Compressor Power Calculator
Calculates the shaft power needed to compress a gas from a given inlet pressure to a target outlet pressure using isentropic or polytropic compression theory. Essential for sizing compressors in chemical and gas processing plants.
Last updated: May 2026
About this calculator
The power required for adiabatic (isentropic) or polytropic compression is derived from the steady-flow energy equation applied to an ideal gas. The formula is: P = [Q × P₁ × 10⁵ × (n/(n−1)) × ((P₂/P₁)^((n−1)/n) − 1)] / (η × 60000), where Q is volumetric flow rate (m³/min), P₁ is inlet pressure (bar), P₂ is outlet pressure (bar), n is the polytropic/isentropic exponent (γ for isentropic, typically 1.4 for air), and η is compressor efficiency as a decimal. The factor 10⁵ converts bar to Pa, and 60 000 converts W·min to kW. The pressure ratio P₂/P₁ raised to the exponent (n−1)/n captures the thermodynamic work of compression. Higher pressure ratios, lower efficiency, or larger flow rates all increase power demand. For isentropic compression of diatomic gases, n = γ ≈ 1.4.
How to use
Example: Compress air at Q = 10 m³/min from P₁ = 1 bar to P₂ = 5 bar with n = 1.4 (isentropic, air) and η = 75%. Step 1: Pressure ratio = 5/1 = 5. Step 2: Exponent = (1.4−1)/1.4 = 0.4/1.4 ≈ 0.2857. Step 3: 5^0.2857 ≈ 1.584; subtract 1 → 0.584. Step 4: n/(n−1) = 1.4/0.4 = 3.5. Step 5: Numerator = 10 × 1 × 100000 × 3.5 × 0.584 = 2,044,000. Step 6: Power = 2,044,000 / (0.75 × 60000) ≈ 45.4 kW. A 75% efficient compressor requires about 45.4 kW to handle this duty.
Frequently asked questions
What is the difference between isentropic and polytropic compression in compressor power calculations?
Isentropic compression assumes a perfectly adiabatic, reversible process with no heat exchange — it uses the isentropic exponent γ (ratio of specific heats, ≈1.4 for air). Polytropic compression uses an empirical exponent n that accounts for real heat transfer and internal irreversibilities, with n typically between 1.2 and 1.4 for most industrial gases. Isentropic power gives the theoretical minimum for adiabatic machines, while polytropic power is more representative of actual multi-stage centrifugal or axial compressors. For positive-displacement machines, isothermal (n = 1) power is often used as a benchmark.
How does compressor efficiency affect the required shaft power?
Compressor efficiency η appears in the denominator of the power formula, so lower efficiency directly increases shaft power demand. A compressor with 75% efficiency requires 33% more power than a theoretically perfect (100% efficient) machine for the same duty. Efficiency losses arise from fluid friction, leakage, bearing losses, and heat transfer. Typical centrifugal compressors operate at 70–85% isentropic efficiency, while well-maintained reciprocating compressors can reach 80–90%. Selecting a compressor matched to its best-efficiency point is critical for minimising operating costs.
When should a multi-stage compressor be used instead of a single-stage unit?
Multi-stage compression with intercooling is used when the overall pressure ratio exceeds about 4:1 for a single stage. High single-stage pressure ratios cause excessive discharge temperatures, increased mechanical stress, and poor volumetric efficiency due to gas re-expansion. Staging with intercooling brings the process closer to isothermal compression, significantly reducing total power. As a rule of thumb, each stage should handle a pressure ratio of roughly 3–4:1. The power calculator here applies to a single stage; for multi-stage systems, compute power for each stage separately and sum.