Arrhenius Equation Calculator

A process with A = 10¹³ and an activation energy of 150 kJ/mol runs at a rate constant of 1607.67 at 800 K.

Calculate:

Rate constant at a temperatureActivation energy from two rate constantsRate constant at a new temperature

Pre-exponential factor A (same unit as k):

Activation energy Eₐ (kJ/mol):

Temperature T₁:

Rate constant k =

1607.66748110272

Precision

Full answer, then cut to fewer decimals (not rounded):

1607.66748110272
1607.6674811027
1607.667481102
1607.66748110
1607.6674811
1607.667481
1607.66748
1607.6674
1607.667
1607.66
1607.6

Eₐ/RT: 22.55106657
Rise in k per 10 K near T₁: 1.321025368

Step-by-step solution

k = A e^(−Eₐ/RT) = 10000000000000 × e^(−22.55106657)
k = 1607.667481

Arrhenius Equation Formula

k = A e^(−Eₐ/RT)

ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂)

Worked Example

A process with A = 10¹³ and Eₐ = 150 kJ/mol at 800 K:

k = A e^(−Eₐ/RT) = 10000000000000 × e^(−22.55106657)
k = 1607.667481

Rise in k per 10 K near T₁: 1.321025368

GATE tip

Diffusion, creep, oxidation and grain growth all follow Arrhenius behaviour. The same two-point formula gives their activation energies from two temperatures.

More Kinetics and Diffusion Calculators

Diffusion Calculator

(Cₓ − C₀)/(Cₛ − C₀) = 1 − erf(x / (2√(Dt)))

D = D₀ exp(−Q/RT); diffusion distance ~ √(Dt)

Example: Carburising 0.2 % C steel at 950 °C with a 1.2 % C surface for 10 hours: Concentration at depth Cₓ = 0.774281 wt%.

Open the diffusion calculator →
Avrami Equation Calculator

y = 1 − exp(−k tⁿ)

n Avrami exponent; t₀.₅ = (ln 2 / k)^(1/n)

Example: A transformation with k = 0.01 and n = 2.5 after 5 time units: Fraction transformed y = 42.8229 %.

Open the avrami equation calculator →

Frequently asked questions

How do I get Eₐ from an Arrhenius plot?

Plot ln k against 1/T: the slope is −Eₐ/R. Two points are enough with the two-point formula here.

Why does a small temperature rise speed things up so much?

k depends exponentially on 1/T; with Eₐ = 150 kJ/mol near 800 K each extra 10 K raises the rate by about 30 %.

Sources

The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

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Scientific Converters. (2026, October 15). Arrhenius Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/arrhenius-equation-calculator/

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Scientific Converters, "Arrhenius Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/arrhenius-equation-calculator/