Centrifugal Compressor Power Calculator

Calculate centrifugal compressor power, gas isentropic coefficient, throughput, molar weight, or inlet/outlet temperature from the other five values.

Centrifugal Compressor Power Formula

The calculator uses the following base equation for centrifugal compressor power:

P = 2.31 * (T₂ - T₁) / MW * Q * k

P = compressor power, in kilowatts (kW)
k = gas isentropic coefficient
T₁ = inlet temperature, in °C
T₂ = outlet temperature, in °C
MW = molar weight of the gas, in g/mol
Q = throughput, in kg/hr
2.31 = constant used by this calculator for the selected units

If one of the other variables is missing, the calculator rearranges the same equation:

k = P / (2.31 * (T₂ - T₁) / MW * Q)

T₁ = T₂ - (P / (2.31 * k / MW * Q))

T₂ = T₁ + (P / (2.31 * k / MW * Q))

MW = 2.31 * (T₂ - T₁) * Q / (P * k)

Q = P / (2.31 * (T₂ - T₁) / MW * k)

Temperatures entered in °F are converted to °C before the equation is applied. Throughput is converted to kg/hr, and power is calculated internally in kW before being shown in the selected output unit.

Common Gas Properties and Unit Conversions

Use these values as rough reference points when checking inputs. Actual gas properties vary with composition and operating conditions.

Gas	Approx. molar weight (g/mol)	Typical isentropic coefficient, k
Air	28.97	1.40
Nitrogen	28.01	1.40
Oxygen	32.00	1.40
Carbon dioxide	44.01	1.29 to 1.31
Methane	16.04	1.30 to 1.32
Hydrogen	2.016	1.40 to 1.41

Quantity	Conversion used
Short ton/hr to kg/hr	1 short ton/hr = 907.185 kg/hr
lb/hr to kg/hr	1 lb/hr = 0.453592 kg/hr
hp to kW	1 hp = 0.7457 kW
°F to °C	°C = (°F – 32) * 5 / 9

Example Calculations

Example 1: Calculate compressor power

Suppose the gas isentropic coefficient is 1.4, the inlet temperature is 25 °C, the outlet temperature is 95 °C, the molar weight is 28.97 g/mol, and throughput is 1,000 kg/hr.

P = 2.31 * (95 - 25) / 28.97 * 1000 * 1.4

P = 7812.22 kW

Example 2: Calculate outlet temperature

Suppose compressor power is 500 kW, the gas isentropic coefficient is 1.3, the inlet temperature is 30 °C, the molar weight is 16.04 g/mol, and throughput is 400 kg/hr.

T₂ = 30 + (500 / (2.31 * 1.3 / 16.04 * 400))

T₂ = 36.68 °C

FAQs

Why does the outlet temperature need to be different from the inlet temperature?

The formula uses the temperature rise, T₂ – T₁. If both temperatures are the same, the temperature rise is zero. That would make power zero in the power calculation, and it would cause division by zero in some rearranged calculations.

What is the gas isentropic coefficient?

The gas isentropic coefficient, often written as k or gamma, is the ratio of specific heats for the gas. It affects how temperature changes during compression. For many diatomic gases such as air and nitrogen, it is close to 1.4. For gases such as methane or carbon dioxide, it is usually lower.

Why do my results look very large or very small?

Check the units first. The calculation is based on °C, kg/hr, g/mol, and kW internally. A common source of error is entering tons or pounds while the wrong throughput unit is selected, or mixing °F and °C temperature values. Also confirm that molar weight and isentropic coefficient match the gas being compressed.