How to use this calculator
- Establish the baseline point. Measured airflow, fan RPM, static pressure and brake power at the same moment on the same system.
- Pick the solve direction. Enter the new RPM after a sheave/VFD change — or the target airflow to back-solve the required speed.
- Read the scaled point. Flow scales linearly, pressure with the square, power with the cube; percent changes are shown for each.
- Check the motor. Compare the new brake power against the nameplate and service factor before committing to a speed-up.
How it works
A fan riding a fixed system curve obeys three similarity relations — the
fan affinity laws. With speed ratio
r = N₂/N₁:
Q₂ = Q₁·r P₂ = P₁·r² W₂ = W₁·r³
The linear law is intuitive; the square and cube are where designs go wrong. Pressure rising with r² means duct leakage and noise climb fast; power rising with r³ means small airflow gains are expensive and small reductions are nearly free. The calculator makes the cube explicit and flags speed-ups that outgrow the motor.
Fan-side companions: the static pressure calculator tells you whether the system, not the fan, is the real problem (it usually is); the duct friction loss calculator prices the system curve itself; and the belt RPM calculator handles the sheave arithmetic that sets N₂ on belt-driven fans.
Worked example
Verified against the live calculator
A fan delivers 1,000 cfm at 800 RPM,
0.50 in w.g. and 1.0 hp brake. Speeding it up
to 1,000 RPM (r = 1.25):
Q₂ = 1,250 cfm P₂ = 0.50 × 1.25² = 0.78 in w.g. W₂ = 1.0 × 1.25³ = 1.95 hp
A 25% airflow gain costs 95% more power — the 1 hp motor is now badly undersized, and that is before belt and bearing loads. Run the same numbers downward (800 → 640 RPM) and the fan still moves 800 cfm on 0.51 hp: half the energy for 80% of the air, the arithmetic behind every VFD retrofit pitch.
Frequently asked questions
What are the three fan laws?
For the same fan on the same system: airflow scales with speed (Q ∝ N), static pressure with speed squared (P ∝ N²), and brake power with speed cubed (W ∝ N³). They follow from fan similarity and hold as long as the system curve and air density stay fixed.
How much more power does 10% more airflow take?
About 33%. Flow needs 10% more speed, and power goes with the cube: 1.1³ = 1.331. That cube is why "just speed up the fan" so often ends with an overloaded motor — and why slowing a fan down saves so much energy.
Do the fan laws work for VFD speed changes?
Yes — they are the entire basis of VFD fan savings. At 80% speed a fan moves 80% of the air on 51% of the power. The same math applies to sheave changes on belt drives; only the way you set the new RPM differs.
When do the fan laws NOT apply?
When the system changes (dampers, filters loading up, duct modifications move the system curve), when comparing different fans or wheel sizes, near surge/stall regions, and when density changes (temperature/altitude) without correction. They predict the same fan riding the same system curve to a new speed.
Method & assumptions
- Same fan, same wheel, same system curve, constant air density. Damper moves, filter loading and duct changes shift the system curve and void the simple scaling.
- Brake (shaft) power scales with the cube; motor input power also depends on motor and drive efficiency at the new load point.
- Density correction (altitude, temperature) multiplies pressure and power by ρ₂/ρ₁ before the laws are applied.
- Stay clear of the fan's surge/stall region — similarity does not rescue an unstable operating point.