Input Parameters
Calculated Results
Enter values above and press “Calculate” to see results.
Formula used
For an external gear pump, the theoretical volumetric displacement per revolution is based on the hollow cylinder formed between the gear tip and root diameters:
VD = (π / 4) × (Do² − Di²) × L
- VD – displacement per revolution (m³/rev or cm³/rev)
- Do – outside (tip) diameter of gear teeth
- Di – inside (root) diameter of gear teeth
- L – gear width (tooth face width)
When VD is expressed in cm³/rev and pump speed N
is in rpm, the theoretical flow rate in litres per minute is:
Qth = VD × N / 1000
Volumetric efficiency compares the measured actual flow to the theoretical flow:
ηv = (Qactual / Qth) × 100%
How to use this calculator
- Measure the outer tip diameter, inner root diameter and gear width of one gear.
- Select the unit that matches your measurements (mm, cm, m or inches).
- Enter the pump shaft speed in revolutions per minute.
- Either provide an estimated volumetric efficiency or leave the default value.
- If you have test bench data, enter the measured actual flow to compute efficiency.
- Press Calculate displacement and flow to see all results.
- Use Download CSV to export inputs and results to a spreadsheet.
- Use Download PDF to save a PDF snapshot of the results section.
This tool assumes an external gear pump with uniform clearances and does not replace manufacturer data for final equipment selection.
Example data table
The example below uses a typical small hydraulic gear pump with one gear measured as follows and operated at 1600 rpm. Actual flow is assumed 95 L/min.
| Outer diameter Do | Inner diameter Di | Gear width L | Speed N | Measured flow | Displacement | Theoretical flow | Volumetric efficiency |
|---|---|---|---|---|---|---|---|
| 80 mm | 55 mm | 25 mm | 1600 rpm | 95.0 L/min | 66.27 cm³/rev | 106.03 L/min | 89.6 % |
Use this table as a reference to verify your own measurements and to check that your results are in a realistic range.
Gear pump displacement: detailed overview
Applications of external gear pumps
Gear pumps are widely used in hydraulic power packs, lubrication systems and mobile machinery. Their compact design, simple construction and predictable displacement make them ideal whenever a fixed flow is required from a rotating shaft over long operating periods. They remain dependable even in demanding industrial environments and harsh conditions.
Influence of diameters on displacement
The displacement per revolution depends primarily on the volume between the gear tooth tips and roots. For a given outside diameter, increasing the difference between outer and inner diameters increases the annular area and therefore raises the volumetric output of the pump in every application. Small dimensional changes can significantly influence available hydraulic power.
Effect of gear width on output
Gear width also plays a critical role. Wider gears provide more volume per revolution because the hollow cylindrical region extends further along the shaft. However, very wide gears may increase bearing loads and can make it harder to control internal leakage paths and maintain acceptable efficiency. Designers must balance output, durability and efficiency.
Role of rotational speed in flow
Rotational speed determines how many times each revolution’s volume is delivered every minute. Higher speed increases theoretical flow rate linearly, but mechanical limits, noise, cavitation and suction conditions constrain the maximum safe operating speed for any specific hydraulic circuit or pump installation. Always respect manufacturer speed limits and recommended operating ranges.
Understanding volumetric efficiency
Volumetric efficiency compares the actual delivered flow to the theoretical value predicted from geometry and speed. Leakage across gear tips, side clearances and end plates reduces the effective flow, especially at high pressures, low viscosities, elevated temperatures or with worn hydraulic components and housings. Good filtration and correct viscosity help preserve efficiency.
Using the calculator in design work
Using the gear pump displacement calculator, designers can estimate flow at different speeds and evaluate how efficiency changes with measured test bench data. This helps in selecting compatible valves, actuators, reservoir sizes and cooling capacity for industrial, agricultural, marine and mobile hydraulic systems. Documented calculations also support safety reviews and audits.
Benefits for documentation and collaboration
The tool also supports both metric and imperial length units, simplifying work with international design drawings. By combining rigorous geometric formulas with flexible input options, it provides a transparent method for understanding pump performance and documenting calculation assumptions for maintenance, upgrades and future reference. Results can be shared easily with project stakeholders. This improves communication between mechanical designers, hydraulic specialists, maintenance teams and quality assurance personnel throughout the project.
Frequently asked questions
What is gear pump displacement?
Gear pump displacement is the theoretical volume of fluid moved during one shaft revolution. It depends on the gear outside diameter, root diameter and gear width. Knowing displacement helps predict flow rate at different speeds and compare different pump sizes during hydraulic system design.
Why do I need volumetric efficiency?
Volumetric efficiency shows how closely the real delivered flow matches the ideal theoretical flow. Internal leakage, clearances, wear and operating pressure reduce efficiency. Using volumetric efficiency helps account for these losses when sizing pumps, motors, actuators and other hydraulic components in practical installations.
Can I mix metric and imperial dimensions?
No. All length dimensions used in a single calculation should share the same unit system. The calculator lets you choose millimetres, centimetres, metres or inches. Mixing units in one calculation would distort the geometry and produce incorrect displacement and flow results.
How accurate is this displacement calculation?
The calculation is accurate when the entered dimensions truly represent the gear tooth tip diameter, root diameter and face width. However, manufacturing tolerances, internal clearances and wear mean real pumps may deviate slightly. Always validate critical designs against manufacturer data sheets and laboratory test results.
What happens if I increase pump speed?
Increasing pump speed raises theoretical flow rate in direct proportion to rotational speed. However, higher speed can increase noise, cavitation risk, shaft loading and heat generation. Always check manufacturer limits and ensure suction conditions, reservoir design and filtration can support the increased operating speed safely.
Can this tool replace manufacturer information?
No. The calculator is a powerful engineering aid for estimation, comparison and education, but it does not replace certified manufacturer data. Always compare results with official performance curves, technical catalogues and safety guidelines before final pump selection, especially in critical or regulated hydraulic applications.