Last updated: July 3, 2026
Arrhenius Equation Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
This Arrhenius equation calculator computes the rate constant k from the pre-exponential factor A, activation energy Ea in J/mol, and temperature T in kelvin using k = A × e^(−Ea/(RT)). It also reports the exponent −Ea/(RT), the exponential Arrhenius factor, and an interpretation note.
To calculate a rate constant with the Arrhenius equation, multiply A by e raised to negative activation energy divided by R times absolute temperature. Use R equals 8.314 joules per mole kelvin, Ea in joules per mole, and T in kelvin.
Key Takeaways
- The Arrhenius equation is k = A × e^(−Ea/(RT)).
- A and k have the same units for the selected reaction order.
- Enter activation energy in J/mol and temperature in kelvin.
- Higher temperature or lower activation energy increases the exponential factor and raises k.
- Use measured multi-temperature data when estimating A and Ea for critical work.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
k = A × e^(−Ea/(R × T))
Where:
- k=Rate constant(same units as A)
- A=Pre-exponential (frequency) factor(same units as k)
- Ea=Activation energy(J/mol)
- R=Universal gas constant(8.314 J mol⁻¹ K⁻¹)
- T=Absolute temperature(K)
Worked Examples
Room-temperature first-order reaction
A reaction with A = 1×10¹³ s⁻¹ and Ea = 75 kJ/mol at 298.15 K.
- 1Compute RT = 8.314 × 298.15 = 2478.819 J/mol.
- 2Compute the exponent: −Ea/(RT) = −75000 ÷ 2478.819 = −30.256.
- 3Evaluate the exponential factor: e^(−30.256) = 7.24×10⁻¹⁴.
- 4Multiply by A: k = 1×10¹³ × 7.24×10⁻¹⁴ = 0.724 s⁻¹, reported as about 0.72 s⁻¹.
Higher-temperature reaction
A reaction with A = 5×10¹¹ s⁻¹, Ea = 50 kJ/mol, and T = 350 K.
- 1Compute RT = 8.314 × 350 = 2909.9 J/mol.
- 2Compute the exponent: −50000 ÷ 2909.9 = −17.183.
- 3Evaluate e^(−17.183) = 3.45×10⁻⁸.
- 4Multiply by A: k = 5×10¹¹ × 3.45×10⁻⁸ = 17242.85 s⁻¹, about 1.72×10⁴ s⁻¹.
Zero activation-energy check
When Ea is zero, every exponential barrier term equals one and k equals A.
- 1Set Ea = 0, so the exponent is −0/(8.314 × 300) = 0.
- 2Evaluate e⁰ = 1.
- 3Multiply by A: k = 1×10¹⁰ × 1 = 1×10¹⁰.
Introduction
The Arrhenius equation links a reaction rate constant to temperature, activation energy, and the pre-exponential factor. This calculator evaluates k = A × e^(−Ea/RT) for a single temperature, making it useful for kinetics homework, lab reports, and process estimates. If you need to determine Ea from two rate measurements, use the activation energy calculator; for time-dependent decay after you know k, compare the half-life calculator. The equation follows the classic IUPAC description of the Arrhenius equation and standard chemical kinetics treatments.
What does the Arrhenius equation calculate?
The calculator returns the rate constant k predicted for a chosen absolute temperature. The pre-exponential factor A represents the collision or encounter scale, while e^(−Ea/RT) is the temperature-dependent fraction of molecular events energetic enough to cross the activation barrier. Because A carries the same units as k, the calculator can be used for first-order, second-order, or other rate laws as long as A is entered in the matching units.
A and k have identical units for the chosen rate law.
Ea must be entered in J/mol, not kJ/mol.
T must be absolute temperature in kelvin.
R is fixed at 8.314 J mol⁻¹ K⁻¹.
Arrhenius formula step by step
Start by multiplying R and T to get a thermal energy scale per mole. Divide the activation energy by RT and apply the negative sign to form the dimensionless exponent. Then evaluate the exponential term and multiply by A. The exponential factor is often tiny at room temperature when Ea is large, so scientific notation is normal.
A 75 kJ/mol barrier at 298.15 K gives an exponent near −30.26, which reduces A by about fourteen orders of magnitude.
Why temperature changes k so strongly
Temperature appears in the denominator of the exponent, so increasing T makes −Ea/RT less negative and increases e^(−Ea/RT). This is why modest heating can produce a large rate increase for high-barrier reactions. For electrochemical temperature relations, compare the Nernst equation calculator, and for concentration-dependent rates keep solution values consistent with the molarity calculator.
Units and conversions
Use joules per mole for Ea because R is 8.314 J mol⁻¹ K⁻¹. If your activation energy is reported as 50 kJ/mol, enter 50000 J/mol. Temperature must be kelvin: T(K) = T(°C) + 273.15. The rate constant unit is inherited from A: s⁻¹ for first-order reactions, L mol⁻¹ s⁻¹ for common second-order reactions, and so on.
| Quantity | Required input | Common mistake |
|---|---|---|
| Activation energy | J/mol | Entering kJ/mol without ×1000 |
| Temperature | K | Entering °C directly |
| Pre-exponential factor | same unit as k | Mixing rate-law units |
| Gas constant | 8.314 J mol⁻¹ K⁻¹ | Using calorie units with joules |
Assumptions and limitations
The simple Arrhenius form assumes that A and Ea are approximately constant over the temperature interval of interest and that the reaction mechanism does not change. Curved Arrhenius plots can occur for complex mechanisms, enzyme denaturation, tunneling, transport limitation, or phase changes. For authoritative kinetic data, compare against the NIST Chemical Kinetics Database or a peer-reviewed source before extrapolating far beyond measured temperatures.
For engineering or safety decisions, fit multiple measured rate constants rather than relying on a single estimated A and Ea pair.
Connection to Arrhenius plots
Taking the natural logarithm gives ln(k) = ln(A) − Ea/(RT). A plot of ln(k) versus 1/T has slope −Ea/R and intercept ln(A). This calculator evaluates one point on that line. A multi-point plot is better for estimating parameters, while this single-point calculation is ideal when A and Ea are already known. A derivation and examples are available in the LibreTexts Arrhenius law chapter/Kinetics/06%3A_Modeling_Reaction_Kinetics/6.02%3A_Temperature_Dependence_of_Reaction_Rates/6.2.03%3A_The_Arrhenius_Law).
Quick Reference Card
Arrhenius Equation — Quick Reference
Quick reference • Arrhenius Equation Calculator
k = A × e^(−Ea/(RT)), R = 8.314 J mol⁻¹ K⁻¹Valid range: A > 0, Ea ≥ 0 J/mol, T > 0 K; best when mechanism and parameters are constant over the temperature range
Common Values
⚠ Watch Out
- •Do not enter Celsius temperature directly; convert to kelvin first.
- •Do not enter Ea in kJ/mol unless you convert it to J/mol.
- •Keep A units consistent with the desired rate constant units.
- •Avoid extrapolating far outside temperatures used to determine A and Ea.
- •Mechanism changes can invalidate a single Arrhenius parameter set.
Pro Tips
- →Check the exponent size; very negative values naturally produce tiny k values.
- →Use scientific notation for A and k to avoid rounding away important scale information.
- →Compare calculated k values with experimental rate constants when available.
- →For multiple temperatures, plot ln(k) versus 1/T to inspect linearity.
- →Report temperature and units with k because rate constants are context-dependent.
FAQs
What equation does this calculator use?
It uses k = A × e^(−Ea/(RT)), where A is the pre-exponential factor, Ea is activation energy in J/mol, R = 8.314 J mol⁻¹ K⁻¹, and T is temperature in kelvin.
What units should A have?
A must have the same units as the rate constant k for your rate law. For a first-order reaction A and k are usually s⁻¹; for a second-order reaction they may be L mol⁻¹ s⁻¹.
Can I enter activation energy in kJ/mol?
Convert kJ/mol to J/mol first by multiplying by 1000. For example, 75 kJ/mol should be entered as 75000 J/mol.
Why does temperature need to be in kelvin?
The Arrhenius equation uses absolute thermodynamic temperature. Celsius values would make the RT term physically wrong and produce a meaningless rate constant.
What happens when Ea is zero?
The exponent is zero, e⁰ equals one, and the calculated rate constant equals the pre-exponential factor A.
Is the Arrhenius equation valid for every reaction?
It is a powerful empirical model for many reactions over modest temperature ranges, but complex mechanisms, phase changes, tunneling, transport limits, or catalyst changes can make A and Ea temperature-dependent.