Air Compressor Power Calculator (Polytropic, Multistage with Intercooling)
Shaft power, the isothermal minimum, isothermal efficiency and discharge temperature of an air compressor from inlet flow, pressures, polytropic exponent, efficiency and number of stages.
Results
The dashed line marks the value you entered.
What this tool does
Compressing a gas takes the least work if it is kept cool; compressing it adiabatically takes the most. The polytropic work P = [n÷(n−1)]·p₁V̇₁·(r^((n−1)/n) − 1) lies in between, and splitting the compression into N stages with cooling back to the inlet temperature between them cuts the work and the discharge temperature — the chart compares it with the isothermal minimum. The flow must be at inlet conditions, not 'free air' at a different pressure and temperature. The exponent for a real compressor sits between 1 and 1.4 (air); the overall efficiency should come from the maker.
Formula
P = N × [n ÷ (n − 1)] p₁ V̇₁ (r^((n−1)/n) − 1) with r = (p₂ ÷ p₁)^(1/N) · isothermal: P = p₁ V̇₁ ln(p₂ ÷ p₁) · T₂ = T₁ r^((n−1)/n)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
qv | Air flow at inlet conditions | m³/min |
p1 | Inlet pressure (absolute) | bar |
p2 | Discharge pressure (absolute) | bar |
nx | Polytropic exponent (1 = isothermal, 1.4 = adiabatic for air) | — |
ef | Overall efficiency (shaft to air) | % |
ns | Number of stages (intercooled to inlet temperature) | — |
t1 | Inlet air temperature | °C |
PS | Shaft power needed | kW |
PI | Ideal polytropic power | kW |
PT | Isothermal power (the theoretical minimum) | kW |
IE | Isothermal efficiency | % |
SP | Specific power | kW per m³/min |
RS | Pressure ratio per stage | — |
T2 | Air temperature leaving each stage | °C |
Worked example
- Air flow at inlet conditions5 m³/min
- Inlet pressure (absolute)1.013 bar
- Discharge pressure (absolute)8 bar
- Polytropic exponent (1 = isothermal, 1.4 = adiabatic for air)1.3
- Overall efficiency (shaft to air)70 %
- Number of stages (intercooled to inlet temperature)1
- Inlet air temperature20 °C
- Shaft power needed31.93 kW
- Ideal polytropic power22.35 kW
- Isothermal power (the theoretical minimum)17.44 kW
- Isothermal efficiency54.6 %
- Specific power6.39 kW per m³/min
- Pressure ratio per stage7.90
- Air temperature leaving each stage199 °C
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.