Arrhenius temperature-life estimate
Enter a component's life at a reference temperature, its operating temperature and the activation energy (Ea); the tool calculates the acceleration factor AF = exp(Ea/k · (1/T₁ − 1/T₂)), the estimated life at the operating temperature and the difference from the rough "10 °C rule".
Ea typically ranges from a tenth of an eV to a few eV and is specific to the component; different failure mechanisms of the same component have different Ea. A small error in Ea makes a large difference in the acceleration factor (see the sensitivity table below).
The Ea in the example (0.7 eV) only shows how the calculation works; it is not a valid value or a recommendation for your component.
The calculation runs in your browser; the values you enter are not sent anywhere.
Enter the activation energy Ea in eV (greater than zero, at most 5).
A helper calculation; verify against the standard/catalogue before publishing. The model is simplified and gives an estimate only for single-mechanism ageing accelerated by temperature; for reliability decisions use manufacturer data, tests and field failure records together.
Let's combine your temperature monitoring data with life estimates and find which equipment is more sensitive to thermal ageing.
Request a conversation01
How to use it
A
Enter the reference temperature, the operating temperature and the life at the reference temperature; choose their units.
B
Enter your component's activation energy Ea (eV) from your own source.
C
Read the acceleration factor and estimated life; examine the difference from the 10 °C rule, the curve and the Ea sensitivity.
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What does the Arrhenius model say?
Many thermally activated ageing processes (insulation degradation, chemical reactions, lubricant breakdown, drying out of electrolytic capacitors) accelerate exponentially with temperature. The Arrhenius relation expresses the rate as exp(−Ea / kT); the ratio of rates between two temperatures is the acceleration factor AF.
If a life L₁ at a reference temperature is known, the life at a higher temperature is estimated as L₂ = L₁ / AF. Temperature is entered as kelvin (absolute); the tool converts °C and °F for you.
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Activation energy Ea and sensitivity
Ea shows how sensitive the process is to temperature: at a high Ea a small rise in temperature shortens life a lot. Ea is specific to the component and the failure mechanism and must always be determined carefully; this tool suggests no ready value.
Even a small uncertainty in Ea changes AF greatly; so look at the tool's Ea sensitivity table and read the result as a range rather than a single number.
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Why the 10 °C rule is only a rough measure
The rule "life halves for every +10 °C" is close to Arrhenius for a particular Ea and temperature range; for another Ea or range it is wrong. The tool also shows the equivalent Ea that would give the same result as the rule; compared with your own Ea you see how optimistic or pessimistic the rule is.
The rule should not be used as a basis, only for a rough idea.
FAQ
- Where do I find the Ea value?
- In the component manufacturer's datasheet or reliability tests, or from your own accelerated life test. This tool suggests no value because Ea is specific to the component and the failure mechanism.
- Which temperature should I enter: ambient or the component itself?
- What governs ageing is the component's own (internal, junction or winding) temperature. Ambient is only an approximation; to account for self-heating enter the measured or calculated temperature of the component.
- What if the temperature is lower than the reference?
- AF falls below one and the estimated life comes out longer than the reference life. Extrapolating to temperatures far from the reference is not reliable; the mechanism may change.
- Is the result a guaranteed life?
- No. The result is an estimate of the reference life scaled by the temperature effect. Life is a statistic, and other effects such as vibration, humidity and cycling are not in the model.
- Why is the life chart logarithmic?
- Because life changes exponentially with temperature, a linear axis makes the curve very steep. On a logarithmic axis the Arrhenius relation and the 10 °C rule can be compared with each other.
Follow thermal ageing with temperature monitoring
Let's find which components your temperature data shows to be at risk of thermal ageing, and plan the monitoring.