Spicer Displacement Calculator & How to Use It

The Spicer displacement calculator is a tool that estimates the fluid displacement of a hydraulic pump or motor per revolution, typically expressed in cubic inches or cubic centimeters. You enter the pump’s bore diameter, stroke length, and number of pistons (or gear dimensions for gear pumps), and the calculator returns the displacement per revolution, which is essential for sizing pumps, motors, and reservoirs. This article explains the formulas, how to use the calculator correctly, and common pitfalls to avoid.

Formula

The displacement of a piston pump or motor is calculated using the formula:

Displacement (in³/rev) = (π/4) × D² × S × N

• D = bore diameter (inches)
• S = stroke length (inches)
• N = number of pistons
• π/4 = area of a circle divided by diameter squared (0.7854)

The result is the theoretical volume of fluid displaced per revolution, assuming 100% volumetric efficiency. For metric units, multiply the cubic-inch result by 16.387 to get cubic centimeters.

Worked Example

Using the default values from the calculator above:

1. Bore diameter = 1.5 in
2. Stroke length = 1.0 in
3. Number of pistons = 9

First, compute the piston area: π/4 × (1.5)² = 0.7854 × 2.25 = 1.767 in²

Next, multiply by stroke: 1.767 × 1.0 = 1.767 in³ per piston

Finally, multiply by the number of pistons: 1.767 × 9 = 15.90 in³/rev

The calculator rounds to two decimals, giving 15.90 in³/rev (or 260.5 cc/rev).

When to Use the Displacement Calculator

This calculator is useful in several hydraulic system design scenarios:

• Sizing pumps – To determine the flow rate needed for a given actuator speed, you need displacement per revolution.
• Matching motors – Motor displacement determines torque output and speed for a given flow.
• Reservoir sizing – Knowing total system displacement helps estimate oil volume needed.
• Comparing pump types – Axial piston, radial piston, and gear pumps have different displacement calculations.

For gear pumps, the formula differs: displacement ≈ (π/4) × (outside diameter² – inside diameter²) × face width. This calculator is for piston-type pumps/motors only.

How to Choose the Right Inputs

Accurate inputs are critical for a correct result. Here are the measurements you need:

• Bore diameter – Measure the cylinder bore, not the piston rod diameter. For axial piston pumps, this is the piston bore size.
• Stroke length – The maximum distance the piston travels. For a swashplate pump, this is determined by the swashplate angle; the stroke is often less than the physical piston length.
• Number of pistons – Count all pistons in the pump or motor. Common numbers are 7, 9, or 11.

If you are working from a manufacturer datasheet, these values are usually listed. If not, you may need to disassemble and measure – but always consult the manual first.

Common Mistakes and Misconceptions

One frequent error is using the swashplate angle to calculate stroke incorrectly. The stroke is the axial distance the piston moves, which equals the swashplate diameter times the tangent of the angle. Another mistake is mixing units: if you measure bore in millimeters, the result will be in cubic millimeters unless you convert. Always convert to inches or centimeters before using the formula.

Also, the calculator gives theoretical displacement. Actual output is lower due to internal leakage, so multiply by volumetric efficiency (typically 90–98%) for real-world flow.

Finally, don’t confuse displacement with flow rate. Flow rate = displacement × speed (RPM). For example, a 15.9 in³/rev pump at 1800 RPM delivers 15.9 × 1800 = 28,620 in³/min, which converts to about 124 GPM (1 gallon = 231 in³).

Limitations of the Formula

The piston pump formula assumes a perfect cylinder and uniform piston motion. In reality, factors like piston wobble, compressibility of the fluid, and clearance leakage affect actual displacement. For design purposes, the theoretical value is a starting point; always verify with manufacturer data or testing.

For gear pumps, the displacement depends on gear tooth geometry, not bore/stroke, so this calculator won’t work for them. Similarly, vane pumps use a different formula based on rotor and cam ring dimensions.

If you need to calculate flow rate or torque, you’ll need additional inputs like speed and pressure. The displacement alone is not enough.

Frequently Asked Questions

What is the difference between displacement and flow rate?

Displacement is the volume of fluid moved per revolution (in³/rev or cc/rev). Flow rate is the volume moved per unit time (GPM or L/min) and equals displacement multiplied by rotational speed. For example, a pump with 10 in³/rev at 1200 RPM delivers 12,000 in³/min, which is about 51.9 GPM.

Can I use this calculator for a gear pump?

No, the formula here is for piston pumps/motors. Gear pump displacement is calculated using the gear tooth dimensions: displacement ≈ (π/4) × (OD² – ID²) × face width, where OD is outside diameter and ID is inside diameter of the gear teeth.

How do I convert displacement to cubic centimeters?

Multiply the cubic-inch value by 16.387. For example, 15.9 in³/rev × 16.387 = 260.5 cc/rev. The calculator includes this conversion as a second output.

What is a typical displacement for a hydraulic pump?

It varies widely. Small pumps for log splitters might be 5–10 in³/rev, while large industrial pumps can be 100 in³/rev or more. The right size depends on the required flow and operating speed.

Why does my pump produce less flow than calculated?

Volumetric efficiency is never 100%. Internal leakage past pistons and valves reduces output. Typical efficiencies are 90–98% for new pumps. Also, operating at high pressure increases leakage. Multiply the theoretical displacement by efficiency to estimate actual flow.

Does the number of pistons affect the smoothness of flow?

Yes, more pistons generally provide smoother flow with less pulsation. A 9-piston pump has less ripple than a 7-piston pump. However, the displacement formula doesn’t account for pulsation; it only gives the average volume per revolution.

Related

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• Percent to Rate Calculator: How to Convert

in d | Bore diameter | in | 1.5 | 0
in s | Stroke length | in | 1.0 | 0
in n | Number of pistons | - | 9 | 1
out disp | Displacement per rev | in³/rev | (pi/4) * d^2 * s * n | 2
out disp_cc | Displacement per rev | cc/rev | ((pi/4) * d^2 * s * n) * 16.387 | 1