A reciprocating pump moves liquid through repeated piston or plunger strokes. This calculator models single-acting cylinders: each cylinder draws in liquid on one stroke and delivers it on the other. Enter bore, stroke, RPM, cylinder count and an assumed volumetric efficiency to estimate displacement, flow and mean piston speed.
Reciprocating Pump Interactive Calculator
Vary bore, stroke, speed, cylinder count, and volumetric efficiency to see pump displacement, flow, and piston speed update on an animated cutaway.
Equation Used
- Single-acting cylinders with one displacement event per crank revolution per cylinder.
- Entered volumetric efficiency represents the ratio of delivered capacity to theoretical displacement.
- No rod-volume correction, pressure, valve loss, acceleration head, cavitation, force, power or safe-speed prediction.
The cutaway shows one cylinder. During intake, the suction valve is open and the delivery valve is shut; during delivery, those states reverse. Cylinder count changes the total flow calculation without adding cylinders to the drawing.
Intake and delivery
The crank and connecting rod move the piston back and forth. As chamber volume increases, liquid enters through the suction check valve while the delivery check is shut. As volume decreases, the suction check shuts and liquid leaves through the delivery check. This single-acting arrangement delivers on one stroke per crank revolution.
In a real pump, pressure differences and valve dynamics govern opening and closing. The animation ties ideal valve states to piston movement; it does not calculate cracking pressure, spring force or delayed valve response.
Parts in the cutaway
- Piston and cylinder: define the swept volume.
- Suction and delivery checks: direct the liquid through the chamber.
- Crank and connecting rod: produce the reciprocating motion.
- Crosshead and guide: constrain the drawn piston rod to a straight path.
The proportions are schematic. Bore and stroke are calculation inputs, not a complete set of manufacturing dimensions. Pressure rating, seal selection, clearances and structural strength need the details of the actual pump.
Using a capacity estimate
Reciprocating pumps are used for liquid transfer, chemical dosing and pressure-pumping duties. For example, Cat Pumps describes its model 230 as a triplex reciprocating plunger pump. A product’s pressure capability, materials and operating limits come from its own specifications, not from the displacement calculation here.
Use the tool to compare how bore, stroke, RPM and the number of identical cylinders affect average capacity. The entered efficiency adjusts the estimate for the delivery fraction you assume. It is held constant when you change RPM unless you change it yourself.
A complete pump selection also needs the fluid, inlet conditions, discharge pressure, drive and duty. A larger calculated flow is not proof that a particular pump can run faster or handle a more demanding service.
Displacement and flow equations
Let D be bore, S be stroke, N be crank speed in RPM, z be the number of identical single-acting cylinders and eta_v be volumetric efficiency as a decimal.
When V_s is in litres, those flow results are litres per minute. The calculator converts the millimetre inputs to metres, then converts volume to mL/stroke and flow to L/min. Stroke Volume refers to one cylinder; flow includes all entered cylinders.
Use S in metres for speed in m/s. The factor two counts travel along the stroke and back during one revolution; it does not mean two delivery strokes. This is a mean speed, not the instantaneous or peak speed of the piston.
For flow in m³/s, with A in m² and S in metres, use Q = ASNz × eta_v/60. The card labelled Actual Flow is this efficiency-adjusted estimate, not a measurement. No pressure or power calculation is performed.
Worked example using the default inputs
Enter D = 50 mm, S = 100 mm, N = 120 RPM, z = 1 and volumetric efficiency = 90%.
- Area: π × 50²/4 = 1,963.495 mm².
- Stroke volume: 1,963.495 × 100 = 196,349.54 mm³, or 196.35 mL/stroke.
- Theoretical flow: 0.196350 L × 120 × 1 = 23.56 L/min.
- Estimated flow: 23.5619 × 0.90 = 21.21 L/min.
- Mean piston speed: 2 × 0.100 × 120/60 = 0.40 m/s.
Change only Cylinders to 3 and theoretical flow becomes 70.69 L/min, with estimated flow 63.62 L/min at the same efficiency. Stroke volume per cylinder and mean piston speed stay unchanged.
Changing only RPM to 240 with one cylinder doubles theoretical flow to 47.12 L/min and mean piston speed to 0.80 m/s. That is an arithmetic comparison, not permission to double the speed of an actual pump.
What changes the calculated capacity?
| Input change | Effect while other inputs stay fixed |
|---|---|
| Double bore | Four times the swept volume and flow; mean piston speed is unchanged. |
| Double stroke | Twice the swept volume, flow and mean piston speed. |
| Double RPM | Twice the flow and mean piston speed; volume per stroke is unchanged. |
| Double cylinder count | Twice the flow; per-cylinder stroke volume and mean speed are unchanged. |
| Change efficiency | Only the estimated Actual Flow changes. |
These relationships describe this single-acting model. They do not compare maintenance life, cost, pulsation or pressure capability among piston, diaphragm, gear and centrifugal pumps.
Reciprocating-pump questions
What does Actual Flow mean here?
It is an estimate: Theoretical Flow multiplied by the efficiency percentage you enter. It is not a measured result or a prediction of efficiency from speed, pressure or fluid properties.
Does Stroke Volume include all cylinders?
No. It is the swept volume of one cylinder on one pumping stroke. The flow outputs multiply that volume by the entered cylinder count and RPM.
Why is only one cylinder shown when I select three?
The cutaway illustrates one single-acting cylinder and its two check valves. Cylinder count changes total calculated flow. The display does not draw the other cylinders or calculate their combined pulsation.
Can I use these results for a double-acting pump?
Not directly. This model counts one delivery stroke per revolution per cylinder. A double-acting calculation must account for delivery on both strokes and the area occupied by the rod on the rod side.
Does the speed slider give a safe operating range?
No. It is a calculation range. Permissible speed depends on the selected pump, inlet supply, lubrication, fluid and duty. Use the pump manufacturer’s limits rather than the slider endpoints.
Can this calculator determine pressure or motor power?
No. Neither pressure nor mechanical efficiency is an input. Equal estimated flow does not imply equal pressure capability, required motor power or interchangeable pump construction.
What if a discharge line is closed?
A driven positive-displacement pump can develop damaging pressure against a blocked discharge. The system needs pressure control and relief appropriate to its pump and components. Follow the manufacturer’s system requirements; this calculator does not size or set those devices.
Can it diagnose low flow or set a pulsation dampener?
No. The efficiency input summarizes an assumed delivery ratio. It does not identify leakage, inlet restrictions, valve behaviour or cavitation, and it does not calculate dampener volume or precharge. Those questions require the actual equipment and operating conditions.
Technical reference
- Joe Evans, Positive Displacement Pumps Part I — Reciprocating Pumps — single-acting piston-pump cutaway, check-valve sequence, displacement formula and volumetric-efficiency relationship.
Cat Pumps model 230: triplex plunger-pump example. Cat Pumps FAQs: pressure control and system requirements.
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