# Rate Constant Calculator

URL: https://speedycalculator.com/calculators/chemistry/rate-constant/
Last updated: 2026-10-30

> The rate constant calculator finds k for zero-, first-, second- and higher-order reactions – from the half-life, from a measured rate and the rate law, from the concentration change over time, or for an elementary step – and gives the units of k, the half-life and the rate.

## Inputs

- Find k from
- Reaction order
- Initial concentration [A]₀ (mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³)
- Half-life t½ (s, min, h, days, years, ms)
- Concentration [A] after time t (mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³)
- Elapsed time t (s, min, h, days, years, ms)
- Elementary step
- Measured reaction rate (M/s, M/min, M/h, mM/s, µM/s)
- Concentration [A] (mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³)
- Order with respect to A
- Concentration [B] (mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³)
- Order with respect to B

## Results

- Overall reaction order
- Rate constant k
- Units of k
- Half-life at [A]₀
- Time to 90% conversion
- Initial rate
- Rate if [A] is doubled

## Formula

```
rate = k[A]ᵐ[B]ⁿ  ·  t½: zero order [A]₀/(2k), first order ln 2/k, second order 1/(k[A]₀)  ·  integrated: [A]₀ − [A] = kt, ln([A]₀/[A]) = kt, 1/[A] − 1/[A]₀ = kt
```

## Explanation

The rate constant k is the proportionality factor in a rate law. For a reaction with rate = k[A]ᵐ[B]ⁿ, the exponents m and n are the orders with respect to each reactant and their sum is the overall order. Orders are found by experiment – they need not equal the coefficients of the balanced equation – except for elementary steps, where the order equals the molecularity: a unimolecular step is first order, a bimolecular step second order.

Because the rate has units of concentration per time, the units of k change with the overall order: M·s⁻¹ for zero order, s⁻¹ for first order, M⁻¹·s⁻¹ for second order and so on. k depends on temperature (through the Arrhenius equation) but not on concentration.

This calculator finds k four ways: from a half-life, using the half-life formula for the chosen order; from one measured rate and the concentrations in the rate law; from the integrated rate law, using the initial concentration, a later concentration and the time between them; or for an elementary step, where the molecularity fixes the rate law. It also reports the overall order, the units, the half-life, the time to 90% conversion and the initial rate.

### How to use the Rate Constant Calculator

- **Find k from**
- **Reaction order**
- **Initial concentration [A]₀**
- **Half-life t½**
- **Concentration [A] after time t**
- **Elapsed time t**
- **Elementary step**
- **Measured reaction rate**
- **Concentration [A]**
- **Order with respect to A**
- **Concentration [B]**
- **Order with respect to B**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Pick the method, enter the data and the order. The calculator rearranges the relevant formula for k – half-life formula, rate law or integrated rate law – using concentrations in mol/L and times in seconds, then converts k to per minute or per hour if you choose.

### Worked example

**From a half-life:** a first-order reaction has t½ = 30 min = 1800 s, so k = ln 2 ÷ 1800 = **3.85 × 10⁻⁴ s⁻¹** (0.0231 min⁻¹). 90% conversion takes ln 10 ÷ k ≈ 5980 s, about 99.7 min.

**From the rate law:** rate = k[A][B]² with a measured rate of 2.4 × 10⁻⁵ M/s at [A] = 0.10 M and [B] = 0.20 M gives k = 2.4 × 10⁻⁵ ÷ (0.10 × 0.20²) = 6.0 × 10⁻³ M⁻²·s⁻¹; the overall order is 3.

**Integrated law:** [A] falls from 0.50 M to 0.20 M in 600 s. First order: k = ln 2.5 ÷ 600 = 1.53 × 10⁻³ s⁻¹; second order: k = (1/0.20 − 1/0.50) ÷ 600 = 5.0 × 10⁻³ M⁻¹·s⁻¹.

### Rate laws by order

OrderRate lawIntegrated formHalf-lifeUnits of kStraight-line plot0k[A] = [A]₀ − kt[A]₀ / 2kM·s⁻¹[A] vs t1k[A]ln[A] = ln[A]₀ − ktln 2 / ks⁻¹ln[A] vs t2k[A]²1/[A] = 1/[A]₀ + kt1 / (k[A]₀)M⁻¹·s⁻¹1/[A] vs t

### Inputs explained

FieldWhat to enterFind k fromChoose one: Half-life (single reactant), Measured rate and the rate law, Concentration change over time (integrated rate law), Elementary step (molecularity sets the order)Reaction orderChoose one: Zero order, First order, Second orderInitial concentration [A]₀Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³Half-life t½Units: s, min, h, days, years, msConcentration [A] after time tUnits: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³Elapsed time tUnits: s, min, h, days, years, msElementary stepChoose one: Unimolecular: A → products (rate = k[A]), Bimolecular: A + B → products (rate = k[A][B]), Bimolecular: 2A → products (rate = k[A]²), Termolecular: 2A + B → products (rate = k[A]²[B])Measured reaction rateUnits: M/s, M/min, M/h, mM/s, µM/sConcentration [A]Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³Order with respect to AChoose one: 0, 1, 2, 3Concentration [B]Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³Order with respect to BChoose one: 0 (no second reactant), 1, 2

### What each result means

- **Units of k** = [Overall reaction order]
- **Initial rate** = [Rate constant k]×[Initial concentration [A]₀]^[Reaction order]
- **Rate if [A] is doubled** = [Measured reaction rate]×2^[Order in A used]

## Worked example

Inputs — Find k from: Half-life (single reactant); Reaction order: First order; Initial concentration [A]₀: 0.5 mol/L (M); Half-life t½: 1,800 s.

Results — Overall reaction order = 1; **Rate constant k = 0.000385 per second (M¹⁻ⁿ·s⁻¹)**; Units of k = s⁻¹; Time to 90% conversion = 5,979.4706 s; Initial rate = 0.000193 M/s.

## Key terms

- **Rate law**: Equation relating the reaction rate to concentrations, rate = k[A]ᵐ[B]ⁿ.
- **Reaction order**: The exponent of a concentration in the rate law; the overall order is their sum.
- **Half-life (t½)**: Time for the reactant concentration to fall to half its starting value.
- **Molecularity**: The number of particles colliding in an elementary step (uni-, bi- or termolecular).
- **Integrated rate law**: The rate law solved for concentration as a function of time.

## FAQ

**What is the rate constant?**
The proportionality constant k in a rate law such as rate = k[A][B]. It is fixed for a given reaction at a given temperature and does not depend on concentration.

**What are the units of the rate constant?**
M¹⁻ⁿ·s⁻¹ for overall order n: M·s⁻¹ (zero order), s⁻¹ (first), M⁻¹·s⁻¹ (second), M⁻²·s⁻¹ (third).

**How do I get k from a half-life?**
First order: k = ln 2 ÷ t½ = 0.693 ÷ t½. A half-life of 30 min gives k = 0.0231 min⁻¹ = 3.85 × 10⁻⁴ s⁻¹. Zero order: k = [A]₀ ÷ 2t½; second order: k = 1 ÷ ([A]₀·t½).

**How do I find k from concentration data?**
Use the integrated rate law. If a first-order reactant falls from 0.50 M to 0.20 M in 600 s, k = ln(0.50/0.20) ÷ 600 = 1.53 × 10⁻³ s⁻¹.

**Does the rate constant change with temperature?**
Yes – according to the Arrhenius equation k = A·e^(−Ea/RT). Many reactions roughly double their k for a 10 °C rise near room temperature.

**Is the order the same as the coefficient?**
Only for elementary steps. For overall reactions the order must be measured; for example 2 N₂O₅ → 4 NO₂ + O₂ is first order in N₂O₅.

**Why does the half-life of a first-order reaction not depend on concentration?**
Because t½ = ln 2/k contains no concentration term – radioactive decay is the classic example.


## Sources

- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)
- [IUPAC Compendium of Chemical Terminology (Gold Book)](https://goldbook.iupac.org/)
- [LibreTexts Chemistry](https://chem.libretexts.org/)