Arrhenius Equation Calculator
Get the rate constant and half life from A, Ea, and temperature.
What it does
Heat speeds chemistry out of proportion. A ten degree rise often doubles a rate, and the Arrhenius equation says why: the share of molecules clearing the energy barrier grows exponentially with temperature. Two inputs set the barrier and the collision traffic; temperature does the rest.
The tool above runs the numbers. Enter A, activation energy in kJ/mol, and Celsius to get the rate constant plus a first order half life. Defaults describe a fast reaction (A = 1e11 /s, Ea = 50 kJ/mol) at 25 C, so the page opens solved at 173.7367 /s with a 0.004 s half life.
The exponent carries the lesson. At 298.15 K the term Ea/RT equals about 20.17, so only e^(-20.17) of collisions react. Warm to 50 C and k jumps to 827.1872 /s, nearly five times faster for 25 degrees. Slow reactions show the same math from the other side: with Ea = 100 kJ/mol the constant shrinks to 3.018e-5 /s and the half life stretches to 6.38 h.
Formatting follows size. Readable constants print plain with four decimals while tiny or huge ones switch to scientific notation, so both lab kinetics and shelf life estimates stay legible. Kelvin always prints alongside for the record.
Use the table for decade landmarks of the exponent, then run your reaction. The page holds A and Ea fixed across temperatures and reports first order half life only. Catalysts, tunneling, and shifting mechanisms all bend the clean curve, so confirm against measured points before trusting far forecasts.
How to use
- Enter the frequency factor A in per second.
- Enter activation energy in kJ/mol.
- Enter temperature in Celsius.
- Read the rate constant first.
- Read the half life and kelvin.
- Rerun at a second temperature to feel the swing.
Formula
- A
- Collision frequency factor in per second.
- Ea
- Barrier height in kJ/mol.
- T
- Temperature in Celsius, converted inside.
- k
- Rate constant in per second.
Ea enters in kJ/mol (multiplied by 1000 inside), R is 8.314 J/mol/K, and T is kelvin from your Celsius input. A carries per second units for first order work. The half life form fits first order only; other orders need their own integrated laws.
Worked example
Example: k at room temperature
A first order reaction has A = 1e11 /s and Ea = 50 kJ/mol. Find k at 25 C and the half life.
- Convert: T = 25 + 273.15 = 298.15 K.
- Exponent = -50000 / (8.314 x 298.15) = -20.17.
- k = 1e11 x e^(-20.17) = 173.7367 /s.
- Half life = ln2 / 173.7367 = 0.004 s.
- Warming to 50 C lifts k to 827.1872 /s.
- Small temperature moves swing rates by multiples, not percents.
Reference table
| Case | Exponent | k trend |
|---|---|---|
| Ea 50, 25 C | -20.17 | 173.7367 /s |
| Ea 50, 50 C | -18.61 | 827.1872 /s |
| Ea 100, 25 C | -40.34 | 3.018e-5 /s |
| Ea 50, 0 C | -22.02 | 27.4236 /s (colder, slower) |
Limits
- One A and Ea across the range.
- First order half life only.
- Ideal behavior assumed.
- No catalyst or mechanism shifts.
Common mistakes
- Entering Ea in J/mol instead of kJ/mol.
- Using Celsius inside the exponent.
- Confusing A units across reaction orders.
- Reading the half life for non first order.
- Extrapolating far past measured temperatures.
Try it yourself
Quick checks. Answers sit tucked under each question.
Same reaction at 50 C?
k = 827.1872 /s. Half life 0.001 s. About 4.8 times faster.
A = 1e13 /s with Ea = 100 kJ/mol at 25 C?
k = 3.018e-5 /s. Half life 6.38 h. Temperature 298.15 K.
Ea = 60 kJ/mol instead of 50? Set it up by hand.
Exponent = -60000/(8.314 x 298.15) = -24.21. k = 1e11 x e^(-24.21), a far smaller constant with a far longer half life.
Questions
What is the Arrhenius equation?
The temperature rule for rate constants: k = A e^(-Ea/RT). A sets collision frequency and orientation; the exponent sets the fraction with enough energy.
What is activation energy?
The minimum collision energy that reacts, in kJ/mol here. Higher barriers choke the exponent and slow the reaction hard.
Celsius or kelvin input?
Enter Celsius; the tool adds 273.15 inside. A 25 C input runs at 298.15 K.
How is half life found?
For first order, t1/2 = ln2/k. The page reports it in s, min, or h whichever reads cleanest.
What changes at 50 C?
Yes. At 50 C the same reaction gives 827.1872 /s with a 0.001 s half life, about 4.8 times faster than at 25 C.
Does it fit every reaction?
No. It assumes one constant A and Ea across the range, ideal behavior, and first order half life. Mechanisms that shift with T need wider models.