In short: the affinity laws say flow scales directly with speed, head scales with speed squared, and power scales with speed cubed. Slow a pump to 80% of its rated speed and flow drops to 80%, head drops to 64%, but power drops all the way to about 51% — which is exactly why variable-speed control saves so much energy at partial flow.
These figures are planning aids based on the standard affinity-law relationships. They apply to the same pump only — confirm against the manufacturer's curve for final selection.
How the pump affinity laws work
A centrifugal pump's flow, head and power are all tied to how fast its impeller spins (or, equivalently, how large it is). The affinity laws describe exactly how each one changes when you change the speed or trim the impeller diameter, without needing to re-test the pump at every possible setting.
This calculator takes your reference flow, head and power at the original speed, multiplies each by the ratio raised to its own power (1, 2 or 3), and plots all three together so you can see how sharply they diverge. For turning a speed reduction into an actual energy-cost saving over time, use the variable-speed pump savings calculator next.
Worked example. A pump rated 100 GPM, 60 ft of head and 5 HP, slowed to 80% speed: Q₂ = 100 × 0.8 = 80 GPM. H₂ = 60 × 0.8² = 60 × 0.64 = 38.4 ft. P₂ = 5 × 0.8³ = 5 × 0.512 = 2.56 HP — exactly what the calculator shows with its default values.
Same pump only. The affinity laws relate one physical pump to itself at a different speed or trim. They cannot predict how a different pump model, or a significantly different impeller design, would perform — even at a similar flow and head.
Full range table (Q₁ = 100 GPM, H₁ = 60 ft, P₁ = 5 HP)
The complete curve behind the chart above, for the calculator's default reference point. Download exports this full table, not just the selected ratio.
| Ratio | Flow | Head | Power |
|---|---|---|---|
| 40% | 40.0 GPM | 9.6 ft | 0.320 HP |
| 50% | 50.0 GPM | 15.0 ft | 0.625 HP |
| 60% | 60.0 GPM | 21.6 ft | 1.080 HP |
| 70% | 70.0 GPM | 29.4 ft | 1.715 HP |
| 80% (default) | 80.0 GPM | 38.4 ft | 2.560 HP |
| 90% | 90.0 GPM | 48.6 ft | 3.645 HP |
| 100% | 100.0 GPM | 60.0 ft | 5.000 HP |
| 110% | 110.0 GPM | 72.6 ft | 6.655 HP |
Worked examples
80% speed — the calculator's default
51.2% power
Flow drops to 80% and head to 64%, but power drops to just 51.2% of full-speed draw — the core reason variable-speed drives save energy at partial flow.
Half speed (50%)
12.5% power
Half the flow, a quarter of the head, but only one-eighth the power — 100 GPM at 5 HP becomes 50 GPM at just 0.625 HP.
10% overspeed (110%)
+33% power
A modest 10% speed increase raises flow by only 10% but raises power draw by about 33% (6.655 HP vs. 5 HP) — a caution against casually over-speeding a pump to chase a bit more flow.
What else affects the result
System curve, not just pump curve. The affinity laws describe how the pump's own performance shifts — they don't account for how the system it's connected to responds. If the system has significant static head (lifting water to a height, or working against a fixed pressure), the actual new operating point where the pump curve meets the system curve will differ slightly from the pure affinity-law prediction.
Large impeller trims deviate from the ideal. The laws are exact for speed changes and very accurate for modest impeller trims, but trims beyond roughly 20–25% of the original diameter start to depart from the ideal square and cube relationships because the impeller's internal geometry no longer scales proportionally.
Efficiency isn't perfectly constant. The affinity laws assume pump efficiency stays the same across the speed range, which is a good approximation over a moderate range but becomes less accurate at the extremes — very low speeds in particular often run at somewhat lower efficiency than the affinity laws alone would suggest.
Frequently asked questions
What are the pump affinity laws?
Three proportional relationships for the same pump at a new speed or impeller diameter: flow scales directly with the ratio (Q₂/Q₁ = N₂/N₁), head scales with the ratio squared (H₂/H₁ = (N₂/N₁)²), and power scales with the ratio cubed (P₂/P₁ = (N₂/N₁)³). A small change in speed produces a much larger change in power than in flow.
Why does power increase so much faster than flow?
Because power is the product of flow and head, and both of those already scale with speed — flow linearly, head with the square — their product scales with the cube. A pump running at 110% of its rated speed only moves 10% more water, but its motor draws about 33% more power; at 50% speed it moves half the water for just one-eighth the power.
Do affinity laws apply to both speed changes and impeller trims?
Yes, the same three exponents apply whether N is motor speed or D is impeller diameter — trimming an impeller and slowing a motor affect a centrifugal pump's performance the same mathematical way. The laws are most accurate for speed changes and for impeller trims within roughly the top 25% of the original diameter; larger trims start to deviate from the ideal relationship because of changing internal geometry.
How is this different from the variable-speed pump savings calculator?
This calculator applies the raw affinity laws to convert one operating point into another at a new speed or diameter. The variable-speed pump savings calculator takes that same cubic power relationship a step further, turning a speed reduction into an estimated energy cost saving over time — use that one once you already know the numbers here.
What's the practical minimum speed for a VFD-driven pump?
Most centrifugal pumps aren't run much below about 30–40% of rated speed. Below that, flow and cooling around the motor and bearings drop off, and the pump can struggle to maintain the minimum flow needed to avoid internal recirculation and overheating. Check the specific pump manufacturer's minimum continuous stable speed before running near this floor.
Can I use affinity laws to predict a completely different pump's performance?
No. The affinity laws only relate the same physical pump — same casing, same impeller family — running at a different speed or trim. They cannot be used to estimate how a different pump model or a different impeller design would perform, even at a similar duty point.
Sources & references
- Hydraulic Institute. ANSI/HI Pump Standards — affinity laws for centrifugal pumps.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)