles the water's bill. That symmetry is why pump selection cannot cheat: you pay for the work done, however it is packaged between flow and lift. High-flow-low-head and low-flow-high-head duties cost the same water-horsepower, and differ only in which pump geometry delivers it efficiently.
Where does the water horsepower GO in a turbine?
Backwards, honestly: a turbine's water horsepower is what the flow SURRENDERS, and the shaft receives the fluid-side figure times the turbine's efficiency — the same division run in reverse. Hydro sites quote head times flow as the site's wealth precisely because this arithmetic bounds every turbine ever installed there.
Why is the seawater bill 2.5% higher?
Because power scales directly with density: ρ 1,025 lifts 2.5% more weight per cubic metre through the same head. The head itself is unchanged — metres are fluid-blind — but the watts feel the salt. Marine pump specs that quote freshwater figures for seawater duty understate the motor by exactly that 2.5%.
Is this the same as brake horsepower?
No — brake horsepower is measured AT the shaft (what a dynamometer brakes), and it is the water horsepower DIVIDED by pump efficiency, so it is always the bigger number. Water horsepower is the theory; brake horsepower is the invoice. Catalogue tables that blur the two flatter the pump by exactly the efficiency.
Can I use this for the suction side?
The formula prices ADDING energy to flow against head; suction side arithmetic subtracts (NPSH available), where the atmosphere's 10.193680 m allowance and vapour pressure join the ledger. The ρgQH line still underlies it — available NPSH is head above vapour pressure, not power — but the units and the guardrails differ. Suction problems are head problems; this page prices power.