Pump Shaft and Motor Power Calculator
Hydraulic, shaft and motor input power for a pump from flow, head and efficiencies. With the formula, a worked example and typical values.
Try your own numbers
Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates hydraulic power, pump shaft power and motor electrical input from flow, total head, liquid density, pump efficiency and 1 more input. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Select the motor from the shaft power plus a margin (commonly 10 to 20%). Check NPSH and the pump curve separately.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Hydraulic power and efficiency conversion are basic engineering relationships. Pump acceptance standards govern tests and performance, not this generic power equation. |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Flow | 100 m³/h |
| Total head | 30 m |
| Liquid density (kg/m³) | 1,000 |
| Pump efficiency | 0.7 |
| Motor efficiency | 0.92 |
- Ph = 1,000 × 9.80665 × 100 m³/h × 30 m = 8.172 kW
- Shaft = 8.172 / 0.7 = 11.675 kW
- Motor input = 11.675 / 0.92 = 12.69 kW
Assumptions
- g = 9.80665 m/s²
- Steady flow at the duty point
Select the motor from the shaft power plus a margin (commonly 10 to 20%). Check NPSH and the pump curve separately.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Flow | m³/h | greater than 0 m³/h | |
| Total head | m | greater than 0 m | |
| Liquid density (kg/m³) | (number) | 1 or more, up to 20,000 | |
| Pump efficiency | (number) | greater than 0, up to 1 | |
| Motor efficiency | (number) | greater than 0, up to 1 |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Hydraulic power | kW | Shown to 2 decimal places | |
| Pump shaft power | kW | Shown to 2 decimal places | |
| Motor electrical input | kW | Shown to 2 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with flow
| Flow (m³/h) | Hydraulic power (kW) | Pump shaft power (kW) | Motor electrical input (kW) |
|---|---|---|---|
| 10 | 0.82 | 1.17 | 1.27 |
| 25 | 2.04 | 2.92 | 3.17 |
| 50 | 4.09 | 5.84 | 6.34 |
| 100 | 8.17 | 11.67 | 12.69 |
| 200 | 16.34 | 23.35 | 25.38 |
| 400 | 32.69 | 46.7 | 50.76 |
| 1,000 | 81.72 | 116.75 | 126.9 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 60034-1 (rotating electrical machines, rating and performance)
- IEC 60034-30-1 (efficiency classes)
Where the motor nameplate or data sheet gives a value, use it in place of a calculated one. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter flow, total head, liquid density (kg/m³), pump efficiency and motor efficiency. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
g = 9.80665 m/s². Steady flow at the duty point.
Which calculators should I use next?
Common next steps are Motor Full-Load Current and Appliance Running Cost (Energy and Cost). The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Pump Formulas: Hydraulic, Shaft and Motor Power: Pump power formulas: hydraulic power from flow and head, shaft power from pump efficiency, motor input power
- Hydraulic Power and Cylinder Force Formulas: Hydraulic formulas: the power from the flow and pressure
- Motor Efficiency Formulas: Input and Savings: Motor efficiency formulas: input power and losses from shaft power
- Compressor Power Formulas: Air compressor formulas: the isothermal power for a free air delivery and pressure ratio
More Motor Engineering calculatorsAll engineering calculatorsPump Shaft and Motor Power in Elecmetric