A centrifugal pump sizing calculation in Excel starts with the required flow rate and calculates the head needed to move liquid through the system. The worksheet should then determine available net positive suction head, estimate power, and identify the information required to select a pump from manufacturer curves.
The most useful spreadsheet shows how each answer was obtained. Keeping suction losses, discharge losses, pressure requirements, and elevations separate makes the calculation easier to check and update when operating conditions change.
This guide develops an illustrative water-transfer calculation at 50 m³/h. It provides input cells, equations, Excel formulas, and checked results that you can reproduce in a blank workbook.
Quick technical summary
| Item | Method or result |
|---|---|
| Design flow | 50 m³/h |
| Pipe-loss method | Darcy–Weisbach with a turbulent friction-factor approximation |
| Calculated total head | 34.20 m of pumped liquid |
| Calculated NPSHa | 11.46 m |
| Estimated pump shaft power | 6.64 kW at 70% pump efficiency |
| Estimated electrical input | 7.38 kW at 90% motor efficiency |
| Final selection | Requires manufacturer curves, operating-range checks, and service-specific review |
These values describe one illustrative operating case. They are not a universal pump specification.
What does a centrifugal pump sizing spreadsheet calculate?
A hydraulic sizing worksheet determines the system duty:
- Required flow rate.
- Total differential head at that flow.
- Available net positive suction head, or NPSHa.
- Hydraulic power and estimated shaft power.
- Operating cases that the selected pump must accommodate.
Pump selection follows sizing. It uses manufacturer data to identify a suitable model, speed, impeller diameter, efficiency, NPSH requirement, and operating range.
Head represents energy per unit weight of liquid. Pressure and head are related through density:
Δp = ρgH
Here, pressure is in pascals, density in kg/m³, gravitational acceleration in m/s², and head in metres. A head value must therefore be identified as metres of the pumped liquid. See KSB’s explanation of pump head.
Step 1: Define the system boundaries and operating cases
Use the liquid surface in the supply tank as boundary 1 and the liquid surface in the receiving tank as boundary 2. Measure both elevations from the same datum.
For steady, incompressible flow:
H = (p₂ − p₁)/(ρg) + (z₂ − z₁) + (v₂² − v₁²)/(2g) + hL
| Symbol | Meaning | SI unit |
|---|---|---|
| H | Head the pump must add | m |
| p₁, p₂ | Pressure at the selected boundaries | Pa |
| z₁, z₂ | Boundary elevations | m |
| v₁, v₂ | Boundary velocities | m/s |
| hL | Total irreversible loss between boundaries | m |
| ρ | Liquid density | kg/m³ |
| g | Gravitational acceleration | m/s² |
For large tanks, free-surface velocities are negligible. Pipe velocities still matter when calculating friction losses.
Before entering values, identify minimum, normal, and maximum flow; tank-level ranges; vessel-pressure ranges; temperature; and clean versus fouled equipment conditions. Maximum head and minimum NPSHa may occur in different operating cases.
Step 2: Enter the Excel input data
Create a worksheet named Sizing. Put parameter names in column A, values in column B, and units in column C.
The example assumes steady flow of clean, single-phase water with constant properties. Water properties are rounded illustrative values representative of approximately 20°C.
Process and equipment inputs
| Cell | Parameter | Value | Unit |
|---|---|---|---|
| B2 | Required flow | 50 | m³/h |
| B3 | Density | 998 | kg/m³ |
| B4 | Dynamic viscosity | 0.001 | Pa·s |
| B5 | Gravity | 9.81 | m/s² |
| B6 | Supply-tank absolute pressure | 101325 | Pa absolute |
| B7 | Receiving-tank absolute pressure | 151325 | Pa absolute |
| B8 | Supply liquid level above pump datum | 2 | m |
| B9 | Receiving liquid level above pump datum | 17 | m |
| B10 | Liquid vapour pressure | 2340 | Pa absolute |
| B11 | Additional discharge equipment pressure drop | 30000 | Pa |
| B12 | Assumed pump efficiency | 0.70 | decimal |
| B13 | Assumed motor efficiency | 0.90 | decimal |
The receiving tank is 50 kPa above the supply pressure. The additional 30 kPa represents a separate discharge-side equipment loss at the stated flow.
Piping inputs
| Cell | Parameter | Value | Unit |
|---|---|---|---|
| B16 | Suction pipe internal diameter | 0.1023 | m |
| B17 | Suction straight-pipe length | 8 | m |
| B18 | Suction absolute roughness | 0.000045 | m |
| B19 | Total suction fitting coefficient, Kₛ | 3.0 | dimensionless |
| B21 | Discharge pipe internal diameter | 0.0779 | m |
| B22 | Discharge straight-pipe length | 65 | m |
| B23 | Discharge absolute roughness | 0.000045 | m |
| B24 | Total discharge fitting coefficient, Kd | 8.0 | dimensionless |
The roughness and aggregate fitting coefficients are assumptions for this example. For a project, record pipe condition, fitting geometry, valve position, and the reference behind each value.
The discharge coefficient includes the applicable outlet loss into the receiving tank. The separate equipment pressure drop must not duplicate losses already included in Kd.
Use actual pipe internal diameter, not nominal pipe size.
Step 3: Convert flow and calculate velocity
Convert the flow rate:
Q = 50/3600 = 0.013889 m³/s
In cell B27:
=B2/3600For a circular pipe:
v = 4Q/(πD²)
Suction velocity in B28:
=4*$B$27/(PI()*B16^2)Discharge velocity in B33:
=4*$B$27/(PI()*B21^2)Results:
- Suction velocity: 1.690 m/s.
- Discharge velocity: 2.914 m/s.
These values are calculation outputs, not automatic acceptance criteria. Appropriate velocity depends on the liquid, suction conditions, erosion risk, noise, energy cost, and project requirements.
Step 4: Calculate Reynolds number and friction factor
Reynolds number identifies the flow regime:
Re = ρvD/μ
Suction Reynolds number in B29:
=$B$3*B28*B16/$B$4Discharge Reynolds number in B34:
=$B$3*B33*B21/$B$4The results are approximately 172,517 and 226,553, respectively. Both are well within turbulent flow.
For this example, use the Swamee–Jain approximation for the Darcy friction factor:
f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re0.9)]²
The US EPA’s EPANET documentation also uses a Swamee–Jain approximation for turbulent pipe flow, with separate treatment of laminar and transitional regimes. This worksheet deliberately flags the transition region instead of implementing EPANET’s interpolation. See the EPA friction-factor methodology.
Suction friction factor in B30:
=IF(B29<=0,NA(),IF(B29<2000,64/B29,IF(B29<=4000,NA(),0.25/(LOG10(B18/(3.7*B16)+5.74/B29^0.9)^2))))Discharge friction factor in B35:
=IF(B34<=0,NA(),IF(B34<2000,64/B34,IF(B34<=4000,NA(),0.25/(LOG10(B23/(3.7*B21)+5.74/B34^0.9)^2))))| Parameter | Suction | Discharge |
|---|---|---|
| Darcy friction factor | 0.01889 | 0.01914 |
The formulas return #N/A for nonpositive Reynolds number and the flagged transition interval. These conditions require review.
Do not substitute a Fanning friction factor into these formulas: the Darcy factor is four times the Fanning factor.
Step 5: Calculate suction and discharge losses
For each constant-diameter section:
hL = (fL/D + ΣK)v²/(2g)
The first term represents straight-pipe friction. The second represents fittings and local losses.
Suction loss in B31:
=(B30*B17/B16+B19)*B28^2/(2*$B$5)Discharge loss in B36:
=(B35*B22/B21+B24)*B33^2/(2*$B$5)| Section | Head loss |
|---|---|
| Suction piping and fittings | 0.652 m |
| Discharge piping and fittings | 10.374 m |
| Combined piping loss | 11.026 m |
For multiple pipe diameters, calculate each section separately using its local velocity and sum the losses. Confirm the velocity basis used for reducer and expander coefficients.
For comparison with another calculation method, use GrowMechanical’s pipe pressure drop calculator with matching assumptions.
Step 6: Calculate total dynamic head
For the selected large-tank boundaries:
H = (z₂ − z₁) + (p₂ − p₁)/(ρg) + hL,s + hL,d + Δpequipment/(ρg)
The individual components are:
- Elevation difference: 17 − 2 = 15.000 m.
- Vessel-pressure difference: (151325 − 101325)/(998 × 9.81) = 5.107 m.
- Additional equipment loss: 30000/(998 × 9.81) = 3.064 m.
| Cell | Output | Excel formula |
|---|---|---|
| B39 | Elevation difference | =B9-B8 |
| B40 | Vessel-pressure head | =(B7-B6)/(B3*B5) |
| B41 | Equipment-loss head | =B11/(B3*B5) |
| B42 | Total required head | =B39+B40+B31+B36+B41 |
H = 15.000 + 5.107 + 0.652 + 10.374 + 3.064 = 34.197 m
The calculated duty is 50 m³/h at approximately 34.20 m head.
Do not add a second outlet velocity head when the chosen receiving-tank boundary and outlet-loss coefficient already account for that energy loss.
Step 7: Calculate NPSH available
For a large supply tank with negligible free-surface velocity:
NPSHa = (p1,abs − pv)/(ρg) + (z₁ − zdatum) − hL,s
In this example, the pump NPSH datum is zero and the supply surface is 2 m above it.
In B45:
=(B6-B10)/(B3*B5)+B8-B31NPSHa = (101325 − 2340)/(998 × 9.81) + 2 − 0.6515 = 11.459 m
Use absolute pressure for both supply pressure and vapour pressure. Gauge pressure cannot be entered directly into this equation.
Compare NPSHa with the manufacturer’s stated NPSH requirement at the actual operating flow and speed, including the applicable margin. Where a curve reports NPSH3, it represents a 3% head-drop test criterion; equality with NPSHa does not establish cavitation-free operation. See the Hydraulic Institute explanation.
For an illustrative vendor NPSH3 value of 3.0 m:
NPSHa − NPSH3 = 11.459 − 3.0 = 8.459 m
That is a calculated difference, not approval of a pump. Repeat the check at minimum supply level, maximum relevant temperature, reduced source pressure, and increased suction losses.
GrowMechanical’s NPSHa calculator provides a related calculation resource.
Step 8: Calculate hydraulic power, shaft power, and electrical input
Hydraulic power is:
Ph = ρgQH/1000
Here, Q is in m³/s and the result is kW.
Pump shaft power is:
Pshaft = Ph/ηp
For the assumed direct drive, estimated motor electrical input is:
Pelectrical = Pshaft/ηm
| Cell | Output | Excel formula | Result |
|---|---|---|---|
| B46 | Hydraulic power | =B3*B5*B27*B42/1000 |
4.650 kW |
| B47 | Pump shaft power | =B46/B12 |
6.643 kW |
| B48 | Electrical input | =B47/B13 |
7.381 kW |
The efficiencies are assumptions. Replace them with vendor values for the selected operating point.
Motor nameplate kW normally describes mechanical output. Compare the required shaft power with the motor’s available mechanical output, considering the complete operating envelope and applicable derating. Do not select the motor by treating calculated electrical input as its nameplate output requirement.
VFD or transmission losses would require additional efficiency terms if included in the electrical boundary.
Step 9: Build a system curve and select the pump
A single duty point does not establish where a particular centrifugal pump will operate. Plot system head against flow and overlay the manufacturer’s pump curve.
For this system, the fixed component is:
Hfixed = 15.000 + 5.107 = 20.107 m
At 50 m³/h, the flow-dependent component totals approximately 14.09 m.
If friction factors are treated as constant and the equipment loss follows a square-law relationship, an illustrative approximation is:
H(Q) ≈ 20.107 + 14.090(Q/50)²
Here, Q is in m³/h. At 40 m³/h:
H(40) ≈ 20.107 + 14.090(0.8)² = 29.12 m
For a more accurate curve, recalculate Reynolds number and friction factor at each flow and use equipment-specific pressure-drop data.
The pump’s operating point occurs at the intersection of its curve and the system curve. Review efficiency, NPSH, power, and operating limits at that intersection. See the Xylem pump selection guide.
How should the calculation change for industrial services?
The same worksheet structure can support utility-water transfer, process-water distribution, or tank-to-tank pumping in manufacturing and chemical plants. The assumptions must change with the service.
| Service condition | Required adjustment |
|---|---|
| Hot water | Update density, viscosity, and vapour pressure; reassess NPSHa |
| Viscous liquid | Recalculate losses and obtain suitable pump-performance corrections |
| Closed circulation loop | Evaluate the complete loop; building height alone is not net static head |
| Fouling filter or exchanger | Include clean and fouled pressure-drop cases |
| Vacuum supply vessel | Use actual absolute pressure and check flashing risk |
| Slurry or entrained gas | Use an appropriate specialist method and pump selection |
A basic water worksheet does not establish suitability for two-phase, non-Newtonian, or solids-laden service.
Common mistakes and troubleshooting checks
| Mistake or symptom | Check |
|---|---|
| Head is unexpectedly high | Diameter units, duplicate losses, valve position, and equipment pressure drop |
| NPSHa is unexpectedly low | Absolute pressure, vapour pressure, suction level, and suction restrictions |
| Pump delivers too much flow | Actual system resistance and pump/system curve intersection |
| Motor overloads | Maximum absorbed power across the permitted operating range and actual density |
| Spreadsheet understates losses | Missing fittings, incorrect internal diameter, and roughness assumptions |
| Results change after copying formulas | Absolute cell references and row alignment |
Use data validation to reject zero or negative diameter, density, viscosity, and gravity. Require efficiencies above zero and no greater than one. Label pressure inputs clearly as absolute, gauge, or differential.
Keep unrounded values in formulas and round only the displayed results. Record the workbook revision, input sources, and calculation assumptions so another engineer can reproduce the result.
Which standards and checks apply?
The Hydraulic Institute lists ANSI/HI 9.6.1-2024, Rotodynamic Pumps—Guideline for NPSH Margin, and ANSI/HI 9.6.3-2024, Rotodynamic Pumps—Guideline for Operating Regions. Use them with manufacturer guidance and the project specification. See the Hydraulic Institute standards catalogue.
API 610 addresses centrifugal pumps for petroleum, petrochemical, and natural-gas industries. It is relevant when specified for the service; using this spreadsheet does not establish API compliance. Confirm the contractually applicable edition through the API standards catalogue.
Final engineering review should also address material compatibility, seals, temperature and pressure ratings, shutoff conditions, minimum flow, suction arrangement, and transient events. No universal head allowance or NPSH margin replaces those checks.
Frequently asked questions
Can Excel calculate centrifugal pump size?
Excel can calculate flow, required head, NPSHa, and estimated power. Selecting the pump model, impeller, speed, and motor requires manufacturer performance data and operating-condition checks.
What is the Excel formula for pump hydraulic power?
With flow in m³/s, use =Density*Gravity*Flow*Head/1000 for kW. With flow in m³/h, divide by 3,600,000 instead. Divide hydraulic power by pump efficiency to estimate shaft power.
Does total dynamic head include suction losses?
Yes. When applying the energy balance between supply and receiving boundaries, include losses on both sides of the pump. Suction losses also reduce NPSHa.
Should pressure be absolute or gauge?
NPSHa requires absolute pressure. For a pressure difference in the head calculation, both pressures may use the same gauge reference or both may be absolute. Never mix the two bases.
Can the spreadsheet calculate NPSH required?
This worksheet calculates NPSH available from the system. Obtain the pump’s NPSH requirement from the manufacturer for the selected flow, speed, and configuration.
Should I add 10% to the calculated head?
There is no universal 10% rule. Evaluate uncertainty, fouling, operating cases, and project requirements explicitly. Excess head can move the operating point and increase throttling losses.
Is 6.64 kW shaft power enough information to choose a motor?
No. Check maximum absorbed power over the permitted operating range, actual liquid density, starting requirements, ambient conditions, and any derating. The example’s 6.64 kW applies only to its stated duty and assumed efficiency.
Use the worksheet as a traceable design calculation
For the stated assumptions, the spreadsheet produces 50 m³/h at 34.20 m head, 11.46 m NPSHa, and 6.64 kW estimated shaft power. The next step is to compare candidate pump curves across the required operating cases.
GrowMechanical lists a Pump Sizing Calculations Spreadsheet covering head, NPSH, and power. Review its documented scope and sample material before applying it to a project; the tutorial above is an independent worked example.
Explore further engineering resources at GrowMechanical to connect pump sizing with piping calculations and equipment selection.
