Calculation reviewed: 4 October 2026 · Engineering Desk Tools
How to use the Pump affinity laws calculator
Predict new flow, head and power when a centrifugal pump speed changes. Start with measurements or documented values for the equipment and reporting period you actually want to assess. The calculator does not fill in a typical installation for you. Its blank fields help keep a demonstration value from being mistaken for your own operating data.
Choose the required options, enter the values in the labelled units and select Calculate. If a field is rejected, check its range and unit before changing it. The result is accompanied by the equation and assumptions so you can decide whether it answers your engineering question.
Inputs and measurement basis
- Current speed (RPM). Present pump speed, in RPM. The value must be greater than zero.
- New speed (RPM). Proposed pump speed, in RPM. The value must be greater than zero.
- Current flow (m³/h). Flow at the present speed, in m³/h.
- Current head (m). Head at the present speed, in metres.
- Current shaft power (kW). Shaft power at the present speed, in kW.
Record the measurement source and operating condition. Retain unrounded values for verification.
Method and interpretation
For a centrifugal pump running at a different speed, flow changes in proportion to speed, head with the square of speed and power with the cube. A modest speed reduction therefore cuts power sharply, which is the basis of variable-speed energy savings. The relationships hold for the same pump and impeller and assume efficiency stays about the same.
With speed ratio r = N2 / N1: Q2 = Q1 × r. H2 = H1 × r². P2 = P1 × r³.
The laws apply to the same pump and impeller diameter, and assume the efficiency stays about the same. In a system with a large static head, flow does not fall in simple proportion with speed because the system curve does not pass through the origin, so use the pump curve and system curve instead. Savings from a variable speed drive must be checked against the real duty profile. Do not exceed the pump or motor speed limits.
Worked example
This example does not populate the form. Enter your own installation data.
Calculated result: 7.68 kW shaft power at the new speed. Valid for the same pump, impeller and a friction-dominated system. Check the pump curve, static head and minimum flow before changing speed.
Check the arithmetic independently using the displayed equation. Retain intermediate precision and compare the final value with your equipment documentation.
Quick-reference table
These illustrative rows retain the worked example assumptions except for the varied input. They are not certified ratings or manufacturer data. Use the form for intermediate values.
Common mistakes
Applying the laws to a system with large static head, where the operating point moves along a curve that does not pass through zero; ignoring minimum-flow limits at low speed; using the laws for impeller trimming; assuming an energy saving without checking the duty profile. Before relying on the output, check the decimal format, unit scale and source of each value. Recheck unusual results against the formula.
Frequently asked questions
Are the example values used automatically?
No. Inputs remain blank when the tool opens or when you clear them. The worked example and table are reading material below the calculator. Enter the actual values you want to check each time, and label saved reports so their context is not lost.
What does the result mean?
The result is the predicted flow, head and power at the new speed. Treat it as an estimate and confirm it against the pump curve and system curve, especially when the static head is high.
Can I use a zero or a negative value?
The allowed range follows the meaning of each input. A divisor needs a positive value; other fields may allow zero. Check the form labels and error message rather than forcing an invalid value. A rejected input must be corrected before a result can be shown.
Is this a final design or equipment approval?
No. The laws apply to the same pump and impeller diameter, and assume the efficiency stays about the same. In a system with a large static head, flow does not fall in simple proportion with speed because the system curve does not pass through the origin, so use the pump curve and system curve instead. Savings from a variable speed drive must be checked against the real duty profile. Do not exceed the pump or motor speed limits. Use the calculation as support for a checked decision, and review equipment documentation and applicable requirements before changing an installation or operating setting.
How can I save or share a calculation?
Calculate first, then use Copy result or Print report. Some maintenance tools also provide a CSV summary. Reports contain your own entered data, so review them before sharing. You can share the public page URL without including plant records or confidential measurements.
How do I report an unexpected result?
Use the Contact page and include the tool URL, input values, units, expected output and the reference you used. Explain the measurement basis. Exclude confidential information.
Related tools and records
Use related calculations with consistent units, periods and equipment scope.
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