Hydraulic Pump Displacement Calculator & Formula

This calculator works out the theoretical displacement of a hydraulic pump—the volume of fluid it moves per revolution—based on the pump type and its dimensions. You enter the bore diameter and stroke length (for piston pumps) or gear width and depth (for gear pumps), and it returns displacement in cubic inches per revolution and in cubic centimeters per revolution. The result is the starting point for sizing a pump to a system’s flow and speed requirements.

Formula

The displacement of a hydraulic pump is the volume of fluid displaced by the pump’s moving elements in one complete revolution. For a piston pump, it is the cross-sectional area of the piston times the stroke length, multiplied by the number of pistons (if more than one). For a gear pump, it is approximately twice the product of the gear width and the gear depth (the distance from the gear center to the tooth tip).

• Piston pump: Displacement (in³/rev) = (π/4) × D² × S × N, where D is the bore diameter (in), S is the stroke (in), and N is the number of pistons.
• Gear pump: Displacement (in³/rev) ≈ 2 × W × D, where W is the gear width (in) and D is the gear depth (in).

Variables are in inches for US customary units; to convert to cubic centimeters per revolution, multiply by 16.387.

Worked Example

Using the default values from the calculator: a piston pump with a bore diameter of 1.5 inches and a stroke of 2.0 inches.

1. Calculate the piston area: A = (π/4) × (1.5)² = 0.7854 × 2.25 = 1.767 in².
2. Multiply by stroke: Displacement = 1.767 × 2.0 = 3.534 in³/rev.
3. Convert to cm³/rev: 3.534 × 16.387 = 57.9 cm³/rev.

The calculator returns 3.534 in³/rev and 57.9 cm³/rev, matching the manual calculation.

How to Use the Displacement Value

Displacement alone doesn’t tell you flow rate—you need pump speed. Flow (in gallons per minute) equals displacement (in³/rev) times speed (RPM) divided by 231. For example, a 3.534 in³/rev pump at 1800 RPM gives 3.534 × 1800 / 231 = 27.5 GPM. This is theoretical flow; real pumps have volumetric efficiency (typically 85–95%) due to internal leakage, so actual flow is lower. Use the theoretical value for sizing, then apply an efficiency factor from the manufacturer’s data.

Choosing the Right Pump Type

Piston pumps offer higher pressure capability (up to 5000+ psi) and variable displacement options, but they are more expensive and sensitive to contamination. Gear pumps are simpler, cheaper, and more tolerant of dirt, but they are fixed-displacement and usually limited to around 3000 psi. For most mobile equipment, gear pumps are common; for industrial high-pressure systems, piston pumps dominate. Consider the required flow, pressure, and duty cycle when selecting.

Common Mistakes and Misconceptions

• Mixing units: Always keep dimensions in the same unit system. A common error is mixing inches and millimeters, which throws off displacement by a factor of 25.4³.
• Ignoring efficiency: Displacement is theoretical; actual flow is less. Use volumetric efficiency to avoid undersizing.
• Confusing displacement with flow: Displacement is per revolution; flow is per minute. Multiply by speed.
• Gear pump approximation: The 2×W×D formula is a simplification; actual displacement depends on tooth profile and number of teeth. For precise values, consult the pump’s datasheet.

Limitations of the Formula

The piston pump formula assumes a single piston and a flat face; real piston pumps have multiple pistons and often a swashplate angle that changes effective stroke. The gear pump formula is an approximation that works for typical external gear pumps but not for internal gear or vane pumps. For exact displacement, measure the pump or use manufacturer specifications. Also, the formulas do not account for fluid compressibility, which becomes significant above 3000 psi.

Frequently Asked Questions

How do I calculate the flow rate from displacement?

Multiply displacement (in³/rev) by pump speed (RPM) and divide by 231 to get GPM. For example, 3.5 in³/rev at 1500 RPM gives 3.5 × 1500 / 231 = 22.7 GPM. Remember to multiply by volumetric efficiency (e.g., 0.9) for actual flow.

What is the difference between displacement and flow?

Displacement is the volume of fluid moved per revolution, measured in cubic inches or cubic centimeters per revolution. Flow is the volume moved per unit time, typically gallons per minute or liters per minute. Flow equals displacement times speed.

Can I use this calculator for a vane pump?

No, the formulas are for piston and external gear pumps. Vane pumps have a different geometry; their displacement depends on the rotor diameter, vane length, and eccentricity. Use manufacturer data for vane pumps.

Why does my pump’s actual output differ from the calculated displacement?

Several factors: internal leakage reduces volumetric efficiency, especially at high pressure; the pump may have a variable displacement mechanism that changes the effective stroke; and the gear pump formula is approximate. Always check the pump’s efficiency curve.

How do I convert displacement to liters per revolution?

1 cubic inch = 0.016387 liters. So divide the displacement in cubic inches by 61.024 to get liters per revolution. For example, 3.5 in³/rev = 3.5 / 61.024 = 0.0574 L/rev.

Does pump speed affect displacement?

No, displacement is a fixed geometric property of the pump. However, at very high speeds, cavitation can reduce effective displacement because the pump can’t fill completely. At low speeds, leakage becomes proportionally larger, reducing volumetric efficiency.

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in type | Pump type | Piston=1, Gear=2 | 1 | 0
in bore | Piston bore diameter (in) | in | 1.5 | 0
in stroke | Piston stroke (in) | in | 2.0 | 0
in gear_w | Gear width (in) | in | 1.0 | 0
in gear_d | Gear depth (in) | in | 1.5 | 0
out disp_in3 | Displacement (in³/rev) | in³/rev | (type == 1) ? (pi/4 * bore^2 * stroke) : (2 * gear_w * gear_d) | 3
out disp_cm3 | Displacement (cm³/rev) | cm³/rev | disp_in3 * 16.387 | 2