Pump Displacement Calculator & Formula

This pump displacement calculator works out the theoretical volume a pump moves per revolution or per stroke, based on the geometry you enter (bore, stroke, number of cylinders, or gear dimensions). You input the pump’s physical dimensions and speed, and you get the displacement per revolution and the theoretical flow rate at that speed. Displacement is the volume of fluid pushed out in one complete cycle, usually expressed in cubic centimeters per revolution (cc/rev) or cubic inches per revolution (in³/rev).

Formula

For a piston or plunger pump, the displacement per revolution is the swept volume of all the working chambers:

D = (π/4) × d² × L × n

• D = displacement per revolution (cc/rev or in³/rev)
• d = bore diameter (mm or inches)
• L = stroke length (mm or inches)
• n = number of cylinders or pistons

For a gear pump, the displacement is roughly the volume between two gear teeth times the number of teeth and the gear width. A common approximation is:

D ≈ 2 × π × module × teeth × face width × (module × 1.12) (for external gear pumps, where module is the gear tooth size).

The theoretical flow rate is simply displacement times speed:

Q = D × N

• Q = flow rate (L/min or GPM)
• N = rotational speed (RPM)

Remember that this is the theoretical displacement — real pumps have internal leakage, so actual flow is slightly lower, typically 85–95% of theoretical.

Worked Example

Using the default values from the calculator above: bore = 50 mm, stroke = 50 mm, cylinders = 1, speed = 1500 RPM.

1. Convert bore and stroke to centimeters: bore = 5 cm, stroke = 5 cm.
2. Area of the bore: π/4 × (5)² = 0.7854 × 25 = 19.635 cm².
3. Volume per cylinder: 19.635 × 5 = 98.175 cm³.
4. With 1 cylinder, displacement per rev = 98.175 cc/rev.
5. Flow rate = 98.175 cc/rev × 1500 rev/min = 147,262.5 cc/min = 147.26 L/min.

The calculator shows 98.18 cc/rev and 147.26 L/min, matching the manual calculation.

Why Displacement Matters

Displacement is the core specification for any positive-displacement pump — piston, gear, vane, or lobe. It tells you how much fluid the pump moves per revolution, so you can:

• Match a pump to a required flow rate at a given motor speed.
• Size the drive motor (power = pressure × flow).
• Compare pumps of different sizes and types.
• Estimate the speed needed to achieve a target flow.

For example, if you need 50 L/min at 1800 RPM, you need a displacement of 50,000 cc/min ÷ 1800 = 27.8 cc/rev. This calculation is the first step in designing any hydraulic system.

How to Choose the Right Pump Displacement

Selecting the right displacement involves knowing your flow requirement and available speed. Here’s a simple process:

1. Determine the required flow rate (L/min or GPM) from your application — for example, a hydraulic cylinder that must extend in 3 seconds.
2. Identify the available drive speed (RPM) — electric motors often run at 1450 or 2900 RPM, while engine-driven pumps vary.
3. Divide the flow by the speed to get the required displacement per revolution.
4. Add a safety margin for internal leakage (typically 5–10%) and for pressure drops.
5. Check that the pump’s maximum pressure rating exceeds your system’s relief valve setting.

If you’re replacing a pump, measure the old one’s bore, stroke, and number of pistons, or look for a model number. For gear pumps, measure the gear width and tooth count to estimate displacement.

Common Mistakes and Misconceptions

A frequent error is mixing units — using millimeters in the formula while expecting cubic inches. Always convert to consistent units first. Another mistake is confusing displacement with flow rate: displacement is per revolution, flow is per minute.

Many people also forget that the formula gives theoretical displacement. Real pumps have clearance between moving parts, so actual flow is lower. The difference is called “slip” and increases with pressure. For a new pump, slip might be 3–5%; for a worn pump, it can be 20% or more.

Another misconception is that a larger displacement always means more pressure. Displacement only affects flow; pressure is determined by the load and the pump’s ability to overcome resistance. A pump can have high displacement but low pressure rating.

Limits of the Formula

The piston pump formula assumes the bore is circular and the stroke is linear. It doesn’t account for:

• Piston rod volume (in double-acting cylinders, the rod reduces displacement on one side).
• Dead volume at the end of the stroke.
• Valve timing and compressibility of the fluid.
• Internal leakage and wear.

For gear pumps, the simple formula is an approximation. The actual displacement depends on the exact gear profile, backlash, and housing clearances. Manufacturers usually provide measured displacement values — use those when available.

The formula also assumes incompressible fluid. At very high pressures (above 3000 psi), hydraulic oil compresses slightly, reducing volumetric efficiency. This is usually negligible in general sizing.

Practical Applications

Pump displacement calculations are used in many fields:

• Hydraulic systems — sizing pumps for excavators, presses, and machine tools.
• Automotive — oil pumps, fuel pumps, and coolant pumps.
• Agriculture — sprayer pumps and hydraulic implements.
• Marine — steering and trim systems.
• Industrial lubrication — gear pumps for oil circulation.

For example, a log splitter needs 20 L/min at 200 bar. With a 1450 RPM motor, you’d need a displacement of 20,000/1450 ≈ 13.8 cc/rev. A gear pump with that displacement would be a common choice.

Frequently Asked Questions

What is the difference between displacement and flow rate?

Displacement is the volume of fluid moved per revolution (or per stroke), measured in cc/rev or in³/rev. Flow rate is the volume moved per unit time, usually L/min or GPM. Flow rate = displacement × speed. For example, a 10 cc/rev pump at 1500 RPM gives 15 L/min.

How do I convert cc/rev to GPM?

Multiply cc/rev by RPM, divide by 1000 to get L/min, then divide by 3.785 to get GPM. Example: 20 cc/rev × 1500 RPM = 30,000 cc/min = 30 L/min = 7.93 GPM.

Why is my actual flow lower than the calculated displacement?

Internal leakage (slip) reduces actual flow. This increases with pressure and wear. A new pump might have 5% slip, while a worn pump can have 20% or more. Also, if the pump is not fully filled (cavitation), flow drops.

Can I use this calculator for a gear pump?

Yes, but you need the gear dimensions. The formula for gear pumps is different (as shown above), but the calculator’s piston formula won’t apply. For gear pumps, use the manufacturer’s displacement data or the gear formula.

What is a good displacement for a hydraulic pump?

It depends on your application. For a log splitter, 10–20 cc/rev is common. For a small tractor, 20–40 cc/rev. For industrial machinery, it can be hundreds of cc/rev. Always match the pump to your flow and pressure requirements.

Does pump displacement affect pressure?

No. Displacement affects flow, not pressure. Pressure is determined by the load and the system’s relief valve setting. A pump can deliver high flow at low pressure or low flow at high pressure, within its rated limits.

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in bore | Bore diameter | mm | 50 | 0
in stroke | Stroke length | mm | 50 | 0
in cyl | Number of cylinders | - | 1 | 1
in rpm | Pump speed | rpm | 1500 | 0
out disp | Displacement per rev | cc/rev | (pi/4) * (bore/10)^2 * (stroke/10) * cyl | 2
out flow | Theoretical flow | L/min | disp * rpm / 1000 | 2