Arrhenius Equation Calculator
The rate constant of a reaction at a given temperature from its activation energy and pre-exponential factor — and how much faster it goes at a second temperature.
Arrhenius: k = A · e^(−Ea/RT).
How the arrhenius equation calculator works
Arrhenius: k = A · e^(−Ea/RT). The exponential is the fraction of collisions with enough energy to react, so a modest rize in temperature multiplies the rate — the old rule that a reaction doubles every 10 °C comes from an activation energy near 50 kJ/mol at room temperature. Enter a second temperature to see the ratio k₂/k₁ directly.
Formula: k = A · exp(−Ea ÷ (R · T)); k₂/k₁ = exp((Ea ÷ R) · (1/T₁ − 1/T₂))
Worked examples
| Inputs | Rate constant k at T₁ | Note |
|---|---|---|
| A = 10¹³, Ea = 50 kJ/mol, 25 °C → 35 °C | 1.7393e4 | 1.73 × 10⁴; 1.92× faster at 35 °C |
| Ea = 100 kJ/mol at 500 K | 3.5750e2 | 3.6 × 10² (no second temperature) |
| Zero activation energy | 5.0000e0 | k = A at every temperature |
FAQFrequently asked questions
What units should A and k have?
The same units as each other — per second for a first-order reaction, liters per mole per second for second-order. The exponential is dimensionless, so k simply inherits A’s units.
Why kilojoules per mole?
Activation energies are usually quoted that way (typical values are 20–200 kJ/mol); the calculator converts to joules to match R = 8.314 J/mol/K.
Is the rule that rates double every 10 °C true?
Only for activation energies near 50 kJ/mol at room temperature. At 100 kJ/mol a 10 °C rize multiplies the rate nearly four times; at 20 kJ/mol only about 1.3 times.
How do I get Ea from experimental data?
Measure k at two or more temperatures and plot ln k against 1/T; the slope is −Ea/R. With two points, Ea = R × ln(k₂/k₁) ÷ (1/T₁ − 1/T₂).
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- National Institute of Standards and Technology — the US measurement and reference-data authority
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.