Fan Laws Calculator
Affinity laws for fans and pumps: flow, pressure and power after a speed, impeller or density change, or the speed needed for a target flow or pressure.
What a VFD speed change or a different impeller does to flow, pressure and power — and the speed to set for a duty you want — with the cubic power law made visible.
Example: A fan giving 10,000 m³/h at 500 Pa and 2.5 kW at 1,450 rpm, slowed to 1,200 rpm: 8,276 m³/h, 342 Pa and 1.42 kW. For 12,000 m³/h it would need 1,740 rpm and 4.32 kW.
Flow goes with speed.
Power goes with its cube.
The three laws, when they hold, and why a slower fan saves so much more than it loses.
The three laws
For a given fan or pump moving a fluid of fixed density, flow is proportional to rotational speed, pressure (head) to speed squared, and power to speed cubed. Running a fan at 80 % speed therefore gives 80 % of the flow, 64 % of the pressure and only 51 % of the power — the reason variable-speed drives pay back. The same laws with the impeller diameter carry exponents 3, 2 and 5, and pressure and power scale directly with density while volume flow does not.
When they hold
The laws are dimensional similarity: they map one point on the fan curve to the corresponding point at the new speed or size, with the same efficiency. That is exact only if the system resistance also follows a square law through the origin (pure friction, no static head or fixed pressure). With a static head, or with dampers and controls in the loop, the operating point moves along the system curve and the laws must be read off the manufacturer's curves instead. A large change — more than about half in speed or a third in diameter — is flagged for the same reason: efficiency drifts, and mechanical limits (bearing speed, motor rating, first critical speed) are not part of the laws.
Solving for speed
Inverting the flow law gives the speed for a target flow directly (ratio of flows, over the diameter ratio cubed); inverting the pressure law needs the square root of the pressure ratio. The page then reports the whole duty at that speed, including the power, so a motor can be checked. Units do not matter — only ratios enter — as long as each quantity is entered in the same unit before and after.
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SOURCES
- Çengel, Y. A. & Cimbala, J. M., Fluid Mechanics: Fundamentals and Applications — §14-3 pump scaling laws (affinity laws) and their limits
- ASHRAE Handbook — HVAC Systems and Equipment, chapter "Fans": fan laws for geometrically similar fans
Last reviewed 19 September 2026. How results are checked: How we verify.