Gear Pump Calculator: Flow & Displacement

This gear pump calculator works out the theoretical flow rate of an external gear pump from its displacement and shaft speed, and it can also estimate the displacement from basic gear dimensions. You enter either the pump’s displacement per revolution and speed, or the gear geometry (module, tooth count, face width), and the calculator returns the flow rate in liters per minute and gallons per minute.

Formula

The core relationship for any positive displacement pump is simple:

Q = (V × n × η_v) / 1000

Where:

• Q = theoretical flow rate (liters per minute, L/min)
• V = displacement per revolution (cubic centimeters per revolution, cm³/rev)
• n = shaft rotational speed (revolutions per minute, rpm)
• η_v = volumetric efficiency (as a decimal, e.g., 0.92 for 92%)

The division by 1000 converts cm³ to liters. If you work in cubic inches per revolution, the flow in US gallons per minute is:

Q_gpm = (V_in³ × n × η_v) / 231

There are 231 cubic inches in one US gallon.

Worked Example

Using the default values from the calculator above:

• Displacement V = 12.5 cm³/rev
• Speed n = 1450 rpm
• Volumetric efficiency η_v = 92% = 0.92

Step 1: Multiply displacement by speed:

12.5 × 1450 = 18,125 cm³/min

Step 2: Apply volumetric efficiency:

18,125 × 0.92 = 16,675 cm³/min

Step 3: Convert to liters per minute:

16,675 / 1000 = 16.7 L/min

Step 4: Convert to US gallons per minute:

16.7 × 0.264172 = 4.4 gpm

The calculator shows 16.7 L/min and 4.4 gpm, matching this hand calculation.

How Gear Pumps Work

An external gear pump has two meshing gears inside a close-fitting housing. As the gears rotate, teeth unmesh on the inlet side, creating a partial vacuum that draws fluid into the spaces between the teeth. The fluid is trapped between the gear teeth and the housing wall, carried around the outside, and forced out on the discharge side as the teeth re-mesh. Each revolution moves a fixed volume of fluid — that fixed volume is the displacement.

The theoretical displacement of a gear pump depends on the gear geometry. For a pair of identical external gears, a common approximation is:

V ≈ 2 × π × m × z × b × (r_a − r_p)

Where m is the module (mm), z is the number of teeth per gear, b is the face width (mm), r_a is the addendum radius, and r_p is the pitch radius. In practice, manufacturers measure displacement directly by filling the pump with fluid and counting how much comes out per revolution, because exact tooth profiles vary.

Choosing the Right Gear Pump Size

To select a gear pump for an application, you need three things: required flow rate, available shaft speed, and system pressure. The flow rate determines the displacement at a given speed. For example, if you need 20 L/min at 1450 rpm with a typical efficiency of 90%:

V = (Q × 1000) / (n × η_v) = (20 × 1000) / (1450 × 0.90) ≈ 15.3 cm³/rev

You would then pick a pump with a displacement at or slightly above 15.3 cm³/rev. Keep in mind that gear pumps are fixed displacement — you cannot adjust the output volume. Flow control is done by changing shaft speed or by using a bypass valve.

Pressure affects the required drive power, not the displacement. The hydraulic power is:

P = (Q × Δp) / 600

Where P is in kilowatts, Q in L/min, and Δp in bar. For 20 L/min at 100 bar, that is 20 × 100 / 600 = 3.3 kW of hydraulic power, before mechanical losses.

Common Mistakes and Misconceptions

One of the most frequent errors is mixing up displacement units. A pump rated in cm³/rev will give a wildly wrong result if you treat it as mL/rev — actually those are the same (1 cm³ = 1 mL), but the problem comes when a pump is rated in in³/rev and you forget to convert. One cubic inch is 16.387 cm³.

Another common mistake is ignoring volumetric efficiency. Gear pumps are not perfect; internal leakage past the gears and side plates increases with pressure and with fluid temperature. At low pressure, efficiency might be 95% or higher; at high pressure, it can drop to 80% or less, especially with thin fluids like water or light oil. The calculator’s 92% default is a reasonable mid-range estimate for a healthy pump with typical hydraulic oil.

A third misconception is that gear pumps can run dry. They cannot — the gears rely on the fluid for lubrication. Running dry causes rapid wear and seizure. Always prime the pump and ensure the inlet line is flooded.

Real-World Applications and Context

Gear pumps are everywhere in industry because they are simple, compact, and relatively inexpensive. Common uses include:

• Lubrication systems in engines and gearboxes
• Hydraulic power units for presses, lifts, and steering
• Fuel transfer and diesel injection systems
• Chemical dosing and transfer of viscous liquids like molasses, paint, or polymers
• Coolant circulation in machine tools

They handle a wide viscosity range — from thin solvents to thick resins — but they are not ideal for abrasive fluids because the close clearances (typically 10–50 micrometers) will wear quickly. For abrasive slurries, a progressing cavity or peristaltic pump is usually a better choice.

Compared to vane or piston pumps, gear pumps have lower pulsation but also lower maximum pressure ratings. Typical gear pumps operate up to around 200–250 bar for hydraulic duty, while piston pumps can go to 350 bar or more. The trade-off is cost and complexity: gear pumps are cheaper and simpler to maintain.

Limits of the Formula

The flow formula assumes steady, incompressible flow and a constant volumetric efficiency. In reality, efficiency varies with pressure, temperature, fluid viscosity, and shaft speed. The displacement itself is not perfectly constant — it changes slightly with pressure due to housing deflection and thermal expansion.

Also, the formula gives the average flow. Gear pumps produce a small pulsation in flow as each tooth engages and disengages. The pulsation frequency equals the number of teeth times the shaft speed. For most hydraulic systems this is acceptable, but for precision metering applications, you may need a pump with more teeth or an external damper.

Finally, the calculator does not account for inlet conditions. If the inlet line is too small or the fluid is too viscous, the pump can cavitate — vapor bubbles form and collapse, causing noise, vibration, and erosion damage. The practical rule is to keep inlet velocity below about 0.5–1.5 m/s depending on viscosity, and to keep the inlet pressure above the fluid’s vapor pressure.

Frequently Asked Questions

What is the difference between theoretical and actual flow?

Theoretical flow is displacement times speed with no losses. Actual flow is lower because of internal leakage (volumetric loss) and, at high speeds, incomplete filling of the tooth spaces. The ratio of actual to theoretical flow is volumetric efficiency, typically 85–95% for a gear pump in good condition.

Can I use this calculator for internal gear pumps?

Yes, the flow formula Q = V × n × η_v applies to any positive displacement pump — external gear, internal gear, gerotor, vane, or piston. The displacement value V is what changes. As long as you have the displacement per revolution, the calculation is identical.

Why does my pump deliver less flow than the nameplate says?

Several causes: worn gears or side plates increasing internal leakage, low shaft speed (check the motor under load), high system pressure pushing more fluid past clearances, or a partially blocked inlet causing cavitation. Measure the actual speed and pressure first; then inspect the pump for wear.

How do I convert L/min to GPM?

Multiply liters per minute by 0.264172 to get US gallons per minute. To convert the other way, multiply GPM by 3.78541. For imperial gallons, the factor is 0.21997, but most pump specifications use US gallons unless stated otherwise.

What happens if I run the pump faster than rated?

Flow increases proportionally, but so do wear, noise, and the risk of cavitation. The inlet may not be able to supply fluid fast enough, causing vapor bubbles. Most gear pumps have a maximum speed limit, often 3000–4000 rpm for small pumps, above which the manufacturer does not guarantee performance or life.

Does fluid viscosity affect the flow rate?

Yes, indirectly. Viscosity affects volumetric efficiency: thicker fluids leak less, so efficiency is higher, but they also cause more drag and require more power. Very thin fluids leak more, reducing flow. Viscosity also affects whether the pump can fill its tooth spaces at high speed — thick fluids may not fill completely, reducing flow.

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in disp | Displacement per rev | cm³/rev | 12.5 | 0
in rpm | Shaft speed | rpm | 1450 | 0
in vol_eff | Volumetric efficiency | % | 92 | 0
out flow_lpm | Flow rate | L/min | disp * rpm * (vol_eff / 100) / 1000 | 1
out flow_gpm | Flow rate | US gal/min | (disp * rpm * (vol_eff / 100) / 1000) * 0.264172 | 1
out disp_in3 | Displacement | in³/rev | disp * 0.0610237 | 2