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Stirling Cycle Efficiency Calculator

Enter the hot and cold temperatures in kelvin.

How it is calculated

The tool computes the ideal efficiency η = 1 - Tc / Th, where Th is the temperature of the hot source and Tc that of the cold sink, both in kelvin. The efficiency is shown as a percentage together with the ratio Tc / Th to four decimals.

An ideal Stirling cycle with perfect regeneration has the same efficiency as the Carnot cycle between the same two temperatures, so the "efficiency" and "Carnot equivalent" lines always show the same figure. There is no input for regenerator effectiveness, friction or heat-transfer losses, so the result is a ceiling, not a prediction for a real engine. The tool requires Th > Tc > 0: equal temperatures, a cold side above the hot side, or a zero or negative value give no result.

Worked example

Suppose the hot side runs at 900 K and the cold side at 320 K. The temperature ratio is Tc / Th = 320 / 900 = 0.3556. Efficiency is 1 - 0.3556 = 0.6444, which the tool shows as 64.44%. That is the best any heat engine could do between those temperatures, and a real Stirling engine would reach noticeably less. Widening the gap, for example a 900 K source with a 300 K sink, raises the ideal figure to 66.67%.

Try this example →

Common mistakes

  • Entering temperatures in degrees Celsius or Fahrenheit. The formula needs absolute temperature: 600 and 27 typed as Celsius give 95.50%, while the correct kelvin values (873.15 K and 300.15 K) give 65.62%.
  • Putting the cold temperature in the hot field. The tool needs the hot value to be larger and returns nothing otherwise.
  • Quoting the result as the efficiency of a real engine. Regeneration is never perfect and friction and heat-transfer losses always apply, so actual engines come in below this limit.
  • Using the working-gas temperatures instead of the source and sink temperatures. The limit depends on the heat reservoirs the engine actually exchanges heat with.
  • Expecting a second figure to differ. Both lines are equal here by design, since a perfectly regenerated Stirling cycle matches Carnot.

About this calculator

The Stirling cycle efficiency calculator computes the ideal thermal efficiency of a Stirling engine operating between a hot reservoir temperature Th and a cold reservoir temperature Tc, using η = 1 − Tc/Th (both temperatures in kelvin). Remarkably, this is exactly the Carnot efficiency — the theoretical maximum for any heat engine operating between those two temperatures — because the Stirling cycle's isochoric heat exchanges are assumed to happen through perfect regeneration, with no net entropy generated during them.

Real Stirling engines never hit this ideal number because regeneration is never perfect and there are always friction, heat-transfer, and pressure losses, but the theoretical ceiling still guides design decisions about temperature range and regenerator quality. Mechanical engineers designing Stirling engines for solar-thermal power, cryocoolers, or combined-heat-and-power units, and thermodynamics students use this calculator to find the theoretical efficiency limit before accounting for real-world losses.

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  • Editorial team

    With the cold side often pinned near ambient, the hot side is the practical lever: against a 300 K sink, a 900 K source gives 66.67% and a 1,200 K source gives 75%. Both are ceilings, because the tool has no input for regenerator or friction losses, so a real engine lands below them. If you are sizing a solar dish or a waste-heat unit, which source temperature are you assuming?

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