AtlasCalcsUtility Calculation Suite
2026-07-30 9 min

Pump Specific Speed Calculator

Calculate pump specific speed (n_s) — a dimensionless parameter that characterizes pump geometry and performance. Used for pump selection and impeller design optimization.

Calculator

Unit System
Pump Speed (n) [RPM]
Flow Rate (Q) [m³/h]
Head per Stage (H) [m]
Number of Stages

Results

Optimal

Specific Speed (n_s)

797.7-

Dimensionless parameter characterizing pump impeller geometry

Suction Specific Speed (S)

797.7-

Suction capability indicator for NPSH characteristics

Specific Diameter (D_s)

21.7mm

Specific diameter for impeller sizing

Speed Factor

0.8-

Normalized speed factor (n_s / 1000)

Head per Stage

50.0m

Head per stage for multistage pumps

Pump Type Classification

Radial — Standard centrifugal pump

Pump type based on specific speed

Impeller Shape Recommendation

Radial vanes, medium diameter

Recommended impeller geometry for this specific speed

Visualizations

Results Overview

797.7-Specific Speed
797.7-Suction Specific Speed
21.7-Specific Diameter
0.8-Speed Factor
50-Head per Stage

Formula

Specific speed is a dimensionless parameter that characterizes the geometry and performance characteristics of a pump impeller. It is the speed at which a geometrically similar pump would operate to deliver 1 unit of flow at 1 unit of head.

n_s = n × √Q / H^0.75

Alternative Form

S = n × √Q / NPSHr^0.75

Variables

SymbolNameUnitDescription
n_sSpecific Speed-Dimensionless pump classification parameter
nRotational SpeedRPMPump shaft rotational speed
QFlow Ratem³/sFlow rate at best efficiency point
HHead per StagemTotal dynamic head per stage
SSuction Specific Speed-Suction performance parameter
D_sSpecific Diameter-Dimensionless impeller diameter parameter

Explanation

Specific speed n_s is derived from similarity (affinity) laws and characterizes pump type regardless of pump size. A low n_s indicates a radial flow impeller (high head, low flow), while a high n_s indicates an axial flow impeller (low head, high flow). Specific speed is calculated at the Best Efficiency Point (BEP) and is constant for geometrically similar pumps. Suction specific speed S uses NPSH required instead of head and indicates suction capability. Specific diameter D_s = D × H^0.25 / √Q is a complementary parameter for impeller sizing.

Derivation

From turbomachinery similarity: geometrically similar pumps have the same specific speed. The US customary unit form: n_s = n(RPM) × √Q(GPM) / H(ft)^0.75. SI form: n_s = n(RPM) × √Q(m³/s) / H(m)^0.75. The exponent 0.75 derives from the head characteristic of turbomachines where H ∝ u² ∝ (nD)² and Q ∝ nD³.

Step-by-Step Calculation

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

Step 1

Determine pump speed, flow rate at BEP, and head per stage.

Speed n:1500.0 RPM
Flow Q:100.0 m³/h
Head H:50.0 m
Stages:1
Result: Head per stage = 50.0 m
Step 2

Calculate specific speed from the formula.

n_s = n × √Q / H^0.75
n:1500.0 RPM
Q:0.0 m³/s
H:50.0 m
Intermediate: n_s = 1500.0 × √0.0 / 50.0^0.75
Result: n_s = 797.7
Step 3

Classify pump type based on specific speed range.

n_s:797.7
Result: Pump type: Radial — Standard centrifugal pump
Final Answer
797.7

Worked Examples

See how the calculator works with different scenarios.

Scenario

A single-stage centrifugal pump runs at 1450 RPM, delivers 400 m³/h at 80 m head.

Inputs

Speed:1450 RPM
Flow:400 m³/h
Head:80 m
Stages:1

Calculation

Q = 400/3600 = 0.1111 m³/s n_s = 1450 × √0.1111 / 80^0.75 = 1450 × 0.333 / 26.75 n_s = 18.06 (SI dimensionless) ≈ 580 (US units)

Result

n_s = 580 (US units) — Radial Flow Centrifugal Pump

Interpretation

This specific speed indicates a standard radial centrifugal pump. Suitable for medium head, medium flow applications like municipal water supply.

Understanding Your Result

Your Result: Specific Speed (n_s): 797.7 -

Typical range: Radial: n_s = 500-1500 (US). Francis: n_s = 1500-3000. Mixed flow: n_s = 3000-6000. Axial flow: n_s = 6000-15000+. Maximum efficiency varies with n_s: peak efficiency occurs at n_s ≈ 2000-3000.

What This Means

Specific speed classifies pump impeller geometry independently of pump size. It tells you whether a pump will have a radial, mixed, or axial flow impeller design.

Why It Matters

Specific speed guides impeller selection at the conceptual design stage. It determines the feasible range of head and flow for a given pump type, and influences efficiency potential, NPSH characteristics, and cost.

Professional Interpretation

Specific speed is the single most important parameter for pump selection and impeller design. It determines the pump type required for given duty conditions. The pump selected should have its BEP at a specific speed that matches the duty. Operating at the wrong specific speed range forces inefficient off-design operation. For optimal performance, select a pump whose BEP specific speed is within 20% of the duty specific speed.

Recommendations

  • •Use specific speed to select pump type during conceptual design
  • •Calculate specific speed at BEP conditions, not off-design points
  • •For multistage pumps, use head per stage in the calculation
  • •Consider suction specific speed S for NPSH-sensitive applications
  • •Use the n_s-D_s diagram (Cordier diagram) for impeller diameter optimization

Educational Content

Introduction

Specific speed (n_s) is a fundamental dimensionless parameter in turbomachinery design that characterizes pump impeller geometry. It was developed from similarity theory and classifies pumps by their hydraulic design regardless of physical size.

Concept Explanation

Specific speed represents the speed at which a geometrically similar pump would need to rotate to deliver 1 unit of flow against 1 unit of head. A low n_s pump (500-1500) has a narrow, small-diameter impeller with radial flow passages for high head. A high n_s pump (6000-15000+) has a wide, large-diameter impeller with axial flow passages for high flow. The n_s-D_s (Cordier) diagram provides the optimal relationship between specific speed and specific diameter for maximum efficiency.

Applications

▸Pump type selection for given head and flow requirements
▸Impeller geometry design and optimization
▸Pump performance estimation during preliminary design
▸Cavitation assessment via suction specific speed
▸Pump similarity and model testing
▸Troubleshooting pump performance issues
▸Comparing pumps of different sizes and speeds

Benefits

  • •Enables pump type selection before detailed design
  • •Independent of pump size — applies from tiny to massive pumps
  • •Directly relates to impeller geometry
  • •Predicts efficiency potential
  • •Guides preliminary sizing and cost estimation

Limitations

  • •Requires knowledge of BEP flow and head
  • •Different definitions exist (US vs. SI units) requiring careful unit conversion
  • •Does not account for impeller detailed geometry (vane angles, blade count)
  • •Single parameter cannot fully characterize complex pump designs

Best Practices

  • •Always note whether using US customary or SI specific speed definitions
  • •Calculate specific speed at the BEP, not at other operating points
  • •Use head per stage for multistage pumps
  • •Combine n_s with D_s (specific diameter) on the Cordier diagram for complete characterization
  • •Verify selected pump type with manufacturer catalog data

Common Misconceptions

Myth: Specific speed has units of speed (RPM).
Truth: Despite the name and the RPM in the numerator, specific speed is a dimensionless parameter. The units cancel when consistent units are used throughout the formula.
Myth: A pump has a unique specific speed for all operating points.
Truth: Specific speed is defined only at the BEP flow. At off-design points, the calculated value is not valid for pump classification.
Myth: Higher specific speed always means better efficiency.
Truth: Maximum achievable efficiency varies with specific speed. Peak efficiency occurs at n_s ≈ 2000-3000. Both very low and very high specific speeds have lower peak efficiency potential.

Practical Tips

  • •US customary specific speed = SI specific speed × 51.65 (approximate conversion)
  • •For preliminary selection, centrifugal pumps cover n_s = 500-3000, mixed flow n_s = 3000-6000, axial n_s = 6000-15000
  • •Suction specific speed S should generally be between 8000-12000 (US units) for good suction performance
  • •The Cordier diagram links n_s and D_s for optimal efficiency design
  • •For multistage pumps, always use head per stage — total head divided by number of stages
  • •Impeller tip speed and specific speed together determine the feasible head per stage
  • •Axial flow pumps (high n_s) have the lowest NPSH requirements

Common Mistakes

Using total head instead of head per stage for multistage pumps
Always divide total head by the number of stages before calculating specific speed. Using total head gives an artificially low specific speed that misrepresents the impeller type.
Confusing US and SI specific speed definitions
US n_s uses GPM and ft; SI n_s uses m³/s and m. The US value is approximately 51.65× larger. Always specify which system you are using.
Calculating specific speed at off-design operating points
Specific speed is meaningful only at the Best Efficiency Point. Off-design calculations produce values that do not correctly classify the pump design.
Ignoring the effect of specific speed on efficiency potential
Maximum achievable pump efficiency varies with n_s. A pump with n_s = 1000 can achieve ~85% efficiency, while n_s = 10000 is limited to ~75%.

Assumptions

This calculator makes the following assumptions to provide estimates:

BEP Conditions: Specific speed is defined at the Best Efficiency Point. All calculations assume the pump operates at BEP conditions.
Geometric Similarity: Specific speed comparison assumes geometrically similar pumps. Different manufacturers may achieve the same n_s with different detailed designs.
Incompressible Flow: Specific speed theory is based on incompressible flow. For compressible fluids, alternative parameters are used.
Single-Phase Flow: Assumes clean fluid without entrained gases or solids. Two-phase flow significantly affects pump performance and specific speed classification.

Limitations

Be aware of these limitations when using this calculator:

Single-Parameter Classification: Specific speed alone cannot fully characterize a pump design. Detailed geometry (vane angles, blade count, shroud design) also affects performance.
BEP Dependence: Specific speed requires knowledge of BEP conditions. For pumps without published curves, field testing is needed to determine BEP.
Unit Sensitivity: The numerical value of specific speed differs by a factor of ~51.65 between US and SI units, causing confusion. Always verify which definition is used.
No Viscosity Correction: Specific speed theory assumes water-like fluids. High viscosity alters the effective BEP and impeller classification.

Frequently Asked Questions

Answers to common questions about this calculator.

What is pump specific speed?
Specific speed (n_s) is a dimensionless parameter that classifies pump impeller geometry. It is defined as n_s = n × √Q / H^0.75 where n is rotational speed, Q is flow at BEP, and H is head per stage at BEP.
What are typical specific speed ranges for different pump types?
Radial flow (centrifugal): n_s = 500-1500 US. Francis type: n_s = 1500-3000. Mixed flow: n_s = 3000-6000. Axial flow (propeller): n_s = 6000-15000+. Below 500: multistage or positive displacement.
What is the difference between US and SI specific speed?
US n_s uses GPM and ft units. SI n_s uses m³/s and m units. The US value is approximately 51.65 times the SI value. US: n_s = 1000 ≈ SI: n_s = 19.4.
Why is specific speed important for pump selection?
Specific speed determines which pump type (radial, mixed, axial) is optimal for your head and flow requirements. Selecting the wrong type results in poor efficiency, high NPSH requirements, and potential operational problems.
How does specific speed affect pump efficiency?
Maximum achievable efficiency varies with n_s. Peak efficiency (85-90%) occurs at n_s ≈ 2000-3000. Efficiency drops at both very low and very high specific speeds.
What is suction specific speed?
Suction specific speed S = n × √Q / NPSHr^0.75. It characterizes the suction capability of a pump. Higher S values (8000-12000 US) indicate better suction performance and lower NPSH requirements.
How do I calculate specific speed for a multistage pump?
Use head per stage (total head divided by number of stages) in the specific speed formula. Flow rate is the total pump flow (same for all stages). The calculated n_s represents each stage.
What is the Cordier diagram?
The Cordier diagram plots specific speed (n_s) against specific diameter (D_s) and shows the optimal relationship for maximum efficiency. It is a key tool in pump impeller design and selection.
What is specific diameter (D_s)?
Specific diameter D_s = D × H^0.25 / √Q where D is impeller diameter. It complements specific speed to fully characterize impeller geometry. The Cordier diagram uses both parameters.
How does specific speed relate to impeller diameter?
For a given specific speed, there is an optimal specific diameter (from the Cordier diagram). The actual impeller diameter D = D_s × √Q / H^0.25. Higher n_s requires larger D_s.
Can specific speed change with pump operating conditions?
Specific speed is only meaningful at the BEP. At off-design conditions, the calculated n_s value does not represent the pump design and should not be used for classification.
What specific speed range is best for high-head applications?
Low specific speed (n_s = 500-1500 US) is best for high-head applications. These radial flow impellers generate high head at moderate flow rates. For very high head, use multistage pumps.
What specific speed range is best for high-flow applications?
High specific speed (n_s = 6000-15000+ US) is best for high-flow applications. Axial flow impellers move large volumes at low head. For maximum flow, use axial or mixed-flow pumps.
How do I convert specific speed between US and SI units?
US n_s = 51.65 × SI n_s (approximate). Exact conversion: US n_s = (US_RPM × √US_GPM) / US_ft^0.75. SI n_s = (RPM × √m³/s) / m^0.75. Use 1 GPM = 0.00006309 m³/s, 1 ft = 0.3048 m.
What is the specific speed of a typical centrifugal pump?
A typical single-stage centrifugal pump has n_s = 1000-2000 (US). This covers most industrial and municipal water pumps. Process pumps: n_s = 800-1500. API 610 pumps: n_s = 500-2000.
How does specific speed affect NPSH requirements?
Lower specific speed pumps generally have higher NPSH requirements. Axial flow pumps (high n_s) can operate with very low NPSH. Suction specific speed S more directly indicates NPSH characteristics.
What is the specific speed of a boiler feed pump?
Boiler feed pumps typically have n_s = 500-1000 (US). These are low specific speed, multistage radial flow pumps designed for very high head (500-2000 m) at moderate flow rates.
What is the effect of specific speed on pump curve shape?
Low n_s pumps have steep H-Q curves (head drops significantly with flow). High n_s pumps have flat H-Q curves (head nearly constant over flow range). Axial pumps may have unstable (drooping) curves.
How do I select between pumps of different specific speeds?
Choose the pump type whose n_s range matches your duty. Calculate n_s from your required head and flow. Select a pump with BEP n_s within 20% of your calculated value.
What is the relationship between specific speed and pump size?
Specific speed is independent of pump size. A small and a large pump can have the same n_s if they are geometrically similar. Size affects efficiency but not specific speed.
How does pump specific speed affect power requirements?
Specific speed does not directly determine power. Power depends on flow, head, and efficiency. However, efficiency varies with n_s, so pumps with n_s = 2000-3000 generally have the lowest specific power.
What is the typical specific speed for a submersible pump?
Submersible pumps cover a wide range: deep well (low n_s, 500-1000 multistage), sewage (mixed flow, n_s = 3000-5000), and drainage (axial flow, n_s = 6000-10000).
How does impeller diameter vary with specific speed?
For the same head and flow, higher n_s requires larger impeller diameter (from the Cordier diagram relationship). Low n_s impellers are smaller diameter but wider.
What is the maximum specific speed achievable?
Practical maximum is about n_s = 15000-20000 (US) for axial flow pumps. Beyond this, the impeller blades become very short and efficiency drops rapidly. Some special designs reach n_s = 25000.
How does specific speed affect operating range stability?
Low n_s pumps have a wide stable operating range. High n_s pumps (especially axial flow) may have an unstable region at low flow where the curve droops. Avoid operating in the unstable region.
What is the specific speed of a gear pump?
Specific speed is not commonly used for positive displacement pumps because the flow is primarily determined by displacement and speed, not by head. PD pumps are classified differently.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

Specific Speed (n_s)
A dimensionless parameter n_s = n√Q/H^0.75 that characterizes pump impeller geometry and performance type.
Suction Specific Speed (S)
A parameter S = n√Q/NPSHr^0.75 that characterizes pump suction capability and NPSH requirements.
Specific Diameter (D_s)
A dimensionless parameter D_s = D × H^0.25 / √Q used with n_s in the Cordier diagram for impeller sizing.
Cordier Diagram
A graphical representation of the optimal relationship between specific speed and specific diameter for maximum pump efficiency.
Radial Flow
Impeller design where fluid flows radially outward from the center. Used for low n_s (high head, low flow).
Mixed Flow
Impeller design where fluid flows at an angle combining radial and axial components. Used for medium n_s.
Axial Flow
Impeller design where fluid flows axially through the impeller, like a propeller. Used for high n_s (low head, high flow).
BEP (Best Efficiency Point)
The flow rate at which pump efficiency is maximized. Specific speed must be calculated at BEP conditions.
Francis Impeller
A specific mixed-flow impeller design named after James B. Francis, commonly used for medium specific speeds (n_s = 1500-3000).
Affinity Laws
Mathematical relationships for scaling pump performance: Q ∝ n, H ∝ n², P ∝ n³ for geometrically similar pumps.
Cavitation
Vapor bubble formation and collapse in the pump when pressure drops below vapor pressure, causing erosion.
Similarity Theory
The principle that geometrically similar pumps have the same specific speed and follow Affinity Laws for performance scaling.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

ISO 9906API 610HI 1.1-1.2ANSI/HI 9.6.1ASME PTC 8.2ISO 5199

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Page Information

Last Updated:

2026-07-30

Version:

2.0.0

License:

Free to use for educational and professional purposes.