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.
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.