How do I determine activation energy?

Properly, by testing at three or more temperatures and fitting the slope of ln(life) against 1/T. Published values are a starting point for planning, but a life claim that rests on an assumed Ea is only as strong as that assumption.

Does Arrhenius apply to humidity or vibration failures?

No. Arrhenius covers thermally activated mechanisms only. Humidity-driven corrosion uses Peck’s model, thermal cycling uses Coffin-Manson, and voltage or mechanical stress uses an inverse power law.

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Arrhenius Acceleration Factor Calculator

The Arrhenius model describes how a temperature-driven failure mechanism speeds up when you raise the temperature. It lets you run a test at elevated temperature for weeks and make a defensible claim about years of field life — provided the mechanism is genuinely thermally activated and does not change at the higher temperature.

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Formula

Acceleration factorAF = exp[ (Ea / k) · (1/T_use − 1/T_stress) ]

Boltzmann constantk = 8.617 × 10⁻⁵ eV/K

Temperature conversionT(K) = T(°C) + 273.15

Absolute temperature is mandatory — using °C directly is the single most common error with this model.

Equivalent field lifeField life = Test duration × AF

Worked example

An electronic assembly is tested for 500 hours at 125 °C. The field ambient is 50 °C and the dominant mechanism has an activation energy of 0.7 eV.

T_use = 50 + 273.15 = 323.15 K; T_stress = 125 + 273.15 = 398.15 K
1/T_use − 1/T_stress = 0.00309454 − 0.00251162 = 5.8292 × 10⁻⁴
Ea / k = 0.7 / 8.617 × 10⁻⁵ = 8123.5
AF = exp(8123.5 × 5.8292 × 10⁻⁴) = exp(4.735) = 113.8

500 test hours at 125 °C represent about 56,900 field hours at 50 °C — roughly 6.5 years of continuous operation. Note the sensitivity: assuming Ea = 0.5 eV instead of 0.7 would drop the AF to about 29, cutting the claim by nearly a factor of four. Activation energy must be justified, not assumed.

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How to interpret the result

Ea ≈ 0.3–0.5 eV	Typical of some plastic-package and mechanical-diffusion mechanisms.
Ea ≈ 0.7 eV	Common default for general electronic component ageing and oxidation.
Ea ≈ 0.9–1.1 eV	Electromigration and some dielectric breakdown mechanisms.
Ea > 1.2 eV	Very strongly accelerated; verify experimentally before relying on it.

Common mistakes

Using Celsius instead of Kelvin. This does not produce a slightly wrong answer — it produces a meaningless one.
Borrowing an activation energy from a different failure mechanism. Ea is a property of the mechanism, not the part.
Testing above a material transition — a glass transition, a solder melting point, a phase change. Beyond it you are accelerating a different mechanism entirely and the extrapolation is invalid.
Applying a single AF when several mechanisms with different activation energies are active at once.

Frequently asked questions

How do I determine activation energy?: Properly, by testing at three or more temperatures and fitting the slope of ln(life) against 1/T. Published values are a starting point for planning, but a life claim that rests on an assumed Ea is only as strong as that assumption.
Does Arrhenius apply to humidity or vibration failures?: No. Arrhenius covers thermally activated mechanisms only. Humidity-driven corrosion uses Peck’s model, thermal cycling uses Coffin-Manson, and voltage or mechanical stress uses an inverse power law.

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Arrhenius Model is part of a suite of 126 reliability, maintenance and quality engineering tools covering life data analysis, accelerated testing, system reliability, FMEA and root cause, SPC, and design for reliability. It runs in the browser and as native iOS and Android apps, so the same calculation is available at a desk or in front of the asset.

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