Thermal Efficiency Calculator (Formula, Work & Heat Input)

Calculate thermal efficiency from net work output and heat input, as energy or power, or find the work output or heat input from a known efficiency.

Thermal Efficiency Formula

Thermal efficiency measures how much of the supplied heat is converted into useful work. It is a dimensionless performance ratio for heat engines, power cycles, and other thermodynamic systems, but it is usually reported as a percentage.

etaₜₕ = (Wₒᵤₜ) / (Qᵢₙ)

When you want the answer in percent, multiply the ratio by 100.

etaₜₕ(%) = (Wₒᵤₜ) / (Qᵢₙ) \times 100

Quantity	Meaning	Typical units
Thermal efficiency	The fraction of heat input converted into useful work	Decimal or percent
Work output	Net work produced by the engine or cycle	J, kJ, cal, BTU
Heat input	Total thermal energy supplied to the system	J, kJ, cal, BTU

Rearranged Equations

If you know any two values, the missing value can be found directly. This is useful when sizing a system, checking test data, or back-calculating required heat input.

Wₒᵤₜ = etaₜₕ \times Qᵢₙ

Qᵢₙ = (Wₒᵤₜ) / (etaₜₕ)

Use efficiency as a decimal when applying the rearranged equations. If your efficiency is shown as a percentage, convert it before solving.

How to Use the Thermal Efficiency Calculator

Enter the useful work output produced by the system.
Enter the total heat input supplied to the system.
Make sure the energy units are compatible.
Calculate the efficiency and interpret the result as the share of heat converted into useful work.

This calculator is most useful when all values refer to the same engine cycle, operating period, or test condition.

Example Calculation

If a heat engine receives 2500 J of heat and produces 800 J of useful work, the thermal efficiency is:

etaₜₕ = (800) / (2500) = 0.32 = 32%

That means 32% of the input heat became useful work, while the remaining energy left the system as waste heat, exhaust losses, cooling losses, friction, or other irreversibilities.

Related Energy Balance

In many applications, it is also helpful to estimate the heat rejected by the system.

Q rejected = Qᵢₙ - Wₒᵤₜ

Q rejected = 2500 - 800 = 1700 J

This relationship helps explain why even a reasonably efficient engine still rejects a large amount of energy.

How to Interpret the Result

Low efficiency: Only a small portion of the supplied heat becomes useful work.
Higher efficiency: A larger share of the heat input is converted into useful output.
Zero percent: No useful work is produced.
One hundred percent: Perfect conversion of heat into work, which real heat engines do not achieve.
Above one hundred percent: Usually indicates mixed units, incorrect measurements, or an input mistake.

Common Reasons Thermal Efficiency Is Limited

Heat loss to the surroundings
Mechanical friction
Incomplete combustion or imperfect heat release
Pumping and auxiliary power losses
Irreversibilities during compression and expansion
Exhaust energy that leaves before being converted into work

Theoretical Maximum Efficiency

For an ideal heat engine operating between a hot reservoir and a cold reservoir, the maximum possible efficiency is bounded by the Carnot limit.

etaₘₐₓ = 1 - (T c) / (Tₕ)

Absolute temperature must be used for this relationship, typically in kelvins. Real systems always operate below this theoretical maximum because real processes include losses and non-ideal behavior.

Brake and Indicated Thermal Efficiency

Select Brake / indicated thermal efficiency, choose the output-power basis, and enter power, fuel mass flow and the fuel-specific lower heating value (LHV). Brake power is shaft output; indicated power is in-cylinder output before mechanical losses. Use one operating condition and the same heating-value basis throughout.

η (%) = 100 × P / (ṁ × LHV / 3.6), with P in kW, ṁ in kg/h and LHV in MJ/kg. Specific fuel consumption = 1000 × ṁ / P in g/kWh when P is positive. For 100 kW, 20 kg/h and 45 MJ/kg, fuel power is 250 kW, efficiency is 40%, and specific consumption is 200 g/kWh. Fuel heating values vary; enter your measured or specified LHV.

MIT’s engine-performance notes define fuel power from mass flow and energy per unit mass.

Efficiency from Heat Rejected

Select From heat input and heat rejected to use η (%) = (1 − Qout / Qin) × 100 and Wnet = Qin − Qout. Enter positive heat-transfer magnitudes for the same cycle or time period. For 2500 J in and 1700 J rejected, efficiency is 32% and net work is 800 J. Energy inputs must be paired with energy inputs, or power rates with power rates.

Ideal-Cycle Calculations

Select Maximum (Carnot) efficiency and enter the hot and cold reservoir temperatures on the selected scale. The calculator converts them to kelvin before using ηmax (%) = (1 − Tc / Th) × 100. For 600 K and 300 K, the ideal upper limit is 50%; real engines operate below this limit. See OpenStax’s Carnot discussion.

The Ideal Otto-cycle efficiency mode uses ηOtto (%) = [1 − 1 / r^(γ − 1)] × 100, where r is compression ratio and γ = cp/cv. With r = 8 and the editable ideal-air assumption γ = 1.4, efficiency is about 56.47%. This constant-specific-heat model does not predict measured petrol-engine performance. MIT derives the ideal Otto relationship.

For steam-cycle enthalpies and pump/turbine performance, use the Rankine Cycle Efficiency Calculator. For useful steam-energy output divided by fuel-energy input, use the Boiler Efficiency Calculator; boiler efficiency and heat-engine work efficiency use different output definitions.

Applications of Thermal Efficiency

Internal combustion engines
Steam turbines and Rankine cycles
Gas turbines and Brayton cycles
Heat engines and power-plant cycles (boiler heat-delivery efficiency uses a different useful-output definition)
Laboratory heat-engine experiments
Energy audits and performance testing

Common Mistakes to Avoid

Using heat input and work output from different time periods
Mixing units without converting them properly
Confusing gross heat input with net usable heat input
Using percentage form in place of decimal form when rearranging equations
Treating thermal efficiency as the same metric as overall plant efficiency or electrical efficiency

FAQ

What does thermal efficiency tell you?

It tells you how effectively a system converts thermal energy into useful work. A higher value means less of the input heat is being wasted.

Can thermal efficiency be negative?

Not for a correctly defined heat engine operating normally. A negative result usually points to sign convention issues or incorrect data entry.

Can I use kilojoules, calories, or BTU?

Yes. Any energy unit can be used as long as the heat input and work output are expressed consistently.

Is thermal efficiency the same as coefficient of performance?

No. Thermal efficiency is used for heat engines that convert heat into work, while coefficient of performance is used for refrigerators and heat pumps.

Thermal Efficiency Calculator screenshot