What this calculator finds

By entering only the absolute temperatures of the hot and cold reservoirs, it computes the maximum possible heat-to-work conversion efficiency between them. This is not the actual efficiency of a specific engine but the physically attainable upper limit for those temperatures.

Why it matters

• Benchmarking how close a power plant or engine comes to the theoretical limit
• Assessing the potential gain from raising the hot-reservoir temperature
• Serving as a reference benchmark in thermodynamic cycle design and teaching

Carnot Efficiency Formula

The efficiency depends only on the ratio of the two reservoirs’ absolute temperatures. Temperatures must be entered on an absolute scale (K or °R).

How the formula works

• A higher hot temperature T_H lowers the ratio T_C/T_H, raising the efficiency η.
• A lower cold temperature T_C (colder heat rejection) also raises efficiency.
• When the two temperatures are equal (T_C = T_H) efficiency is 0; only at the unreachable T_C = 0 K would efficiency reach 100%.

Worked example

For T_H = 800 K and T_C = 300 K, η = 1 − 300/800 = 0.625, i.e. 62.5%. No heat engine operating between these temperatures can exceed 62.5%.

Practical tips

• Never enter °C/°F directly — convert to Kelvin (K = °C + 273.15) or Rankine (°R = °F + 459.67) first.
• Real engines often reach only 40–70% of the Carnot value; comparing them via “second-law efficiency” reveals room for improvement.
• Raising the hot temperature is usually more practical and effective for boosting efficiency than lowering the cold side.

Limitations & cautions

• The Carnot value assumes reversible, frictionless, loss-free operation; real engines are always lower due to friction, heat loss and irreversibility.
• It assumes constant-temperature reservoirs, so treat it only as an approximate benchmark for real cycles (e.g. Rankine, Brayton) where temperatures vary.
• The performance (COP) of refrigerators and heat pumps is defined differently — do not confuse it with this efficiency.