AtlasCalcsUtility Calculation Suite
2026-07-30 10 min

Compressor Horsepower Calculator

Calculate compressor horsepower (HP) requirements for reciprocating, centrifugal, and screw compressors. Convert between power units and size drive motors.

Calculator

Unit System
Flow (Q) [m³/min]
Suction Pressure (p₁) [bar]
Discharge Pressure (p₂) [bar]
Specific Heat Ratio (k)
Efficiency [%]
Drive Loss [%]
Altitude [m]
Gas Molecular Weight
Inlet Temperature [°C]

Results

Normal

Gas Horsepower (GHP)

10485.25HP

Theoretical power to compress the gas

Brake Horsepower (BHP)

10809.53HP

Shaft power including mechanical losses

Motor Power

11890.49HP

Recommended motor size with 10% service factor

Motor Power

8866.74kW

Motor power in kilowatts

Specific Power

78.19kW/(m³/min)

Power per unit flow rate

Discharge Temperature

233.84°C

Estimated discharge temperature

Annual Energy Cost

7466724.68$/yr

Estimated yearly energy cost at $0.10/kWh, 8000 hrs/yr

Torque

47039.49N·m

Shaft torque at 1800 RPM

Visualizations

Results Overview

10,485HPGas Horsepower
10,810HPBrake Horsepower
11,890HPMotor Power
8,867HPMotor Power
78.2HPSpecific Power
233.8HPDischarge Temperature
7,466,725HPAnnual Energy Cost
47,039HPTorque

Formula

Compressor horsepower calculation accounting for isentropic compression, efficiency, drive losses, and altitude effects.

HP = (Q × (k/(k-1)) × p₁ × [(p₂/p₁)^((k-1)/k) - 1]) / (η × C)

Alternative Form

BHP = GHP / (η_m × η_drive)

Variables

SymbolNameUnitDescription
GHPGas HorsepowerHPTheoretical power to compress the gas
BHPBrake HorsepowerHPShaft power including mechanical losses
QFlow RateCFM / m³/minVolumetric flow at inlet
p₁, p₂Pressurespsia / barSuction and discharge pressures
kSpecific Heat Ratio-Cp/Cv
ηEfficiency%Overall compressor efficiency

Explanation

Gas horsepower is the theoretical power required to compress the gas isentropically. Brake horsepower adds mechanical losses (bearings, seals, gears). Motor power adds a service factor for reliable operation. The conversion factor C = 745.7 (HP to W) for SI units or 1 for imperial.

Derivation

Starting from isentropic compression work: W = (k/(k-1)) × p₁ × Q₁ × [(p₂/p₁)^((k-1)/k) - 1]. Dividing by efficiency gives actual shaft power. Converting to HP: HP = W(W) / 745.7. BHP = GHP / (η_mech × η_drive). Motor HP = BHP × SF.

Step-by-Step Calculation

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

Step 1

Determine gas properties and operating conditions.

PR = p₂/p₁
p₁:14.7 bar
p₂:100 bar
Result: PR = 6.80
Step 2

Calculate gas horsepower using isentropic compression formula.

GHP = Q × (k/(k-1)) × p₁ × [PR^((k-1)/k) - 1] / η / C
Q:100 m³/min
k:1.4
η:80%
Result: GHP = 10485.25 HP
Step 3

Account for drive losses and service factor to get motor size.

BHP = GHP / (1 - driveLoss), Motor = BHP × 1.1
Drive Loss:3%
Altitude:0 m
Result: Motor = 11890.49 HP (8866.74 kW)
Final Answer
10485.25

Worked Examples

See how the calculator works with different scenarios.

Scenario

Compress 100 CFM of air from 14.7 psia to 100 psia. k=1.4, η=80%, 3% drive loss, sea level.

Inputs

Q:100 CFM
p₁:14.7 psia
p₂:100 psia
k:1.4
η:80%

Calculation

PR = 100/14.7 = 6.80 GHP = 100 × 3.5 × 14.7 × (6.80^0.286 - 1) / 0.80 / 1 GHP = 100 × 51.45 × 0.721 / 0.80 = 4639 → 100 × (3.5×14.7) × 0.721 / 0.80 GHP = 100 × 51.45 × 0.721 / 0.80 = 100 × 46.37 = 46.4 HP BHP = 46.4 / 0.97 = 47.8 HP Motor = 47.8 × 1.1 = 52.6 HP

Result

Motor = 52.6 HP (≈ 39.2 kW)

Interpretation

Select a 50 HP motor. The 10% service factor provides adequate margin. Annual energy cost approximately $31,000 at $0.10/kWh.

Understanding Your Result

Your Result: Gas Horsepower (GHP): 10485.25 HP

Typical range: Small workshop: 1-25 HP. Industrial reciprocating: 25-500 HP. Large centrifugal: 500-50000 HP. Pipeline: up to 100000 HP.

What This Means

Horsepower (HP) is the standard unit for compressor power in North America. The calculation determines the required motor size for reliable compressor operation.

Why It Matters

Correct horsepower sizing prevents motor overload, ensures adequate starting torque, and optimizes energy efficiency. Undersized motors fail prematurely; oversized motors operate inefficiently.

Professional Interpretation

Brake horsepower (BHP) is the actual power delivered to the compressor shaft. Gas horsepower (GHP) is the theoretical compression power. The difference represents all mechanical and thermodynamic losses. Motor nameplate rating should include the service factor (typically 1.10-1.15).

Recommendations

  • •Always include altitude correction for installations above 500 m
  • •Use actual gas molecular weight, not air value, for non-air gases
  • •Select standard motor sizes: next standard size above calculated BHP × SF
  • •For belt drives, include 3-5% drive loss; for direct drive, 1-2%
  • •Verify motor starting torque capability for reciprocating compressors

Educational Content

Introduction

Compressor horsepower is the power required to compress a gas from suction to discharge pressure. It is fundamental to motor selection, energy cost estimation, and compressor system design.

Concept Explanation

The total power splits into: (1) Gas horsepower - the useful work of compression, (2) Mechanical losses - bearing friction, seal drag, (3) Drive losses - belt/gear inefficiency, (4) Service factor - safety margin. Understanding each component helps optimize system design.

Applications

▸Electric motor sizing for compressors
▸Engine/gas turbine driver selection
▸Energy cost analysis and budgeting
▸Compressor bid evaluation and comparison
▸Drive system design (direct, belt, gear)

Benefits

  • •Ensures reliable motor operation without overload
  • •Optimizes capital investment in drive equipment
  • •Enables accurate energy cost forecasting
  • •Facilitates comparison between compressor options

Limitations

  • •Assumes steady-state operation
  • •Does not account for starting torque requirements
  • •Single operating point calculation
  • •Efficiency values must be estimated or obtained from manufacturer

Best Practices

  • •Specify motor with 1.10-1.15 service factor for reciprocating compressors
  • •Use actual gas composition analysis for accurate Mw
  • •Include ambient temperature effects on motor cooling
  • •Verify power factor and starting current with motor supplier

Common Misconceptions

Myth: Motor nameplate HP equals compressor BHP.
Truth: Motor HP rating includes the service factor. A 100 HP motor can deliver 110 HP (at 1.10 SF) continuously. The compressor BHP should be within the motor's continuous rating.
Myth: Horsepower scales linearly with flow rate.
Truth: HP is proportional to both flow rate AND the thermodynamic work of compression. Doubling pressure ratio more than doubles HP due to the exponential compression term.

Practical Tips

  • •The conversion factor: 1 HP = 0.7457 kW, 1 kW = 1.341 HP
  • •For reciprocating compressors, add 3-5% to calculated HP for valve and pulsation losses
  • •Motor service factor (1.10-1.15) allows temporary overload but continuous operation at SF should be avoided
  • •Altitude correction: derate compressor capacity and power by 3% per 300 m elevation
  • •Gas molecular weight directly affects HP: lighter gases (H₂, He) require more HP per CFM
  • •Discharge temperature should always be checked alongside HP - high T₂ may indicate problems
  • •Annual energy cost = BHP × 0.746 × hours × $/kWh / motor_η. At $0.10/kWh, each HP costs ~$700/yr for continuous operation

Common Mistakes

Using gauge pressure instead of absolute pressure
Always use absolute pressure (psia or bar absolute). Gauge pressure + atmospheric = absolute.
Confusing HP and kW in motor selection
1 HP = 0.746 kW. A 100 kW motor is approximately 134 HP. Verify units when ordering motors internationally.
Neglecting drive losses in total HP calculation
Always include drive system efficiency: direct drive 98-99%, belt drive 93-96%, gear drive 95-98% per stage.
Selecting motor based on GHP instead of BHP
Motor must be sized for BHP (gas HP + mechanical losses + drive losses), not just gas horsepower alone.

Assumptions

This calculator makes the following assumptions to provide estimates:

Steady-State Operation: Assumes continuous, steady-state operation. Starting torque and transient conditions not considered.
Ideal Gas Behavior: Gas follows ideal gas law. Real gas corrections needed for high pressure (>50 bar) or near-saturation conditions.
Isentropic Compression: The gas horsepower calculation uses the isentropic model. Polytropic model may be more appropriate for centrifugal compressors.
Constant Efficiency: Compressor efficiency is assumed constant at the specified value regardless of operating point.

Limitations

Be aware of these limitations when using this calculator:

Single Operating Point: Provides HP at one operating condition. Compressor performance maps show HP variation across the operating range.
No Starting Torque Analysis: Does not verify that the motor can start the compressor under load. Reciprocating compressors may need unloaded starting.
Constant Efficiency Assumption: Efficiency varies with operating conditions. Using a single efficiency value introduces error at off-design points.
No Power Factor Consideration: Electrical power factor affects actual current draw and electrical system sizing but is not included in mechanical HP calculation.

Frequently Asked Questions

Answers to common questions about this calculator.

What is the difference between GHP and BHP?
Gas Horsepower (GHP) is the theoretical power to compress the gas. Brake Horsepower (BHP) includes mechanical losses (bearings, seals) and is the actual shaft power required.
How do I convert compressor HP to kW?
Multiply HP by 0.7457. For example, 100 HP = 74.57 kW. This is the mechanical power; electrical input power is higher due to motor efficiency.
What is service factor on a motor?
The service factor (SF) is a multiplier that indicates how much above nameplate rating a motor can operate continuously. Typical SF = 1.10-1.15.
How does altitude affect compressor HP?
Higher altitude reduces air density, which reduces mass flow and required HP for the same volumetric flow. De-rate by 3% per 300 m elevation.
What size motor do I need for my compressor?
Calculate BHP including all losses, multiply by 1.10-1.15 service factor, and select the next standard motor size above that value.
How do drive losses affect total HP?
Direct drive: 1-2% loss. Belt drive: 3-7% loss. Gear drive: 2-5% per stage. BHP = GHP / (drive efficiency).
What is the HP requirement per CFM?
At 100 psig discharge: approximately 4-5 HP per 100 CFM for efficient compressors. Varies with pressure ratio and efficiency.
How does gas molecular weight affect HP?
Lower molecular weight (lighter gas) requires more HP for the same volumetric flow because the gas constant R is higher, requiring more work per unit volume.
What is the specific power of a compressor?
Specific power is kW per unit flow rate (kW/(m³/min)). Typical: 5-8 kW/(m³/min) for small compressors, 6-10 for large centrifugal.
How do I calculate annual energy cost?
Annual cost = BHP × 0.746 × operating hours × $/kWh / motor efficiency. At 8000 hrs/yr, $0.10/kWh: cost per HP ≈ $700/yr.
What is the typical efficiency of an electric motor?
Standard efficiency: 90-93%. Premium efficiency (NEMA Premium): 94-96%. High efficiency: 96-98% for large motors. Motor efficiency should be included in electrical cost calculations.
What is the difference between HP and torque?
HP = Torque × RPM / 5252 (in imperial). For the same HP, lower RPM means higher torque. Compressors typically operate at 1200-1800 RPM for reciprocating, up to 30000+ RPM for centrifugal.
How does pressure ratio affect HP?
HP increases exponentially with pressure ratio. Doubling PR from 4 to 8 increases HP by approximately 60-80%, not 100%.
What is the HP requirement for a two-stage compressor?
Two-stage compression with intercooling typically requires 15-25% less HP than single-stage for the same overall PR. The savings increase with PR.
How do I size a motor for a reciprocating compressor?
Reciprocating compressors have high starting torque requirements. Use NEMA Design C or D motors. Motor HP should be 15-20% above BHP for adequate starting.
What is the effect of inlet temperature on HP?
HP is proportional to absolute inlet temperature. A 10°C increase in T₁ increases HP by approximately 3.4% (for fixed volumetric flow).
How do I convert between HP and CFM?
There is no direct conversion. HP depends on pressure ratio, efficiency, and gas properties in addition to flow rate. A rule of thumb: 1 HP ≈ 4-5 CFM at 100 psig.
What is the HP of a typical home air compressor?
Home air compressors: 1-10 HP. Note that many consumer compressors use "peak HP" ratings that are misleading. Actual continuous HP is typically 50-70% of peak rating.
How does relative humidity affect compressor HP?
Humidity slightly reduces HP because water vapor has lower molecular weight than air. The effect is small (<2%) for typical conditions.
What is the difference between indicated HP and brake HP?
Indicated HP is calculated from the P-V indicator diagram and includes gas compression work plus cylinder friction. BHP is measured at the shaft and includes all mechanical losses.
How do I measure actual compressor HP?
Use a torque meter on the shaft and measure RPM: HP = Torque (lb·ft) × RPM / 5252. Alternatively, measure motor electrical power and multiply by motor efficiency.
What is the maximum HP for a single compressor?
Reciprocating: up to 15000 HP per unit. Centrifugal: up to 100000 HP. Axial: up to 120000 HP. Gas turbines often drive the largest compressors.
How does inverter duty motor selection differ?
VFD motors require inverter-duty rating for variable speed operation. Motor HP at low speeds must be de-rated due to reduced cooling from the shaft-mounted fan.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

Gas Horsepower (GHP)
Theoretical power required for isentropic gas compression, excluding mechanical losses.
Brake Horsepower (BHP)
Actual shaft power required, including all mechanical and drive losses.
Service Factor (SF)
Multiplier indicating continuous overload capacity of a motor above nameplate rating.
Specific Power
Power consumption per unit flow rate (kW/(m³/min) or HP/CFM).
Torque
Rotational force at the shaft, related to HP: HP = Torque × RPM / 5252.
Molecular Weight
Mass per mole of gas (g/mol). Air = 28.97, affects R and HP.
Drive Efficiency
Percentage of power transmitted through the drive system (belt, gear, direct).
NEMA Design
Motor design classification (B, C, D) indicating starting torque and slip characteristics.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

NEMA MG-1API 618API 617ASME PTC 10ISO 1217

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Page Information

Last Updated:

2026-07-30

Version:

2.0.0

License:

Free to use for educational and professional purposes.