Arrhenius Acceleration Factor Calculator

AF=e(Eak(1Tuse−1Tstress))AF = e^{\left(\frac{E_a}{k}\left(\frac{1}{T_{use}} - \frac{1}{T_{stress}}\right)\right)}
  • Ea = Activation energy (eV)
  • k = Boltzmann constant = 8.617333262145e-5 eV/K
  • Tuse = Use temperature (K)
  • Tstress = Stress temperature (K)
  • Use Life = Desired use duration (hours)
  • Test Duration = Time to simulate under stress (hours)

Based on the original Arrhenius formulation: Svante Arrhenius, Z. Phys. Chem. 4 (1889) 226.

MaterialEa (eV)
Plastic0.4-1.2
Semiconductor0.2-0.6
Metal0.5-0.9
Ceramic0.9-1.5

AF from durations (Use Life / Test Duration): 16

AF from Arrhenius equation (Ea + temperatures): 29.0284

To simulate 8000 hours of use at 50°C, test for 500 hours at 100°C.

AF from durations and AF from Arrhenius differ by more than 10%. Check units, temperatures, and assumed Ea.
Need help applying this to a real validation program? Contact Reliatools.

How it works

The Arrhenius acceleration factor (AF) tells you how much faster a thermally activated failure mechanism ages at an elevated test temperature versus normal use:

AF=exp⁡[Eak(1Tuse−1Tstress)]AF = \exp\left[\frac{E_a}{k}\left(\frac{1}{T_{use}} - \frac{1}{T_{stress}}\right)\right]

where Ea is the activation energy (eV), kis Boltzmann's constant (8.617 × 10−5 eV/K), and temperatures are in kelvin(°C + 273.15).

Example:A part used at 55 °C and tested at 125 °C, with Ea = 0.7 eV, gives AF ≈ 78— one test hour equals about 78 field hours. Use the radio buttons to solve for any field instead: targeting a 175× acceleration from a 55 °C baseline requires a stress temperature of about 141 °C.

Use this for diffusion- and reaction-driven wear-out. For fatigue or thermal-cycling failures, use the Coffin-Manson calculator; to turn an AF into a screening plan, see the Burn-In Wizard.