# Pump Affinity Laws Calculator (Q∝n, H∝n², P∝n³)

Apply the pump affinity laws to the same pump at different speeds or with a different impeller diameter. Speed mode: ratio = n2/n1; diameter mode: ratio = D2/D1. Then Q2 = Q1·ratio, H2 = H1·ratio², P2 = P1·ratio³. Q1, H1 and P1 are optional baseline-condition inputs; if all three are omitted, only the ratio is returned. Flow in m³/s/L/s/L/min/m³/h, head in m/ft, power in W/kW/hp, impeller diameter in m/cm/mm; SI equivalents (m³/s, m, W) are also reported.

> Canonical page: https://elysiatools.com/en/tools/pump-affinity-laws

- **Category:** Math & Numbers

- **Keywords:** affinity laws, pump affinity, pump laws, speed scaling, impeller diameter, flow scaling, head scaling, power scaling, centrifugal pump, pump performance, Q∝n, H∝n², P∝n³, impeller trim, variable speed pump, pump scaling, hydraulics

## Overview

The Pump Affinity Laws Calculator estimates how a pump’s flow, head, and power change with speed or impeller diameter. Choose speed mode or diameter mode, enter the baseline and new values, and optionally provide Q₁, H₁, and P₁ to calculate the scaled operating values.

## Inputs

- **Mode** (select): Speed mode uses the speed ratio n2/n1. Diameter mode uses the impeller diameter ratio D2/D1.
- **Speed n₁ (rpm)** (number): Initial pump speed n1 (rpm). Required when Mode = Speed.
- **Speed n₂ (rpm)** (number): New pump speed n2 (rpm). Required when Mode = Speed.
- **Impeller Diameter D₁** (number): Initial impeller diameter D1. Enter in the selected Diameter Unit. Required when Mode = Diameter.
- **Impeller Diameter D₂** (number): New impeller diameter D2. Enter in the selected Diameter Unit. Required when Mode = Diameter.
- **Diameter Unit** (select)
- **Initial Flow Q₁** (number): Initial flow Q1 at the baseline speed / diameter. Enter in the selected Flow Unit. Optional.
- **Flow Unit** (select)
- **Initial Head H₁** (number): Initial head H1 at the baseline speed / diameter. Enter in the selected Head Unit. Optional.
- **Head Unit** (select)
- **Initial Power P₁** (number): Initial power P1 at the baseline speed / diameter. Enter in the selected Power Unit. Optional.
- **Power Unit** (select)
- **Decimal Places** (number)

## When to use

- Estimate pump performance after changing motor speed or operating rpm.
- Evaluate flow, head, and power changes for a different impeller diameter.
- Calculate a scaling ratio when baseline flow, head, and power are not available.

## How it works

- Select Speed mode to calculate ratio = n₂/n₁, or Diameter mode to calculate ratio = D₂/D₁.
- Enter the initial and new speed or impeller diameter using the available units.
- Optionally enter baseline flow Q₁, head H₁, and power P₁ with their selected units.
- The calculator applies Q₂ = Q₁·ratio, H₂ = H₁·ratio², and P₂ = P₁·ratio³, then returns the results as JSON with SI equivalents.

## Use cases

- Compare pump output at different variable-speed drive settings.
- Estimate the effect of impeller trimming or replacing an impeller with a different diameter.
- Review expected energy and hydraulic performance changes during pump selection or system adjustments.

## Frequently asked questions

### What are the pump affinity laws?

For the same pump, flow scales with the ratio, head scales with the ratio squared, and power scales with the ratio cubed.

### What is required in Speed mode?

Enter the initial speed n₁ and new speed n₂ in rpm. Baseline flow, head, and power are optional.

### What is required in Diameter mode?

Enter the initial diameter D₁ and new diameter D₂, using meters, centimeters, or millimeters.

### Can I calculate only the scaling ratio?

Yes. If Q₁, H₁, and P₁ are all omitted, the calculator returns only the ratio.

### Which units are supported?

Flow supports m³/s, L/s, L/min, and m³/h; head supports m and ft; power supports W, kW, and hp; diameter supports m, cm, and mm.

## Related tools

- [Absolute Value Calculator](https://elysiatools.com/en/tools/absolute-value-calculator): Calculate the absolute value of positive, negative, or decimal numbers and explain the sign relationship
- [Air Changes per Hour (ACH, n = Q/V)](https://elysiatools.com/en/tools/air-changes-per-hour): Compute the air change rate (ACH / n) of a room from the outdoor supply airflow Q and the room volume V: n = Q/V (1/h). Three modes: solve ACH (given Q and V), solve airflow (given n and V), or solve volume (given n and Q). Flow in m³/s/m³/h/CFM, volume in m³/ft³/L. Also reports the well-mixed single-zone purge time to reach a target residual fraction ε (default 1%): t = −ln(ε)/n hours.
- [Bearing Life L10 Calculator](https://elysiatools.com/en/tools/bearing-life-l10): Calculate the basic rating life of a rolling bearing: L10 = (C/P)^p, with p = 3 for ball bearings and p = 10/3 for roller bearings. When a speed is provided, converts to L10h in operating hours.
- [Bolt Torque Clamp Force Calculator](https://elysiatools.com/en/tools/bolt-torque-clamp-force): Convert between bolt tightening torque and axial clamp force. T = K·F·d, where K is the nut factor (~0.20 for dry steel). Solve torque from force, or force from torque.
- [Cable Ampacity Calculator (IEC 60364-5-52)](https://elysiatools.com/en/tools/cable-ampacity-calculator): Estimate copper cable current-carrying capacity per the simplified IEC 60364-5-52 reference method. Combines cross-section, insulation (PVC 70°C / XLPE 90°C), installation method, and ambient temperature to derive the corrected allowable ampacity (A).
- [Capacitor Reactive Power Calculator (Q_c = 2πfCU²)](https://elysiatools.com/en/tools/capacitor-reactive-power): Compute the reactive power produced by a known capacitor: Q_c = 2π·f·C·U². Supports single-phase, three-phase star (Y) and delta (Δ) connections. Returns Q_c in var/kvar, capacitive reactance Xc, and capacitor current Ic. Complementary to the power-factor-correction tool (which sizes a capacitor for a target cosφ).
- [Chain Sprocket Ratio Calculator](https://elysiatools.com/en/tools/chain-sprocket-ratio): Calculate the ratio, driven speed and chain linear speed of a chain drive. i = z₂/z₁ = n₁/n₂, chain speed v = z₁·p·n₁/60000. Enter the pitch to compute chain speed.
- [CM to MM](https://elysiatools.com/en/tools/cm-to-mm): Convert centimeters to millimeters with configurable decimal precision

## Samples

- [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion
- [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion
- [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion
- [Web Image Processing Rust Samples](https://elysiatools.com/en/samples/web-image-processing-rust): Web Rust image processing examples including image read/save, scaling, and format conversion