Gas Turbine Power Output Calculator and Brayton Cycle

Gas turbine power from the enthalpy drop, or a full simple Brayton cycle from the pressure ratio.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

In the first mode enter the gas mass flow, the turbine inlet and outlet temperatures, the specific heat and the mechanical efficiency. The enthalpy is cp times the temperature, and the power is the mass flow times the enthalpy drop times the mechanical efficiency.

In the second mode enter the compressor inlet temperature, the pressure ratio and the compressor and turbine efficiencies. The calculator works out the compressor outlet temperature, the turbine outlet temperature, the compressor and turbine work, the back work ratio, the net power and the thermal efficiency.

The compressor takes more than half of the turbine work, so the net power is much less than the turbine power. The results are for an ideal gas with constant specific heat.

Formulas used

  • P = \dot m\,(h_3 - h_4)\,\eta_m
  • h = c_p T
  • \eta_{ideal} = 1 - r_p^{-(\gamma-1)/\gamma}

Worked example

With the default numbers in the calculator above:

  1. Inlet enthalpy: 1610.00 kJ/kg
  2. Outlet enthalpy: 1035.00 kJ/kg
  3. Power output: 56350.00 kW (56.35 MW)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? A complete Brayton cycle from the pressure ratio.

  1. Compressor outlet temperature (ideal, then with the efficiency): 638.32 K
  2. Turbine outlet temperature (ideal, then with the efficiency): 773.72 K
  3. Compressor work per kg: 402.87 kJ/kg
  4. Turbine work per kg: 720.22 kJ/kg
  5. Net work per kg: 317.35 kJ/kg
  6. Back work ratio (the share of the turbine work that drives the compressor): 0.56
  7. Heat added in the combustor per kg: 875.93 kJ/kg
  8. Thermal efficiency: 36.23 %
  9. Net power output: 31100.24 kW (31.10 MW)
  10. Ideal efficiency for this pressure ratio: 50.83 %

Common questions

What is the back work ratio?

The share of the turbine work that drives the compressor. For a gas turbine it is typically 40 to 60 percent.

Why is the thermal efficiency less than the ideal?

Because the compressor and turbine are not perfect (isentropic efficiency below 1).

Does it include fuel?

The heat added is worked out from the temperature rise. The fuel flow also depends on the fuel heating value and combustion efficiency.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Cengel and Boles, Thermodynamics: An Engineering Approach (Brayton cycle); Saravanamuttoo, Gas Turbine Theory.

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