An air compressor transfers mechanical energy to air, raising its pressure. This diagram shows a single-acting piston compressor: crank rotation drives the piston, inlet valves admit air and delivery valves pass compressed air onward. Enter bore, stroke, pump speed and volumetric efficiency to estimate inlet-referenced flow and mean piston speed. Pressure capability and motor power are not calculated.
Air Compressor Interactive Calculator
Estimate single-cylinder displacement, inlet-referenced flow and mean piston speed from bore, stroke, pump rpm and an entered volumetric efficiency.
Equation Used
Cylinder area times stroke gives swept volume. Multiplying by pump rpm gives displacement per minute; the entered volumetric efficiency scales this to an inlet-referenced flow estimate. It is not compressed discharge volume or a certified free-air-delivery rating, and no reference-pressure or temperature correction is applied.
- Single-cylinder, single-acting reciprocating compressor.
- Bore and stroke are entered in inches.
- One compression stroke per crank revolution.
- The entered volumetric efficiency represents net filling effects, including clearance-gas expansion, valves and leakage. It is not solved from pressure or speed.
The single-acting compression cycle
The crank and connecting rod move the piston back and forth. On the return stroke, gas left in the clearance space expands before inlet pressure can open the inlet valve. Fresh air then fills the cylinder. On the compression stroke, both valves are initially closed; the delivery valve opens when cylinder pressure can overcome downstream pressure and valve resistance.
One side of the piston performs the compression in this single-acting model, giving one swept volume per crank revolution. It is not a four-stroke combustion-engine cycle. The illustrated valve events explain the sequence, but their exact timing is not calculated from pressure.
Main components
- Crank and connecting rod: convert rotation into piston motion.
- Piston and cylinder: change the enclosed gas volume.
- Inlet and delivery valves: direct the gas flow.
- Receiver and controls: in a complete installation, store air and coordinate supply with demand.
- Cooling, drainage and treatment: address heat, condensate and required air quality.
Pressure-switch settings, relief protection, clearances, service intervals and safe operating speed belong to the specific equipment design. They cannot be inferred from the four inputs here. A receiver’s rated pressure is not interchangeable with a compressor’s normal cut-out pressure.
Matching air supply to demand
Compressed air can operate tools, control valves and pneumatic actuators, or supply a process that specifies suitable air quality. A useful selection compares required flow at the operating pressure with the compressor’s rated delivery and permitted duty.
Demand varies with the equipment and how it is used. A receiver can buffer short peaks while pressure falls through an allowed range, but it cannot remedy a sustained average demand greater than compressor delivery. Air treatment, distribution pressure losses, leakage and recovery time also affect the complete system.
The displacement calculator is an explanatory starting point. It does not select an installed compressor or establish suitability for breathing, medical, food-contact or other air-quality-sensitive service.
Displacement and estimated flow
For bore D and stroke L in inches, swept volume V = πD²L/4 in cubic inches per revolution. With one single-acting cylinder and pump speed N in rev/min, ideal displacement is VN/1,728 in ft³/min. The divisor converts cubic inches to cubic feet.
The displayed Delivered Flow is ideal displacement multiplied by entered volumetric efficiency η. The control takes a percentage, so an input of 85 is used as 0.85. To interpret this as inlet-referenced delivery, η must correspond to that definition and the actual conditions. It is not thermodynamic or motor efficiency.
Mean piston speed is 2LN/12 in ft/min: the piston travels two strokes per revolution and there are 12 inches per foot. This is an average magnitude, not instantaneous or maximum piston speed.
Use pump rpm, which may differ from motor rpm through a belt or gear drive. Multiple cylinders, double-acting geometry and multistage compression need the appropriate model; do not add different stage displacements as though each supplied separate free air.
No pressure input is present. Discharge pressure, reference conditions, power, temperature, mechanical limits and pressure-dependent efficiency are therefore not predictions of this calculator.
Worked example: one cylinder
Assume a 3.0-inch bore, 2.5-inch stroke, 700 rpm pump speed and 85% volumetric efficiency. These are hypothetical inputs, not operating specifications for a named machine.
Swept volume is π × 3.0² × 2.5 / 4 ≈ 17.6715 in³/rev. Ideal displacement is 17.6715 × 700 / 1,728 ≈ 7.1586 CFM.
The efficiency-scaled flow is 7.1586 × 0.85 ≈ 6.0848 CFM. Mean piston speed is 2 × 2.5 × 700 / 12 ≈ 291.67 ft/min.
If continuous demand were 14 CFM on the same reference basis, this estimated delivery would not satisfy it. A larger receiver could provide temporary stored air but would not close the continuous supply deficit. Increasing rpm in the calculator scales the result at the assumed efficiency; it does not establish that the actual pump, valves, drive or cooling can operate at that speed.
Compressor mechanisms
| Type | Compression element | Selection depends on |
|---|---|---|
| Reciprocating piston | A piston varies cylinder volume. | Rated delivery, pressure, duty, cooling and controls. |
| Rotary screw | Intermeshing rotors reduce trapped gas volume. | Operating range, part-load control, air treatment and system demand. |
| Scroll | Orbiting scroll geometry reduces gas-pocket volume. | Equipment-specific pressure, delivery, duty and air-quality requirements. |
Noise, service life, oil carryover, duty and cost cannot be assigned universal values from these type names. Compare the manufacturer’s specifications under the conditions required by the application.
Compressor calculation questions
No. It is swept displacement scaled by the entered volumetric efficiency, interpreted at the inlet reference conditions. Actual discharge volume depends on gas density at discharge.
At fixed stroke, rpm and efficiency, the calculation varies with bore squared. Doubling bore multiplies swept volume and estimated flow by four, but does not establish the drive power or structural suitability.
Pressure is not an input. Volumetric efficiency is entered directly rather than calculated from pressure ratio, clearance or valve behavior.
It can delay a pressure drop by storing air, but cannot meet sustained average demand above the compressor’s delivery. Burst duration, pressure range and recovery time must be assessed separately.
No. Volumetric efficiency relates gas delivery on a defined volume basis to swept displacement. It does not measure electrical or thermodynamic efficiency.
No. It contains no electrical, valve-leakage or fault-diagnostic model. Follow the equipment’s service instructions rather than dismantling pressurized parts or bypassing intake protection.
No. Relief protection must match the receiver and equipment requirements. Normal control settings and maximum allowable working pressure are distinct, and the displacement calculation determines neither.
No. Moisture, particles, intake contamination and the specified air-quality class still matter. Treatment and verification depend on the application.
References and further reading
U.S. Department of Energy: Improving Compressed Air System Performance covers supply, demand, storage and system efficiency. OSHA 1910.169: Air Receivers addresses receiver installation and protective equipment within its stated scope. Neither source makes this displacement estimate an equipment rating.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
