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Pump Affinity Laws Calculator

Calculate new pump flow, head, and brake horsepower (BHP) when changing impeller RPM or diameter based on the mechanical affinity laws.
GPM
Feet
BHP
RPM / in
RPM / in

New Flow (Q₂)

414.3 GPM
Directly proportional

New Head (H₂)

82.4 Feet
Squared ratio

New Power (P₂)

11.38 BHP
Cubed ratio
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What is The Physics of PumpAffinity?

The technical foundation and mathematics behind the PumpAffinityCalc tool.

Mathematical Foundation

Core Equation
Q1Q2=N1N2&H1H2=(N1N2)2&P1P2=(N1N2)3\frac{Q_1}{Q_2} = \frac{N_1}{N_2} \quad \& \quad \frac{H_1}{H_2} = \left(\frac{N_1}{N_2}\right)^2 \quad \& \quad \frac{P_1}{P_2} = \left(\frac{N_1}{N_2}\right)^3
QQ= Fluid volumetric flow rate delivery (GPM).
HH= Hydraulic head pressure generated against the piping system (ft of head).
PP= Brake horsepower drawn by the driving electrical pump motor (BHP).
NN= Impeller rotational speed (RPM) or physical diameter modification (inches).

Laws & Principles

  • The Pump Affinity Laws dictate that shaft horsepower demand mathematically scales by the cube of the impeller speed. Reducing pump RPM by exactly half physically requires only 1/8th (12.5%) of the original motor horsepower.
  • The laws strictly assume geometrically similar pump casings and absolute constant system efficiency, meaning extreme low-speed calculations may analytically underpredict actual VFD parasitic losses.

Step-by-Step Example Walkthrough

" A 10 HP chilled water booster pump delivering 400 GPM at 1,750 RPM is throttled down by a Variable Frequency Drive to 1,400 RPM to save facility energy. "

  1. 1. Calculate the speed reduction ratio (N2 / N1) = 1,400 / 1,750 = 0.80 (80%).
  2. 2. Flow capacity (Q) drops linearly: 400 GPM * 0.80 = 320 GPM.
  3. 3. Brake Horsepower drops by the cube (0.80³ = 0.512 multiplier): 10 HP * 0.512 = 5.12 BHP.
Final Result: 5.12 Brake Horsepower

Quick Answer: What does the This Calculator do?

Use this calculator to get fast, accurate results. Results are calculated instantly — no sign-up or download required.

How to Use This Calculator

  1. 1.Enter your values into the input fields above. All inputs are labelled with the expected unit of measurement.
  2. 2.Results update instantly as you type — no submit button required.
  3. 3.Use the Share button to copy a direct link to your current inputs for later reference.
  4. 4.Scroll to the Knowledge Hub below for underlying formulas, worked examples, and reference values.

Pro Tips

Best Practices

  • ✓Double-check your units. Ensure all inputs use consistent units. The calculator labels indicate which unit is expected.
  • ✓Add a safety margin. For materials and structural calculations, design slightly above the calculated minimum.

Common Mistakes

  • ✗Don't skip verification. For safety-critical or regulatory decisions, have results reviewed by a qualified professional.
  • ✗Don't ignore edge cases. Extreme input values may exceed the formula's valid range. Check the Knowledge Hub for valid input bounds.

Frequently Asked Questions

What does the This Calculator calculate?

Use this calculator to get fast, accurate results.

Is the This Calculator free to use?

Yes — completely free. No sign-up, no download, and no ads. Results are calculated instantly in your browser.

How accurate is the This Calculator?

The This Calculator uses industry-standard formulas. For safety-critical, financial, or regulatory applications always verify results with a licensed professional.

Can I use the This Calculator on my phone?

Yes. Calcady is fully mobile-responsive. The This Calculator works on any device — smartphone, tablet, or desktop — with no app required.

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