Accelerated Life Test Factor Calculator (Arrhenius)

Understanding the Arrhenius acceleration factor calculator — concept and principle

Accelerated life testing runs products hot so that temperature-driven failures appear in weeks instead of years. The acceleration factor (AF) tells you how many hours of normal use one hour at the stress temperature represents. Enter the activation energy of the failure mechanism, the use and stress temperatures and the test duration, and the calculator returns AF, the equivalent use hours and the equivalent years.

One hot hour stands in for 26 hours of normal use — and the factor depends strongly on Ea.

How it is calculated

AF = exp[(Ea / k) × (1/T_use − 1/T_stress)]

Ea: activation energy of the failure mechanism, in electronvolts (eV).
k: Boltzmann constant, 8.617 × 10⁻⁵ eV/K.
T_use, T_stress: absolute temperatures in kelvin (°C + 273.15).

Equivalent use hours = test hours × AF; equivalent years = use hours ÷ 8,760 (24/7 use).

The principle

The Arrhenius equation says a reaction rate grows as exp(−Ea/kT): only molecules with energy above the barrier Ea react, and the share of such molecules rises steeply with temperature. Many degradation processes (diffusion, corrosion, oxidation) behave like reactions, so time to failure scales as exp(Ea/kT). The ratio of the two lifetimes is AF. The larger Ea, the more strongly the mechanism reacts to heat and the larger the factor. The model assumes the same mechanism operates at both temperatures; only the speed changes.

Worked example

Inputs: Ea = 0.7 eV, use 40 °C, stress 85 °C, test 1,000 h.
Kelvin: 313.15 K and 358.15 K; 1/313.15 − 1/358.15 = 0.00040123 K⁻¹.
Ea/k = 0.7 ÷ 8.617333 × 10⁻⁵ = 8,123.2 K; product = 3.2593.
AF = e^3.2593 = 26.03.
Equivalent use = 1,000 × 26.03 = 26,030.5 h, or 26,030.5 ÷ 8,760 = 2.97 years.

Each point is the calculator re-run with only “Stress temperature (°C)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Stress temperature (°C)	Acceleration factor
21.2	0.1916471216
42.5	1.228078043
63.8	6.225601044
85	26.03051896
106	92.72285677
128	288.6471899
170	2,017.594856

How to read the result

An AF of 26 means 1,000 test hours without failure stand in for about three years of continuous use at 40 °C, provided the assumptions hold. The result is very sensitive to Ea: with the same temperatures, 0.5 eV gives AF ≈ 10 and 1.0 eV gives AF ≈ 105. Use a mechanism-specific Ea from test data or literature whenever you can.

Common mistakes

Entering Celsius into the formula instead of kelvin.
Choosing a stress temperature that triggers a new failure mode (melting, glass transition, electrolyte boil-off).
Treating the equivalent time as a guaranteed life.

Keep in mind: The Arrhenius model covers temperature only. Humidity, voltage, thermal cycling and vibration need other models (Peck, Eyring, Coffin–Manson), and real qualification plans should follow the applicable standard and engineering review.

Frequently asked questions

Where do activation energy values come from?

From fitting failure times at several temperatures, or from published data for a known mechanism. JEDEC publications list typical ranges for semiconductor mechanisms.

Is the 10 °C rule the same thing?

The rule that life halves for every 10 °C rise is a rough Arrhenius approximation that corresponds to a particular Ea near room temperature; it is not general.

Sources: S. Arrhenius, Zeitschrift für physikalische Chemie 4 (1889), on the temperature dependence of reaction rates · JEDEC JESD91, Method for Developing Acceleration Models for Electronic Component Failure Mechanisms · W. Nelson, Accelerated Testing: Statistical Models, Test Plans, and Data Analyses, Wiley

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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