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Pump Affinity Laws Calculator

Slowing a centrifugal pump with a drive, or trimming its impeller, changes flow, head and power in a predictable way. Enter today’s operating point to see the new one.

Method reviewed October 26, 2026. Version 1.0.0. How it works

Your inputs

Unit system

Shaft (brake) horsepower at the current operating point.

RPM, or drive frequency in Hz, or % speed — any consistent measure.

Result

New flow
1,000gpm
New head
83.3ft
New pump power
26.04hp
New speed
1,483

1,000 gpm at 83.3 ft and about 26.04 hp (-42 % power).

  • The affinity laws hold for circulating systems with little static head. Where static lift is a large part of the head, the operating point moves along the system curve and the savings are smaller.
Speed ratio
0.833
Power change
-42.1%
Show the working
  1. Ratio = Q₂ ÷ Q₁
    0.8333
  2. Flow ∝ ratio
    1,200 × 0.8333 = 1,000 gpm
  3. Head ∝ ratio²
    120 × 0.8333² = 83.33 ft
  4. Power ∝ ratio³
    45 × 0.8333³ = 26.042 hp

Flow, head and power

For a centrifugal pump with unchanged efficiency, flow varies with speed, head with speed squared and power with speed cubed. The same relationships are used for impeller trimming at constant speed, with the diameter ratio in place of the speed ratio.

The cube law is why drives save so much: DOE’s tip sheet on adjustable-speed pumping shows a 45 hp load at 1,200 gpm dropping to about 26 hp at 1,000 gpm and 13 hp at 800 gpm.

When the laws do not apply

The affinity laws describe the pump, not the system. DOE notes they hold for circulating systems and transfer systems with little static head. Where lifting fluid to a height makes up much of the head, the pump cannot slow down as much before flow stops, and savings are smaller.

DOE also notes that impellers are rarely trimmed below about 70 % of their original diameter.

Worked example

These are the example values the calculator opens with, and the result the engine calculates for them.

Inputs

Change
Find the speed for a new flow
Current flow
1,200 gpm
Current head
120 ft
Current pump power
45 hp
Current speed
1,780
New flow wanted
1,000 gpm

Result

New flow
1,000 gpm
New head
83.3 ft
New pump power
26.04 hp
New speed
1,483
Speed ratio
0.833
Power change
-42.1 %

1,000 gpm at 83.3 ft and about 26.04 hp (-42 % power).

Assumptions

  • Centrifugal pump, same fluid, efficiency unchanged between the two operating points.
  • Flow ∝ speed (or diameter), head ∝ speed², power ∝ speed³.

Limitations

  • Systems with significant static head do not follow the laws along the system curve.
  • Motor and drive efficiency change at reduced speed, so electrical savings are smaller than the shaft-power change.

Frequently asked questions

How much power does a pump save at 80 % speed?

Ideally about half: 0.8³ = 0.51 of the original shaft power, in a system with little static head.

Does the motor save the same amount?

Less. Motor and drive efficiency fall at reduced speed, so electrical savings are smaller than the shaft-power change.

Can I speed a pump up?

Power rises with the cube of speed, so check the motor, the pump’s maximum speed and the system pressure rating first.

Sources

  1. Adjustable Speed Pumping Applications (Pumping Systems Tip Sheet #12, May 2007) — U.S. DOE Industrial Technologies Program (via NREL). With no static lift, pump power varies as the cube of speed; affinity laws are valid for circulating systems or transfer systems with little static head; Table 3: 45 hp at 1,200 gpm becomes 26.04 hp at 1,000 gpm and 13.33 hp at 800 gpm.
  2. Improving Pumping System Performance: A Sourcebook for Industry — impeller trimming — U.S. DOE (with the Hydraulic Institute). Affinity laws for impeller trim at constant speed: Q₂ = Q₁ (D₂/D₁), H₂ = H₁ (D₂/D₁)², bhp₂ = bhp₁ (D₂/D₁)³; impellers are rarely reduced below 70 % of their original size.

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