Rate Constant Calculator

Find the rate constant, total reaction order and reaction rate from reactant orders, concentrations and half life.

Handles one, two or three reactants with concentration scales from M to nM and six time scales.

Updated October 2, 2026

CreatorFrank Zhao

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What this calculator does

Chemical kinetics problems usually hand you a scattering of numbers — an order, a concentration, a half life — and ask for one missing piece. The trap is that the relationship changes shape depending on the reaction order, so the wrong formula gives a confident, plausible, wrong answer.

This calculator handles the three rate-law problems that cause the most confusion, and it works in both directions. Tell it the order of reaction for each reactant plus a concentration and a half life, and it returns the rate constant $k$ , the total reaction order and the rate of reaction. Or enter $k$ and work backwards to recover a half life, a rate, or any concentration.

Why the step matters

It covers unimolecular, bimolecular and trimolecular elementary steps, so each reactant can carry its own order. That matters: in a step where one reactant is first order and another is second order, the two half lives follow different laws and must be consistent with the same $k$ .

Where to go next

Built for students working through kinetics homework, and for lab or industrial teams checking an experimental order and half life against each other. If you already know $k$ and want its temperature dependence, use the Arrhenius Equation Calculator instead. For reversible systems, relating a forward and reverse rate constant to an equilibrium constant is the natural next step.

How to use it, step by step

Start from whatever your problem actually gives you. You need at least an order and one other quantity — everything else follows.

Choose the elementary step

Select Unimolecular, Bimolecular or Trimolecular to match how many reactant molecules collide in one step. This adds a block for each molecule, so Molecule B and Molecule C appear only when the step needs them.

Set the order of reaction for each molecule

Pick Zero, First or Second order. Molecule A allows all three; Molecules B and C allow First or Second, because a bimolecular or trimolecular elementary step cannot contain a zero-order reactant. If the calculator flags a zero order on a multi-molecule step, treat that reactant as non-existent and revisit your choice of step.

Enter a concentration and a half life

Give the initial molar concentration and the time for half the sample to react. Concentrations cover $\mathrm{M}$ down to nanomolar; half lives run from microseconds to hours, and the minutes/seconds option takes a value like $2{:}30$ directly.

You can also type straight into the results area — enter a known $k$ or rate and the calculator rotates to solve for whichever field you left empty.

Read the results

Three outputs appear together: the total order of reaction, the reaction constant $k$ , and the rate of reaction. Values the calculator solved for you are shown in blue.

Worked walkthrough

A first-order decomposition has a half life of 100 s at a concentration of 0.25 M. Enter Unimolecular, keep First order, set $[A]=0.25\ \mathrm{M}$ and $T_{1/2}=100\ \mathrm{s}$ . Because a first-order half life does not depend on concentration, the rate constant follows directly:

Rate constant

k = \frac{\ln 2}{T_{1/2}}

=

\frac{0.693147}{100\ \mathrm{s}}

=

6.93147\times10^{-3}\ \mathrm{s}^{-1}

The total order is 1, and the rate law gives:

Rate of reaction

v = k[A]

=

(6.93147\times10^{-3})(0.25)

=

1.73287\times10^{-3}\ \mathrm{M\,s^{-1}}

The key takeaway

Run the same half life at a concentration of 1.00 M and $k$ is still $6.93147\times10^{-3}\ \mathrm{s}^{-1}$ , while the rate becomes $6.93147\times10^{-3}\ \mathrm{M\,s^{-1}}$ — four times larger. A first-order half life is a property of the reaction alone; the rate is a property of the reaction at a particular concentration. Mixing those two up is one of the most common errors in this topic.

The formulas and what each order means

Everything in the calculator comes from two relationships: the rate law, which tells you the instantaneous rate, and the half-life law, which tells you how long the reaction takes to halve the sample. The second one changes with the order, which is why the order matters so much.

The rate law

v = k\,[A]^{m_A}[B]^{m_B}[C]^{m_C}

Each reactant carries its own order as an exponent, $m_A$ , $m_B$ , $m_C$ . A first-order reactant contributes a factor of one, a second-order reactant contributes its square, and a zero-order reactant drops out of the equation entirely — which is exactly what makes a zero-order step’s rate independent of how much reactant is left.

The half-life law

For a single reactant at order $m$ , the time to consume half of it depends on which of the three cases applies:

T_{1/2} = \frac{[A]}{2k}

\qquad (m = 0)

T_{1/2} = \frac{\ln 2}{k}

\qquad (m = 1)

T_{1/2} = \frac{1}{k[A]}

\qquad (m = 2)

Zero order — the half life grows as the sample gets more concentrated. Double the concentration and the half life doubles, because the reaction consumes a fixed amount per unit time regardless of what is left.
First order — the half life is a constant of the reaction alone. It does not change with concentration, so $k$ can be read straight off a single half life measurement.
Second order — the half life shrinks as the concentration rises, so a half life measured at one concentration does not transfer to another.

Total order and the units of k

The total order is just the sum of the individual orders, and it is what sets the units of the rate constant:

n = \sum m_i

\qquad [k] = \mathrm{M}^{\,1-n}\,\mathrm{s}^{-1}

So a first-order constant carries units of $\mathrm{s}^{-1}$ , a second-order one carries $\mathrm{M^{-1}\,s^{-1}}$ , and a zero-order one carries $\mathrm{M\,s^{-1}}$ — the same units as the rate itself. If a calculated $k$ comes out with surprising units, the total order you assigned is probably wrong.

A distinction worth being clear about

The reaction order is an experimental result, not something you can read off the balanced equation. The coefficient in front of a species in the equation tells you stoichiometry; it does not generally tell you the order. Textbooks make the distinction explicitly — see Rate Laws Must Be Determined Experimentally.

Worked examples

Mixed orders on two reactants

A bimolecular step is first order in $A$ and second order in $B$ . With $[A]=0.25\ \mathrm{M}$ , $[B]=0.50\ \mathrm{M}$ and a second-order half life for $B$ of 50 s:

Rate constant

k = \frac{1}{T_{1/2}[B]}

=

\frac{1}{50 \times 0.50}

=

0.04\ \mathrm{M^{-1}s^{-1}}

The total order is 3, so the units are $\mathrm{M^{-2}s^{-1}}$ . The rate law then gives the rate, and — because $A$ is first order — it also predicts $A$ ’s own half life:

Rate of reaction

v = k[A][B]^2

=

0.04 \times 0.25

\times

(0.50)^2

=

2.5\times10^{-3}\ \mathrm{M\,s^{-1}}

Half life of A

T_{1/2,A} = \frac{\ln 2}{k}

=

17.33\ \mathrm{s}

Notice that $A$ ’s half life lands near 17 s while $B$ ’s is 50 s, from the same reaction. That is normal: each half life follows the law for its own order, and both are consistent with the single value of $k$ .

Zero-order reaction with a concentration-dependent half life

A zero-order step at 0.25 M takes 100 s to halve. Both the constant and the rate follow from that:

Rate constant

k = \frac{[A]}{2T_{1/2}}

=

\frac{0.25}{200}

=

1.25\times10^{-3}\ \mathrm{M\,s^{-1}}

Because the total order is 0, the rate equals the constant: the reaction proceeds at 1.25×10⁻³ M s⁻¹ no matter how much reactant remains, until it runs out. Compare that with the same reaction measured at 0.50 M — the half life would be 200 s, doubling as the concentration doubles.

Using two half lives as a cross-check

In a bimolecular step both reactants share one $k$ . If you measure both half lives independently, they must agree on it — which makes them a useful check on your own work.

Take $A$ and $B$ both second order, at $0.25\ \mathrm{M}$ and $0.50\ \mathrm{M}$ , with half lives of 100 s and 50 s. Both give the same constant:

Both half lives agree

k = \frac{1}{T_{1/2,A}[A]}

=

\frac{1}{T_{1/2,B}[B]}

=

0.04\ \mathrm{M^{-1}s^{-1}}

Now change $B$ ’s half life to 200 s while leaving everything else alone. That single edit implies $k = 0.01\ \mathrm{M^{-1}s^{-1}}$ from $B$ but $0.04\ \mathrm{M^{-1}s^{-1}}$ from $A$ — a genuine contradiction. The calculator keeps your entered number on screen, marks it, and tells you which two values disagree, so you can find the wrong order, concentration or time unit yourself instead of being handed a silently averaged result.

One caveat

The cross-check compares the implied constants directly, so it is most reliable when both reactants carry the same order and therefore the same units of $k$ . When the orders differ, treat the warning as a prompt to re-check your inputs rather than as a precise quantitative verdict.

Tips and common mistakes

Convert units first

A half life entered in the wrong unit is the single most expensive mistake here, because $k$ is inversely proportional to it. If you measured 100 minutes and typed 100 as if it were seconds, $k$ comes out 60 times too large and every rate derived from it is wrong. Switch the unit from the field’s menu and let the calculator do the conversion.

Check the units of k

The total order determines the units, so a quick look at them validates your whole setup. If you assigned second order but the rate constant is displayed in $\mathrm{s^{-1}}$ , one of the orders did not register — go back and confirm each selection.

Know what a half life can tell you

A first-order half life fully determines $k$ on its own. A zero-order or second-order half life needs a concentration as well, so if you are solving for $k$ , entering that concentration is not optional.

Treat measurements as estimates

Kinetic measurement carries real uncertainty, and initial-rate methods are sensitive to instrument fluctuations and reaction conditions. Fitting the full concentration–time profile across many points is generally more reliable — see Measuring Reaction Rates if your numbers are close but not quite consistent.

Limitations and disclaimers

This is a teaching and checking tool for textbook rate-law problems. It assumes the ideal rate-law behaviour of a single well-defined reaction step, and it is not a substitute for experimental work or a kinetics model of a real system.

Orders must be supplied, not predicted. The calculator never infers reaction order from a balanced equation. If you do not already know the order — because it came from experimental data or from your course material — this tool cannot get you started.
Single-step kinetics only. Multi-step mechanisms are out of scope. For a reaction with a rate-determining step and fast pre-equilibria, the observed order and rate constant may differ from what any single rate law predicts.
Concentration must be treated as constant. A measured half life assumes the concentration recorded is the one that actually applies as the reaction proceeds. In gas-phase reactions where volume changes, or in systems where the reactant is continuously replenished or removed, the half-life formulas do not apply as written.
Rate constant is temperature-specific. $k$ changes with temperature, and this calculator has no temperature input. Compare values only at the same temperature.
Zero-order reactants are limited to single-molecule steps. Choosing zero order for Molecule B or C is rejected, because a bimolecular or trimolecular elementary step cannot have a zero-order participant.

Before you rely on the result

For laboratory, production or safety decisions, confirm orders and rate constants against your own experimental data and current process documentation. Catalyst systems, enzyme kinetics and reactions in non-ideal solutions can all deviate from the simple power-law form used here.

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