2026-07-30 10 min

Pump Curve Calculator

Generate pump performance curves from known data points or from affinity laws. Analyze system curves and determine pump operating points.

Calculator

Unit System

Shut-off Head H0 (m)

Design Flow Q_d (m^3/h)

Design Head H_d (m)

BEP Efficiency eta_BEP (%)

Min Flow Q_min (m^3/h)

Max Flow Q_max (m^3/h)

System Static Head H_stat (m)

System Friction Coeff k

Number of Points

Results

Optimal

BEP Flow Q_BEP

100.00m^3/h

Flow at best efficiency point

BEP Head H_BEP

80.00m

Head at best efficiency point

BEP Efficiency eta_BEP

85.0%

Maximum pump efficiency

Operating Point Flow

141.42m^3/h

Flow at pump-system curve intersection

Operating Point Head

60.00m

Head at pump-system curve intersection

Operating Efficiency

91.1%

Efficiency at operating point

Power at Operating Point

25.39kW

Power consumption at operating point

Visualizations

Results Overview

100m^3/hBEP Flow Q_BEP

80m^3/hBEP Head H_BEP

85m^3/hBEP Efficiency eta_BEP

141.4m^3/hOperating Point Flow

60m^3/hOperating Point Head

91.1m^3/hOperating Efficiency

25.4m^3/hPower at Operating Point

Formula

The pump H-Q curve is approximated by a parabola from shut-off head H_0 to the design point. The system curve combines static head and friction losses.

H = H_0 - a Q^2 | H_sys = H_stat + k Q^2

Alternative Form

eta = b1 Q + b2 Q^2 + b3 Q^3 (efficiency polynomial)

Variables

Symbol	Name	Unit	Description
H	Pump Head	m	Total dynamic head at given flow
H_0	Shut-off Head	m	Head at zero flow
a	Parabola Coefficient	-	Curve shape coefficient determined from design point
Q	Flow Rate	m^3/h	Volumetric flow rate
H_stat	Static Head	m	System head at zero flow (elevation + pressure)
k	Friction Coefficient	-	System friction loss coefficient

Explanation

The pump curve shows the relationship between flow rate (Q) and total head (H) at constant speed. The parabolic approximation H = H_0 - aQ^2 is a simplified model where H_0 is the shut-off head and the coefficient a determines how rapidly head drops with flow. The system curve H_sys = H_stat + kQ^2 represents the head required by the piping system. The pump operating point is where the pump curve and system curve intersect.

Derivation

For a centrifugal pump, the theoretical head varies with flow based on Euler turbomachinery equation: H_th = (u2^2 - u1^2)/g - (v2^2 - v1^2)/(2g). The actual head includes losses from friction, shock, and recirculation, which vary approximately with Q^2. The parabolic fit H = H_0 - aQ^2 is a practical approximation valid near the BEP. System curves follow from Darcy-Weisbach friction loss: h_f = f(L/D)(v^2/2g) = kQ^2.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Determine pump curve coefficient a from shut-off head H_0 and design point (Q_d, H_d).

a = (H_0 - H_d) / Q_d^2

H_0:100.00 m

H_d:80.00 m

Q_d:100.00 m^3/h

Intermediate: a = (100.00 - 80.00) / 100.00^2

Result: a = 0.002000

Step 2

Construct system curve: H_sys = H_stat + k Q^2. Plot both curves.

H_sys = H_stat + k Q^2

H_stat:20.00 m

k:0.0020

Result: System curve defined with static head 20.00 m and friction coeff 0.0020

Step 3

Find operating point by solving H_pump(Q) = H_sys(Q).

H_0 - a Q^2 = H_stat + k Q^2 -> Q = sqrt((H_0 - H_stat)/(a + k))

H_0:100.00 m

H_stat:20.00 m

a:0.002000

k:0.0020

Intermediate: Q = sqrt((100.00 - 20.00) / (0.002000 + 0.0020))

Result: Q_op = 141.42 m^3/h, H_op = 60.00 m

Final Answer

100.00

Worked Examples

See how the calculator works with different scenarios.

Scenario

A pump has shut-off head 100m, design flow 100 m^3/h at 80m head. System has 20m static head and friction coefficient k=0.002.

Inputs

H_0:100 m

Q_d:100 m^3/h

H_d:80 m

H_stat:20 m

k:0.002

Calculation

a = (100 - 80)/(100^2) = 0.002 Q_op = sqrt((100-20)/(0.002+0.002)) = sqrt(80/0.004) = 141.4 m^3/h H_op = 100 - 0.002(141.4^2) = 60 m

Result

BEP: Q=100 m^3/h, H=80 m, eta=85%. Op Pt: Q=141.4 m^3/h, H=60 m

Interpretation

The pump operates to the right of BEP at 141.4 m^3/h with 60m head. This is acceptable if within the allowable operating range. Efficiency at this point is slightly below BEP.

Understanding Your Result

Your Result: BEP Flow Q_BEP: 100.00 m^3/h

Typical range: Pump curve shapes vary by specific speed: radial (steep drop), mixed (moderate), axial (flat to drooping). BEP typically occurs at 70-90% of maximum flow. Shut-off head is typically 10-40% above BEP head.

What This Means

The pump curve (H-Q curve) shows the head a pump can deliver at various flow rates. The system curve shows the head required by the piping system. The intersection of these curves determines the actual operating point.

Why It Matters

Understanding pump and system curves is fundamental to pump selection and system design. An improperly matched pump will operate away from BEP, causing reduced efficiency, vibration, cavitation, or motor overload.

Professional Interpretation

The parabolic curve fit is a simplification. Actual pump curves have more complex shapes, especially near shut-off and run-out. Always use manufacturer curves for final design. The system curve calculation should account for all components: pipes, valves, fittings, heat exchangers, and elevation changes. Operating point analysis should check the full operating range, not just the design point.

Recommendations

•Select pumps so the operating point falls within 70-110% of BEP flow
•Verify operating point at both design and maximum flow conditions
•For variable speed pumps, check operation across the entire speed range
•Account for aging: pipes roughen over time, increasing system resistance
•Consider parallel pump operation curves for multi-pump systems

Educational Content

Introduction

A pump curve is a graphical representation of a pump's performance, showing the relationship between flow rate (Q) and head (H) at a constant speed. Combined with the system curve, it determines where a pump will actually operate in a given installation.

Concept Explanation

The pump curve represents the energy added to the fluid by the impeller minus internal losses. The curve shape depends on the impeller design (specific speed) and pump geometry. The system curve represents the energy required to move fluid through the piping system, including static head (constant with flow) and friction losses (increase with Q^2). The operating point is the intersection of these curves, where the energy supplied by the pump equals the energy required by the system.

Applications

▸Pump selection and sizing for new installations

▸Troubleshooting existing pump performance issues

▸Analyzing pump operation at off-design conditions

▸Designing control strategies for variable speed pumps

▸Evaluating parallel and series pump configurations

▸System modification impact assessment

Benefits

•Visual understanding of pump-system interaction
•Quantitative prediction of pump operating conditions
•Identification of operating range and limitations
•Support for energy optimization and efficiency improvement
•Essential for pump specification and procurement

Limitations

•Parabolic curve fit is approximate for off-design operation
•Efficiency estimation is simplified
•Does not account for pump wear or fouling
•System curve assumes clean pipe conditions

Best Practices

•Always verify with manufacturer pump curves for final design
•Include all system components in system curve calculation
•Consider minimum and maximum flow limits of the pump
•Account for fluid property variations (viscosity, density)
•Document both pump and system curves for future reference

Common Misconceptions

Myth: A pump always operates at its design point.

Truth: The pump operates at the intersection of its curve with the system curve, which rarely coincides exactly with the design point. The operating point depends on the specific system characteristics.

Myth: The pump curve is linear.

Truth: Pump curves are curved (parabolic or more complex). The head decreases with increasing flow, and the rate of decrease depends on the impeller design and specific speed.

Myth: Larger pumps always deliver more flow.

Truth: A larger pump moved to a different system may deliver less flow if the system curve is steep. The operating point depends on the pump-system interaction, not just the pump size.

Practical Tips

•BEP (Best Efficiency Point) is typically at 70-90% of maximum flow
•Operating at less than 50% of BEP flow can cause recirculation and heating
•Operating at more than 120% of BEP flow may cause cavitation and motor overload
•The system curve is independent of the pump - it only depends on the piping system
•Parallel pumps: add flows at same head. Series pumps: add heads at same flow
•For accurate system curves, calculate friction losses using Darcy-Weisbach, not Hazen-Williams
•Pump curves from manufacturers are for cold water - correct for viscous or hot fluids

Common Mistakes

Using pump BEP as the design operating point

BEP is the most efficient point but the pump curve must intersect the system curve there. Design the system curve to pass through the BEP for optimal efficiency.

Ignoring the system curve in pump selection

A pump cannot be selected without knowing the system curve. The same pump in different systems will operate at different points.

Assuming the system curve is linear

System curves are parabolic (friction varies with Q^2). Only the static head component is constant. Never interpolate linearly between two operating points on a system curve.

Mixing units in curve calculations

Ensure consistent units throughout. Head in meters, flow in consistent units (m^3/h or L/s or gpm). The coefficient k must use the same flow units as the pump curve.

Assumptions

This calculator makes the following assumptions to provide estimates:

Parabolic Curve Shape: The pump curve is approximated as a parabola H = H_0 - aQ^2. Actual curves may deviate from this form, especially near shut-off and run-out.

Constant Speed: The pump curve is valid at a single operating speed. Speed changes shift the curve according to affinity laws.

Cold Water Performance: Curves assume cold water (density = 1000 kg/m^3, viscosity = 1 cP). Corrections are needed for other fluids.

Clean System: The system curve assumes clean pipes with constant roughness. Fouling, scaling, or corrosion will increase friction over time.

Limitations

Be aware of these limitations when using this calculator:

Simplified Curve Fit: The parabolic approximation may not accurately represent the actual pump curve, especially for mixed-flow and axial-flow pumps with non-parabolic characteristics.

No NPSH Analysis: The calculator determines the operating point but does not check NPSH requirements at that point. Always verify NPSH margin separately.

Efficiency Approximation: The efficiency curve is a simple quadratic approximation. Actual efficiency curves have more complex shapes and may differ significantly.

Single Speed Only: The analysis is for a fixed speed. For variable speed applications, recalculate at each speed using affinity laws.

Frequently Asked Questions

Answers to common questions about this calculator.

What is a pump curve?

A pump curve is a graphical representation of a pump's performance showing head (H) versus flow rate (Q) at constant speed. It also typically includes efficiency, power, and NPSHr curves.

What is the system curve?

The system curve shows the head required to move fluid through the piping system at various flow rates. It includes static head (constant) and friction losses (increase with Q^2).

How do I find the operating point?

The operating point is where the pump curve intersects the system curve. Solve H_pump(Q) = H_system(Q) for Q, then find H from either curve.

What is BEP (Best Efficiency Point)?

BEP is the flow rate at which the pump operates at maximum efficiency. It is typically the design target for pump selection as it minimizes energy consumption.

How does the pump curve change with speed?

Speed changes shift the pump curve according to affinity laws: Q varies with n, H varies with n^2. The new curve maintains the same shape but is scaled.

What is the allowable operating range?

Typically 70-110% of BEP flow for standard pumps. Outside this range, efficiency drops, vibration increases, and pump life decreases. Check manufacturer recommendations.

How do parallel pumps affect the system curve?

Parallel operation doubles the flow at each head point. The combined curve is the sum of individual pump flows at each head. The operating point depends on the system curve shape.

How do series pumps affect the system curve?

Series operation doubles the head at each flow point. The combined curve is the sum of individual pump heads at each flow. Series is used for high-head systems.

What is pump run-out?

Run-out is the maximum flow a pump can deliver at zero head (or minimum system resistance). Operating at run-out can overload the motor and cause cavitation.

What is pump shut-off head?

Shut-off head (H_0) is the head developed at zero flow. Operating at shut-off can cause overheating due to recirculation of a small volume of fluid.

How do I generate a pump curve from data points?

Enter two or more (Q, H) data points and the calculator fits a curve through them. Three or more points give a more accurate curve than the simple parabolic fit.

What is the minimum flow for a pump?

Minimum continuous flow is the lowest flow at which the pump can operate without damaging recirculation or temperature rise. Typically 10-30% of BEP flow depending on pump design.

How does impeller trim affect the pump curve?

Trimming the impeller diameter reduces both head and flow. The new curve follows the affinity laws for diameter change (Q ~ D^3, H ~ D^2), shifting the entire curve downward.

What information does the pump curve provide for selection?

The pump curve shows if the pump can deliver the required head at the required flow rate, the efficiency at that point, power consumption, and NPSHr - all essential for proper selection.

How do I read a manufacturer pump curve?

Manufacturer curves show multiple impeller diameters at fixed speed. Read across from your required flow to find available head for each diameter. Also check efficiency contours, power curves, and NPSHr curves.

What is the efficiency curve on a pump curve sheet?

Efficiency is shown as contour lines (islands) on the H-Q curve. The highest efficiency contour is at BEP. Moving away from BEP in any direction reduces efficiency.

How does fluid viscosity affect the pump curve?

High viscosity reduces pump head and efficiency. Correction factors from HI standards reduce the H-Q curve and efficiency curve for viscous fluids.

What is the NPSHr curve?

The NPSHr curve shows the minimum NPSH required at each flow rate to prevent cavitation. It typically increases with flow rate. Always check NPSH margin at the operating point.

How do I calculate the system curve for a complex piping network?

Calculate the total friction loss at several flow rates using the Darcy-Weisbach equation for each pipe segment, then sum with static head. The resulting points define the system curve.

What is the difference between head and pressure?

Head (m or ft) is energy per unit weight of fluid. Pressure = rho x g x H. Pumps produce head, not pressure. The same head corresponds to different pressures for different fluids.

How does pipe aging affect the system curve?

Pipe roughness increases over time due to corrosion, scaling, or fouling, which increases friction losses. The system curve becomes steeper, reducing flow at the same pump head.

What is the affinity parabola on the pump curve?

The affinity parabola (H ~ Q^2) shows the locus of operating points at constant efficiency as speed changes. Operating points along this parabola maintain dynamic similarity.

How do I select a pump using curves?

Overlay the system curve on pump manufacturer curves. Select a pump whose curve intersects the system curve at the desired flow rate and at an efficiency within 90% of BEP.

What causes a pump to operate to the right of BEP?

Low system resistance (lower static head, larger pipes, fewer fittings) shifts the intersection point to the right. The pump delivers more flow at lower head.

What causes a pump to operate to the left of BEP?

High system resistance (high static head, smaller pipes, clogged filters) shifts the intersection to the left. The pump delivers less flow at higher head.

How does the pump curve change with impeller diameter?

Smaller diameter shifts the curve down and left following affinity laws. Manufacturers provide curves for multiple trims on the same curve sheet.

What is the power curve on a pump curve sheet?

The power curve shows brake horsepower (kW) required at each flow rate. Power increases with flow. Operating conditions must not exceed motor rated power.

How do I determine if a pump is suitable for a system?

Check: (1) Operating point flow meets requirements, (2) Operating point efficiency > 80% of BEP, (3) NPSHa > NPSHr + margin, (4) Power < motor rating, (5) Flow within allowable range.

What is the effect of specific speed on pump curve shape?

Low specific speed (radial): steep curve, head drops rapidly with flow. Medium specific speed (mixed): moderate slope. High specific speed (axial): flat or drooping curve.

Can a pump curve droop (head increase with flow)?

Yes, axial flow pumps and some mixed flow pumps can have drooping curves near shut-off. This can cause unstable operation if the system curve intersects the pump curve at multiple points.

Related Calculators

Explore more calculators related to this topic.

Related Guides

Deepen your understanding with these educational resources.

Understanding Pump Curves

Hydraulic Institute educational resources

System Curve Calculation Guide

How to calculate system curves

Pump Selection Using Curves

Grundfos pump selection methodology

Glossary

Technical terms used in mortgage calculations explained in plain language.

H-Q Curve: Pump performance curve showing head versus flow rate at constant speed.
System Curve: Graph of head required by the piping system as a function of flow rate.
BEP: Best Efficiency Point - the flow rate at which pump efficiency is maximum.
Operating Point: Intersection of pump curve and system curve, determining actual flow and head.
Shut-off Head (H_0): Head developed by the pump at zero flow (closed discharge valve).
Run-out: Maximum flow the pump can deliver at minimum system resistance.
Specific Speed (Ns): Dimensionless parameter characterizing pump impeller geometry and curve shape.
Affinity Parabola: Locus of operating points at constant efficiency as pump speed changes.
Parallel Operation: Multiple pumps discharging into a common header to increase total flow.
Series Operation: Multiple pumps arranged sequentially to increase total head.

Authoritative References

Trusted sources and standards referenced by this calculator.

Hydraulic Institute - Pump Curve Standards Engineering Toolbox - Pump Curve Guide Grundfos - Pump Curve Interpretation Pump Handbook by Karassik et al. ASME - Performance Test Codes for Pumps ISO 9906 - Rotodynamic Pump Performance Tests

Applicable Standards

HI 9.6.1ISO 9906ASME PTC 8.2API 610ANSI/HI 1.3ISO 5199

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Last Updated:

2026-07-30

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.