Thermal Efficiency Calculator

Our thermal efficiency calculator helps you figure out how effectively a heat engine or system converts heat energy into useful work.

Whenever heat is supplied to an engine, only part of it is transformed into work — the rest is usually lost to the surroundings. This ratio of useful work to heat input is what we call thermal efficiency.

Do you want to learn the formulas for calculating thermal efficiency, including the general expression and the maximum theoretical Carnot efficiency?

Are you wondering how temperature differences set the ultimate limit on an engine’s performance? If yes, then you’re in the right place!

🌡 Thermal Efficiency Calculator

η = Work_Output / Heat_Input × 100%

Work Output (J or kJ): Heat Input (J or kJ):

General Thermal Efficiency

η = Work_Output / Heat_Input × 100%

η (Eta): Thermal efficiency, expressed in %
Work_Output (W): Useful work or energy produced by the system (J or kJ)
Heat_Input (Q_in): Heat energy supplied to the system (J or kJ)

➝ This formula tells us how effectively the input heat is converted into useful work.

Maximum Theoretical (Carnot) Efficiency

η_carnot = (1 – T_cold / T_hot) × 100%

η_carnot: Maximum theoretical efficiency possible (%)
T_hot: Temperature of the hot reservoir (K)
T_cold: Temperature of the cold reservoir (K)

➝ This sets the upper limit for efficiency of any heat engine, determined only by the temperature difference between the heat source and the sink.

Example 1: General Thermal Efficiency

A steam engine produces 500 kJ of useful work while receiving 2000 kJ of heat energy from the boiler. Calculate the thermal efficiency of the engine.

Step 1: Given Data
Work_Output (W) = 500 kJ
Heat_Input (Q_in) = 2000 kJ

Step 2: Formula

η = (Work_Output / Heat_Input) × 100%

Step 3: Substitution
η = (500 / 2000) × 100%

Step 4: Result
η = 25%
✅ The engine converts 25% of the heat input into useful work.

Term	Meaning	Units
η	Thermal efficiency	%
W	Work Output (useful work done)	J or kJ
Q_in	Heat Input (energy supplied)	J or kJ

Example 2: Carnot (Maximum Theoretical) Efficiency

A heat engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. Find the maximum possible (Carnot) efficiency of the engine.

Step 1: Given Data
T_hot = 600 K
T_cold = 300 K

Step 2: Formula

η_carnot = (1 – T_cold / T_hot) × 100%

Step 3: Substitution
η_carnot = (1 – 300 / 600) × 100%

Step 4: Result
η_carnot = 50%
✅ The maximum possible efficiency is 50%.

Term	Meaning	Units
η_carnot	Maximum possible efficiency	%
T_hot	Temperature of hot reservoir	K (Kelvin)
T_cold	Temperature of cold reservoir	K (Kelvin)

FAQs

What is thermal efficiency?

Thermal efficiency tells us how well a heat engine converts heat energy into useful work. A higher efficiency means less energy wasted as heat loss.

Can any engine be 100% efficient?

No, it’s impossible. Some energy is always lost as waste heat, and the Carnot efficiency sets the maximum limit based on temperatures.

What is Carnot efficiency?

Carnot efficiency is the highest theoretical efficiency an engine can achieve. It depends only on the hot and cold reservoir temperatures.