Thermal Efficiency
Calculate thermal efficiency of heat engines using η = 1 − Q_out/Q_in for real engines or η = 1 − T_c/T_h for Carnot cycles. Free online physics calculator with charts.
About This Calculator
The Thermal Efficiency Calculator helps engineers, students, and thermodynamics professionals evaluate the performance of heat engines. It supports both irreversible (real) heat engines and reversible (Carnot) heat engines, making it suitable for coursework, design analysis, and quick engineering estimates.
For irreversible heat engines, the calculator uses the fundamental thermal efficiency formula η = Wnet,out / Qin = 1 − Qout / Qin. You can enter either the heat rejected (Qout) or the net work output (Wnet) alongside the heat input (Qin) to compute the efficiency. The missing value is automatically derived from the energy balance Qin = Wnet + Qout.
For reversible (Carnot) heat engines, the calculator applies the Carnot efficiency formula ηrev = 1 − Tc / Th, where temperatures must be in absolute units (Kelvin or Rankine). This gives the maximum theoretical efficiency achievable between two thermal reservoirs — real engines always fall below this limit due to irreversibilities such as friction, heat losses, and non-ideal processes.
Regional Notes
Global: Thermal efficiency is a dimensionless ratio expressed as a percentage. The calculator accepts any consistent energy units (J, kJ, BTU, etc.) for heat and work inputs — the efficiency result remains the same as long as units match. Temperature inputs for Carnot mode must be in absolute units (K or °R); convert °C to K by adding 273.15, and °F to °R by adding 459.67.
Common applications: Power plant cycle analysis (Rankine, Brayton), automotive engine performance, HVAC system evaluation, and thermodynamics education. The calculator is based on the standard thermodynamic principles from Cengel & Boles' Thermodynamics: An Engineering Approach.
Frequently Asked Questions
What is thermal efficiency?
Thermal efficiency (η) measures how effectively a heat engine converts heat input into useful work output. It is defined as the ratio of net work output to heat input: η = Wnet,out / Qin = 1 − Qout / Qin. For reversible (Carnot) engines, it depends only on the temperatures of the hot and cold reservoirs: ηrev = 1 − Tc / Th.
How do I calculate thermal efficiency of a heat engine?
Select between Irreversible and Reversible (Carnot) engine modes. For irreversible engines, enter either Qin and Qout, or Qin and Wnet. For Carnot engines, enter the hot and cold reservoir temperatures in Kelvin. The calculator computes the thermal efficiency and displays a full energy breakdown.
What is the Carnot efficiency formula?
The Carnot efficiency formula is ηrev = 1 − Tc / Th, where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir, both in Kelvin (K) or Rankine (°R). This represents the maximum possible efficiency any heat engine can achieve between two reservoirs.
Why must I use Kelvin for Carnot efficiency?
Kelvin is an absolute temperature scale starting at absolute zero, making the ratio Tc/Th physically meaningful. Using Celsius or Fahrenheit would give incorrect results because those scales have arbitrary zero points. Always convert Celsius to Kelvin by adding 273.15 (e.g., 100°C = 373.15 K).
Is this calculator free to use?
Yes, this thermal efficiency calculator is completely free to use with no registration required. Results can be shared via URL for easy bookmarking.
What are typical thermal efficiency values?
Real-world thermal efficiencies: modern coal power plants ~33-40%, natural gas combined cycle ~50-60%, automobile gasoline engines ~20-30%, diesel engines ~30-40%. Carnot efficiency sets the theoretical maximum based on temperature difference.
Can a heat engine have 100% thermal efficiency?
No, according to the Second Law of Thermodynamics, no heat engine can convert all heat input into work. Some heat must always be rejected to a cold reservoir. Even the ideal Carnot cycle requires heat rejection, and real engines have additional irreversibilities that further reduce efficiency.