Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Calculate compressor shaft power based on adiabatic compression theory. Compute theoretical power from inlet/outlet pressure, gas flow rate, temperature, and heat capacity ratio k. Apply to compressor selection and motor sizing.
What this calculator is used for
The theoretical power required to compress a gas is calculated assuming an adiabatic (isentropic) process. Actual shaft power equals this theoretical power divided by the isentropic efficiency of the machine.
Typical engineering use cases
Initial power sizing of air and process gas compressors
Estimating compressor duty in refrigeration and heat-pump cycles
Evaluating staging and intercooling for high pressure ratios
Sensitivity studies on energy use versus operating pressure ratio
Governing equation and methodology
The theoretical adiabatic (isentropic) power is:
P = (γ/(γ-1)) × Q × P₁ × [(P₂/P₁)^((γ-1)/γ) − 1]
where γ is the heat capacity ratio Cp/Cv (air 1.4, steam 1.3, natural gas 1.28), Q the inlet volumetric flow [m³/s], and P₁/P₂ the inlet and outlet absolute pressures. The bracketed term is the adiabatic head. Actual shaft power = theoretical power / η (isentropic efficiency η ≈ 0.70–0.85); real gases require a compressibility factor Z.
Engineering assumptions and limitations
Assumes ideal-gas, isentropic compression
γ varies with temperature and composition, so a representative value is used
High pressures require real-gas (Z-factor) correction
Mechanical losses and interstage pressure drops are handled via efficiency
Practical design notes
When the pressure ratio P₂/P₁ exceeds about 3–4, discharge temperature becomes excessive, so consider multistage compression with intercooling. For a polytropic basis, use polytropic efficiency and exponent n instead of the adiabatic form. During selection, also confirm driver margin, starting torque, and surge margin.
Interpretation: Single-stage to 173 °C is near the limit for many materials and lube oils — that discharge temperature, not the power, is usually what forces you to split into stages with intercooling. Multi-staging also cuts total power versus this single-stage adiabatic figure.
Common Mistakes & Misuse
Reporting the isentropic (adiabatic) power as the driver power — divide by the isentropic efficiency (~0.7–0.8 centrifugal) and add mechanical/motor losses.
Running a single high ratio through one adiabatic stage when intercooled multistage would cut both power and discharge temperature — and exceeding the discharge-temperature limit.
Using k at inlet temperature for a large ratio where the mean-temperature k is more representative of the path.
Treating the gas as ideal at high suction pressure without a Z factor, which biases the actual mass and head.
Frequently Asked Questions
What efficiency should I use for preliminary sizing?
For centrifugal compressors, use 70-80% isentropic efficiency. For reciprocating compressors, 80-90%. For screw compressors, 60-75%. Actual efficiency depends on the specific machine and operating point.
Does this account for intercooling?
This calculates single-stage adiabatic power. For multi-stage compression with intercooling, calculate each stage separately and sum the power. Intercooling reduces total power and discharge temperature.
For preliminary estimation and educational use only. Results may depend strongly on assumptions, input data, fluid or material properties, and the range of validity of the underlying equation. Verify critical calculations independently and follow the applicable code, specification, and formal engineering review process before using any result for design, procurement, fabrication, operation, or safety decisions.