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Pump Affinity Law Calculator

Estimate pump flow, head, and shaft power at a different rotational speed for the same impeller and a similar system.

Why it matters: Pump power changes approximately with the cube of speed, while head changes with the square. This is central to VFD operation and hydronic commissioning.

User inputs

Enter field measurements

6 inputs
Select the unit convention used for all values in this calculation.
gpm or m³/sMeasured or scheduled pump flow at the baseline speed.
ft or mBaseline differential head across the pump.
hp or kWBaseline shaft power at the operating point.
rpmVerified pump rotational speed.
rpmProposed or measured pump speed.

Calculated result

Engineering evaluation

Within screening range
Predicted pump flow (Q₂)400 gpm
Speed ratio (rN)
0.8
Predicted head (H₂)
51.2 ft
Predicted shaft power (W₂)
7.68 hp

Engineering interpretation

For a geometrically unchanged pump operating in a similar system, the entered speed change predicts 400 gpm, 51.2 ft, and 7.68 hp. Confirm the prediction against the manufacturer curve and measured system operating point.

Motor-driven equipment

Estimate electrical demand and energy use

Use nameplate information and an operating schedule to screen motor input power, current, annual energy, and operating cost. Results update automatically.

Optional companion calculation
Choose the motor nameplate output-power convention.
Rated shaft output, not electrical input.
Used to estimate current; it does not change the hp-based energy result.
Use efficiency at the evaluated load point when available.
Use measured or defensible operating load rather than motor nameplate size alone.
Used only for the estimated current calculation.
Assumes all selected motors operate concurrently at the entered load.
Replace the profile with the actual occupied, process, or control schedule.
$/kWh
Use the applicable marginal utility energy charge; demand charges are not included.

Estimated result

Total motor input power (Pin,total)6.21 kW
Current per motor (I)
9.18 A
Total coincident current (Itotal)
9.18 A
Daily energy (Ed)
50 kWh/day
Annual operating hours (Hy)
2,080 h/year
Annual energy (Ey)
12,925 kWh/year
Annual energy cost (Cy)
$1,551/year

Equations and assumptions

Nameplate-based screening method

Pin=PratedLηmI=1000Pin3VPFEy=NPinhddyCy=Eyce

Horsepower is converted using 1 hp = 0.7457 kW. This estimate assumes steady average load and the entered operating-point efficiency. Voltage and power factor affect estimated current, but hp, load, efficiency, quantity, and schedule establish the energy estimate. VFD speed profiles, cycling, standby power, demand charges, and process variation require separate evaluation.

Technical basis: U.S. Department of Energy — Determining Electric Motor Load and Efficiency

Engineering knowledge center

Understand the calculation—not just the answer

2026-08-07 · Free Library
Governing relationships
rN = N₂/N₁
Q₂ = Q₁rN
H₂ = H₁rN²
W₂ = W₁rN³
Current substitution

rN = N₂/N₁ = 1400 / 1750 = 0.8; Q₂ = Q₁rN = 500 × 0.8 = 400 gpm.

Calculation sequence

Step-by-step method

  1. Divide the proposed rotational speed by the baseline speed.
  2. Multiply baseline flow by the speed ratio.
  3. Multiply baseline head by the square of the speed ratio.
  4. Multiply baseline shaft power by the cube of the speed ratio.

Equation legend

Inputs and calculated quantities

Q₁
Baseline flow — gpm or m³/s
H₁
Baseline head — ft or m
W₁
Baseline shaft power — hp or kW
N₁
Baseline speed — rpm
N₂
New speed — rpm
Q₂
Predicted pump flow — gpm
rN
Speed ratio
H₂
Predicted head — ft
W₂
Predicted shaft power — hp

Continue the evaluation

Related calculators

Hydronic Pressure Loss Motor Loading Percent of Design

Engineering calculation disclaimer

These engineering tools are provided for educational, preliminary evaluation, field verification, and commissioning support. Results depend on the accuracy of user-entered information and the assumptions stated for each calculation. Every colored status and comparison is a screening indicator only; project criteria, contract requirements, applicable codes, manufacturer instructions, measurement uncertainty, and authorized engineering judgment govern. The tools do not replace project-specific engineering analysis or the judgment of a licensed professional engineer.

Read the full use and limitation statement