Can I solve for different variables?

Yes! This calculator supports reverse solving. You can solve for: Activation energy (E==a==), Frequency factor (A), Reaction rate coefficient (k), Temperature (T).

Activation energy

Solve activation energy relationships quickly using core chemistry formulas.

Formula shown3 inputs definedUpdated Nov 2025By Automated Chemistry GeneratorFree, no sign-up

Quick Summary

Use this when you need:

Back-calculate activation energy from experimental rate constants
Compare catalysts by seeing how much they lower Ea at the same temperature
Check whether an assumed frequency factor A is consistent with measured k values

You’ll need:Frequency factor (A), Reaction rate coefficient (k), Temperature (T)

You’ll get:Activation energy (E==a==)

How this is calculated

Formula:

Ea = -R * T * ln(k / A)

In plain language:

Rearranging the Arrhenius equation k = A * exp(-Ea / RT) lets us solve for activation energy by multiplying the gas constant R (8.314 J/mol·K) by temperature and the natural log of k divided by A.

The formula is always visible so you can verify the math and explain your numbers to anyone who asks.

What these terms mean

Activation energy (E==a==)

Activation energy (E==a==) used in the calculation.

Frequency factor (A)

Frequency factor (A) used in the calculation.

Reaction rate coefficient (k)

Reaction rate coefficient (k) used in the calculation.

Temperature (T)

Temperature (T) used in the calculation.

When to use this calculator

Back-calculate activation energy from experimental rate constants
Compare catalysts by seeing how much they lower Ea at the same temperature
Check whether an assumed frequency factor A is consistent with measured k values

Last updated: November 19, 2025

Activation energy calculator explained

The activation energy calculator helps you translate Arrhenius data into a value for $E_a$ so you can check whether a catalyst or new reagent lowers the barrier you care about. Enter any three of the Arrhenius parameters: rate constant, temperature, pre-exponential factor, or activation energy, and the tool solves for the missing quantity in one view, which is faster than rearranging the equation manually each time.

Use it whenever you need to compare catalysts at a common temperature, validate kinetic assumptions before scaling a batch, or confirm that measured rate coefficients agree with the frequency factor reported in literature. Because the calculator works directly with SI units, you get numbers that can be dropped into kinetic modeling software without extra conversions.

How the conversion works

The Arrhenius equation relates the rate constant to activation energy:

$k = A \exp\left(\frac{-E_a}{R T}\right)$

Rearranging for $E_a$ gives:

E_a = -R T \ln\left(\frac{k}{A}\right)

where $R = 8.314\ \\text{J}\\,\\text{mol}^{-1}\\,\\text{K}^{-1}$ . The same expression works for any temperature as long as you keep the units consistent, and the calculator keeps the logarithm dimensionless by matching the units of $k$ and $A$ .

Units and conversions

Quantity	Symbol	Typical units	Notes
Activation energy	$E_a$	kJ/mol or kcal/mol	Convert J/mol to kJ/mol by dividing by $10^3$ .
Temperature	$T$	K	Convert deg C to K by adding $273.15$ .
Rate coefficient	$k$	s $^{-1}$ , L mol $^{-1}$ s $^{-1}$ , etc.	Must match the units used for $A$ .
Frequency factor	$A$	same units as $k$	Often reported in s $^{-1}$ for first-order reactions.

Worked examples

High-temperature surface reaction
Given $A = 2.5 \\times 10^{12}\\ \\text{s}^{-1}$ , $k = 4.0 \\times 10^{5}\\ \\text{s}^{-1}$ , and $T = 650\\ \\text{K}$ :

E_a = -8.314\\times650\\times\\ln\\left(\\frac{4.0\\times10^{5}}{2.5\\times10^{12}}\\right) = 8.46 \\times 10^{4}\\ \\text{J}\\,\\text{mol}^{-1}

Reported as $84.6\\ \\text{kJ}\\,\\text{mol}^{-1}$ .

Back-calculating $k$ for a catalyst screen
Given $E_a = 52.0\\ \\text{kJ}\\,\\text{mol}^{-1}$ , $A = 1.0 \\times 10^{11}\\ \\text{s}^{-1}$ , and $T = 450\\ \\text{K}$ :

k = 1.0\\times10^{11}\\times\\exp\\left(\\frac{-52.0\\times10^{3}}{8.314\\times450}\\right) = 9.20 \\times 10^{4}\\ \\text{s}^{-1}

That rate constant feeds directly into time-to-conversion models for the catalyst run.

Tips and pitfalls

Convert all temperatures to kelvin before entering values so the Arrhenius constant remains valid.
Keep the units of $k$ and $A$ identical; otherwise the logarithm term produces nonsense.
When you need activation energy in kcal/mol, run the calculation in SI units and convert at the end to avoid rounding mistakes.
Plot $\\ln k$ against $1/T$ for multiple measurements to confirm that a single $E_a$ describes the data; big curvature signals mechanism changes.

References and further reading

Frequently Asked Questions

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Calculator info

Version:: v1.0.0
Last reviewed:: Nov 15, 2025
Sensitivity:: low
References:: 1

Last updated: November 19, 2025

Activation energy calculator explained

How the conversion works

The Arrhenius equation relates the rate constant to activation energy:

$k = A \exp\left(\frac{-E_a}{R T}\right)$

Rearranging for $E_a$ gives:

E_a = -R T \ln\left(\frac{k}{A}\right)

Units and conversions

Quantity	Symbol	Typical units	Notes
Activation energy	$E_a$	kJ/mol or kcal/mol	Convert J/mol to kJ/mol by dividing by $10^3$ .
Temperature	$T$	K	Convert deg C to K by adding $273.15$ .
Rate coefficient	$k$	s $^{-1}$ , L mol $^{-1}$ s $^{-1}$ , etc.	Must match the units used for $A$ .
Frequency factor	$A$	same units as $k$	Often reported in s $^{-1}$ for first-order reactions.

Worked examples

High-temperature surface reaction
Given $A = 2.5 \\times 10^{12}\\ \\text{s}^{-1}$ , $k = 4.0 \\times 10^{5}\\ \\text{s}^{-1}$ , and $T = 650\\ \\text{K}$ :

E_a = -8.314\\times650\\times\\ln\\left(\\frac{4.0\\times10^{5}}{2.5\\times10^{12}}\\right) = 8.46 \\times 10^{4}\\ \\text{J}\\,\\text{mol}^{-1}

Reported as $84.6\\ \\text{kJ}\\,\\text{mol}^{-1}$ .

Back-calculating $k$ for a catalyst screen
Given $E_a = 52.0\\ \\text{kJ}\\,\\text{mol}^{-1}$ , $A = 1.0 \\times 10^{11}\\ \\text{s}^{-1}$ , and $T = 450\\ \\text{K}$ :

k = 1.0\\times10^{11}\\times\\exp\\left(\\frac{-52.0\\times10^{3}}{8.314\\times450}\\right) = 9.20 \\times 10^{4}\\ \\text{s}^{-1}

That rate constant feeds directly into time-to-conversion models for the catalyst run.

Tips and pitfalls

Convert all temperatures to kelvin before entering values so the Arrhenius constant remains valid.
Keep the units of $k$ and $A$ identical; otherwise the logarithm term produces nonsense.
When you need activation energy in kcal/mol, run the calculation in SI units and convert at the end to avoid rounding mistakes.
Plot $\\ln k$ against $1/T$ for multiple measurements to confirm that a single $E_a$ describes the data; big curvature signals mechanism changes.

Quick Summary

Calculator Tool

How this is calculated

What these terms mean

Activation energy (E==a==)

Frequency factor (A)

Reaction rate coefficient (k)

Temperature (T)

When to use this calculator

Activation energy calculator explained

How the conversion works

Units and conversions

Worked examples

Tips and pitfalls

References and further reading

Frequently Asked Questions

Related Calculators

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Was this calculator helpful?

Found an error?

Calculator info

Activation energy calculator explained

How the conversion works

Units and conversions

Worked examples

Tips and pitfalls

References and further reading

Frequently Asked Questions

Related Calculators

pKa

Beer-Lambert law

Molarity

Mole

Neutralization

Normality

Was this calculator helpful?

Found an error?

Calculator info