2026-07-30 10 min

Compressor Pressure Ratio Calculator

Calculate compressor pressure ratio, stage pressure distribution, and optimize interstage pressures for multistage compressors with intercooling.

Calculator

Unit System

Suction Pressure (p₁) [bar]

Discharge Pressure (p₂) [bar]

Number of Stages

Specific Heat Ratio (k)

Inlet Temperature (T₁) [°C]

Results

Normal

Overall Pressure Ratio

10.00-

Total discharge to suction pressure ratio

PR per Stage

3.16-

Optimal equal PR per stage

Total Specific Work

274.06kJ/kg

Total compression work per kg

Isothermal Efficiency

70.69%

Actual vs ideal isothermal work

Stage 1 Discharge

3.16bar

Stage 1 outlet pressure

Stage 1 Temp

134.18°C

Stage 1 outlet temperature

Stage 1 Work

114.69kJ/kg

Stage 1 specific work

Stage 2 Discharge

10.00bar

Stage 2 outlet pressure

Stage 2 Temp

292.83°C

Stage 2 outlet temperature

Stage 2 Work

159.37kJ/kg

Stage 2 specific work

Visualizations

Results Overview

10-Overall Pressure Ratio

3.2-PR per Stage

274.1-Total Specific Work

70.7-Isothermal Efficiency

3.2-Stage 1 Discharge

134.2-Stage 1 Temp

114.7-Stage 1 Work

10-Stage 2 Discharge

Formula

Pressure ratio calculation for single and multistage compressors with optimal interstage pressure distribution.

r_p = p₂/p₁ (pressure ratio)

Alternative Form

r_p_total = Π(r_p_i) for multistage

Variables

Symbol	Name	Unit	Description
r_p	Pressure Ratio	-	Discharge to suction pressure ratio
p₁	Suction Pressure	bar / psia	Inlet pressure
p₂	Discharge Pressure	bar / psia	Outlet pressure
N	Number of Stages	-	Compression stages

Explanation

For minimum total work with ideal intercooling, equal pressure ratio per stage is optimal. Multistage compression with intercooling between stages reduces total power requirement significantly compared to single-stage compression.

Derivation

Optimal PR per stage = (p₂/p₁)^(1/N). This minimizes total specific work when intercoolers return gas to initial suction temperature after each stage. Derived from minimizing Σ w_i where w_i = (k/(k-1))RT₁[(r_p_i)^((k-1)/k) - 1] subject to Π r_p_i = r_p_total.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Determine overall pressure ratio from suction and discharge pressures.

r_p_total = p₂ / p₁

p₁:1 bar

p₂:10 bar

Result: r_p_total = 10.00

Step 2

Calculate optimal per-stage pressure ratio for multistage compression.

r_p_stage = r_p_total^(1/N)

Stages (N):2

Result: r_p_stage = 3.16

Step 3

Calculate stage discharge temperatures and work distribution.

T₂ = T₁ × r_p^((k-1)/k)

k:1.4

T₁:20 °C

Result: Total specific work = 274.06 kJ/kg

Final Answer

10.00

Worked Examples

See how the calculator works with different scenarios.

Scenario

Compress from 1 bar to 25 bar in 2 stages. k = 1.4, T₁ = 25°C.

Inputs

p₁:1 bar

p₂:25 bar

N:2

k:1.4

Calculation

r_p_total = 25 r_p_stage = 25^(1/2) = 5 Stage 1: 1→5 bar, T₂ = 298 × 5^0.286 = 472 K = 199°C Stage 2: 5→25 bar, T₂ = 298 × 5^0.286 = 472 K = 199°C Total work = 2 × 199 kJ/kg = 398 kJ/kg

Result

r_p_stage = 5.00, Total work = 398 kJ/kg

Interpretation

Two-stage compression with intercooling reduces total work by ~35% compared to single-stage (which would require 612 kJ/kg for PR=25).

Understanding Your Result

Your Result: Overall Pressure Ratio: 10.00 -

Typical range: Single stage: 1.5-5. Two-stage: 5-25. Three-stage: 25-125. Four-stage: 125-625. Limit per-stage PR to 5 for reciprocating, 3 for centrifugal.

What This Means

Pressure ratio determines the thermodynamic difficulty of compression and directly affects discharge temperature, work requirement, and compressor design.

Why It Matters

Correct pressure ratio selection optimizes compressor efficiency and prevents excessive temperatures. Multistage compression with intercooling is essential for high pressure ratios.

Professional Interpretation

Optimal stage pressure ratio depends on compressor type and gas properties. For centrifugal compressors, limit per-stage PR to 1.5-3 for high efficiency. For reciprocating, 3-5 per stage is typical.

Recommendations

•Use equal pressure ratio per stage for minimum work with ideal intercooling
•Limit per-stage PR to 4 for reasonable discharge temperatures with air
•Consider gas k value: higher k increases discharge temperature for same PR
•Account for intercooler pressure drop (1-5% per intercooler) in stage PR calculation
•For variable gas composition, design for worst-case (highest k) scenario

Educational Content

Introduction

Pressure ratio is the fundamental parameter governing compressor performance. It determines work requirement, discharge temperature, and the need for multistage compression.

Concept Explanation

The pressure ratio r_p = p₂/p₁ is not independent of compressor type. Centrifugal compressors have a maximum per-stage PR limited by impeller tip speed. Reciprocating compressors are limited by pressure, temperature, and rod load limits.

Applications

▸Multistage compressor design

▸Intercooling system optimization

▸Compressor selection

▸Gas pipeline station design

▸Refrigeration system design

Benefits

•Optimized power consumption through proper staging
•Prevention of excessive discharge temperatures
•Improved volumetric efficiency
•Balanced mechanical loads across stages

Limitations

•Equal PR per stage assumes ideal intercooling
•Does not account for gas property changes between stages
•Intercooler pressure drop reduces optimization benefit

Best Practices

•Design for equal work per stage when possible
•Allow for intercooler pressure drop in stage calculation
•Consider gas composition changes after intercooling (condensation)
•Validate with compressor manufacturer stage analysis

Common Misconceptions

Myth: More stages always improve efficiency.

Truth: More stages increase capital cost and mechanical complexity. Beyond 4-5 stages, diminishing returns outweigh benefits.

Myth: Pressure ratio per stage is constant for a compressor.

Truth: Pressure ratio varies with flow rate, especially for centrifugal compressors with performance curves.

Practical Tips

•For air (k=1.4), limit per-stage PR to 4 to keep T₂ below 200°C
•For hydrogen/helium (k=1.66), per-stage PR must be lower due to higher temperature rise
•Intercooler pressure drop of 2% per stage reduces the benefit of multistage compression by ~5%
•Optimize number of stages: too few = high temps/low efficiency, too many = cost/complexity
•Isothermal efficiency compares actual work to ideal isothermal compression
•Consider cooling water temperature when specifying intercooler outlet temperature
•Gas composition can change across stages due to condensation of heavier components

Common Mistakes

Ignoring intercooler pressure drop in optimization

Include 1-5% pressure drop per intercooler. This shifts optimal PR per stage slightly above the geometric mean.

Assuming constant gas properties across stages

Re-evaluate k and R at each stage as pressure and temperature change significantly.

Exceeding temperature limits for materials

Check against piston ring (150°C), valve plate (180°C), and cylinder (200°C) limits.

Using overall PR for compressor type selection

Apply per-stage PR limits: centrifugal max 3, reciprocating max 5, screw max 7.

Assumptions

This calculator makes the following assumptions to provide estimates:

Ideal Intercooling: Perfect intercooling returns gas to initial suction temperature. Real intercoolers have approach temperatures of 5-15°C.

Equal Stage Ratios: Optimal PR per stage assumes equal work distribution. Real compressors may have different constraints.

Ideal Gas: Gas follows ideal behavior. Real gas effects at high pressure affect actual PR and work.

Steady Flow: Steady-state continuous flow assumed. Transient effects are negligible.

Limitations

Be aware of these limitations when using this calculator:

No Gas Property Variation: Does not model k and Z variations with pressure and temperature across stages.

Simplified Intercooler Model: Assumes perfect intercooling to initial temperature. Real heat exchangers have finite approach.

No Mechanical Constraints: Does not consider rod load limits, valve lift constraints, or impeller stress limits.

Equal PR Only: Optimal equal PR per stage applies only with ideal intercooling. Non-ideal cooling changes optimum.

Frequently Asked Questions

Answers to common questions about this calculator.

What is compressor pressure ratio?

Pressure ratio is the ratio of discharge pressure to suction pressure: r_p = p₂/p₁. It determines the thermodynamic difficulty of compression.

How do I calculate optimal interstage pressures?

For minimum work with ideal intercooling, use r_p_stage = (p₂/p₁)^(1/N). Stage pressures: p₁, p₁×r, p₁×r², ..., p₂.

Why use multistage compression?

Multistage compression with intercooling reduces total work by 15-43% compared to single-stage, and keeps discharge temperatures within material limits.

What is a good pressure ratio per stage?

For reciprocating: 3-5 per stage. For centrifugal: 1.5-3 per stage. For screw: up to 7 per stage.

How does specific heat ratio (k) affect pressure ratio?

Higher k (e.g., helium at 1.66) causes greater temperature rise for the same PR, requiring more stages or lower PR per stage.

What is the maximum PR for a single stage?

Centrifugal: ~3 (limited by tip speed). Reciprocating: ~5 (limited by temperature and rod load). Screw: ~7 (limited by leakage).

How does intercooling affect optimal PR distribution?

With perfect intercooling, equal PR per stage is optimal. Non-ideal cooling shifts optimum toward lower PR in later stages.

What is isothermal efficiency?

It compares actual multistage work to ideal isothermal compression. Higher isothermal efficiency means the compression process is closer to the thermodynamic minimum.

How does pressure ratio affect discharge temperature?

T₂ = T₁ × r_p^((k-1)/k). Higher PR and higher k both increase discharge temperature exponentially.

What happens if PR per stage is too high?

Excessive discharge temperature damages materials, reduces lubricant life, and decreases volumetric efficiency due to increased clearance gas expansion.

How do I calculate work distribution across stages?

With equal PR per stage and ideal intercooling, work is equally distributed. Each stage does 1/N of total work.

What is the effect of intercooler pressure drop?

Pressure drop increases the effective PR of subsequent stages. A 2% drop per intercooler adds ~5% to total work.

Can a centrifugal compressor achieve PR > 3?

Some high-speed centrifugal stages can achieve PR up to 5-6, but efficiency drops significantly. Multiple stages are preferred for efficiency.

How does molecular weight affect PR capability?

Higher molecular weight gases achieve higher PR per stage for centrifugal compressors due to higher head per impeller.

What is the difference between stage PR and overall PR?

Overall PR = product of all stage PRs (accounting for intercooler pressure drops). For N stages: r_p_total = Π r_p_i.

How do I select the number of stages?

Calculate temperature rise for each possible stage count. Select the minimum number that keeps T₂ below material limits (typically 200°C).

What is the role of the compressibility factor?

At high pressures (>50 bar), Z < 1.0, which reduces actual work compared to ideal gas calculation. Include Z for accuracy.

How does suction temperature affect staging?

Lower suction temperature reduces work and discharge temperature. Intercoolers that achieve lower outlet temperatures improve efficiency.

What is the optimum intercooler outlet temperature?

Ideally, cool to initial suction temperature. Cooling below ambient is not economical. Typical: approach temperature of 5-15°C above cooling water.

How do I handle variable gas composition in staging?

Design for the worst-case gas (highest k, lowest molecular weight). Stage ratios may need adjustment for different operating scenarios.

Related Calculators

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Related Guides

Deepen your understanding with these educational resources.

Multistage Compressor Design Guide

API guidelines for multistage compressor design

Understanding Compressor Pressure Ratios

CAGI educational resources

Intercooler Optimization in Compression Systems

GPSA guide to intercooler design

Glossary

Technical terms used in mortgage calculations explained in plain language.

Pressure Ratio (r_p): Ratio of discharge pressure to suction pressure: p₂/p₁.
Intercooling: Cooling gas between compression stages to reduce temperature and work.
Stage: One compression unit in a multistage system, consisting of an impeller or piston.
Specific Work: Work required per unit mass of gas compressed (kJ/kg).
Isothermal Efficiency: Ratio of ideal isothermal work to actual work.
Polytropic Exponent: Exponent n in pV^n = constant, representing real compression path.
Approach Temperature: Difference between intercooler outlet temperature and cooling medium temperature.
Rod Load: Net force on reciprocating compressor piston rod, limiting pressure ratio.

Authoritative References

Trusted sources and standards referenced by this calculator.

API 617 - Axial and Centrifugal Compressors API 618 - Reciprocating Compressors ASME PTC 10 - Compressors Performance Test Code GPSA Engineering Data Book Compressed Air and Gas Handbook (CAGI)

Applicable Standards

API 617API 618ASME PTC 10ISO 5389CAGI

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Page Information

Last Updated:

2026-07-30

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.