Reaction Rate Constant Calculator

Free Reaction Rate Constant Calculator

This calculator solves the general rate law that connects reaction rate, concentration, and the rate constant k for any reaction order — rate = k[A]^m[B]^n. Give it the reaction orders, the reactant concentrations, and either the rate or the rate constant, and it instantly solves for whichever one you're missing, with the correct compound units for k worked out automatically for you.

It also includes an Advanced Tools mode built around the method of initial rates, the standard lab technique chemists use to actually discover a rate law in the first place. Enter a small table of experiments — each with its own starting concentrations and measured initial rate — and the calculator fits the reaction orders m and n and the rate constant k directly from that data, along with an R² value so you can see how well a simple rate law actually describes your results. Every calculation on this page comes with full, plain-language step-by-step working, completely free and with no sign-up required.

What Is a Rate Constant?

The rate constant, k, is the proportionality constant in a reaction's rate law — the number that turns reactant concentrations into an actual reaction rate. For a reaction with rate law rate = k[A]^m[B]^n, a larger k means the reaction runs faster at any given set of concentrations, all else being equal.

Unlike concentration, temperature, or a catalyst's presence, k is not something you plug into an equation from a textbook table for an arbitrary reaction — it has to be measured experimentally (or, once measured at one temperature, predicted at another using the Arrhenius equation). Every specific reaction has its own rate constant, and that constant changes with temperature even though the rate law's exponents m and n normally do not.

The General Rate Law

For a reaction between reactants A and B, the general (differential) rate law is written:

rate = k[A]^m[B]^n

Here m is the reaction order with respect to A, n is the order with respect to B, and m + n is the overall reaction order. Crucially, m and n are not the stoichiometric coefficients from the balanced chemical equation — they have to be found experimentally, and for many real reactions they simply don't match the coefficients at all. A reaction 2A + B → products might turn out to be first order in A and zero order in B, for instance, even though the balanced equation shows a coefficient of 2 on A.

This differential rate law is different from the integrated rate laws used for zero-, first-, and second-order reactions, which link concentration directly to elapsed time instead of to the instantaneous rate. The differential form is what this calculator's Standard Solver works with; the integrated forms are covered by the dedicated zero-order, first-order, and second-order reaction rate calculators linked below.

Units of the Rate Constant k

One of the most useful things about k is that its units always reveal the overall reaction order, since the units on both sides of the rate law have to match. Reaction rate is always measured in concentration per time (such as M/s), so rearranging rate = k[A]^m[B]^n for k shows that k must carry whatever concentration units are needed to cancel out the concentration terms on the right and leave plain concentration/time behind.

• Zero order overall (m + n = 0): k has units of M/s (concentration/time) — same units as the rate itself.
• First order overall (m + n = 1): k has units of s⁻¹ (inverse time only) — no concentration unit at all.
• Second order overall (m + n = 2): k has units of M⁻¹s⁻¹ (inverse concentration, inverse time).
• Third order overall (m + n = 3): k has units of M⁻²s⁻¹.
• In general, for overall order p: k has units of M^(1−p)·time⁻¹ — exactly the pattern this calculator uses to build the correct unit label automatically once you enter (or fit) the reaction orders.

The Method of Initial Rates

Because m and n can't be predicted from the balanced equation, chemists determine them experimentally using the method of initial rates: run the same reaction several times, changing one reactant's starting concentration at a time while holding the others fixed, and measure how fast the reaction proceeds right at the start (before products build up and complicate things).

The classic pencil-and-paper version compares two experiments where only [A] changes: doubling [A] while [B] stays fixed and watching the rate quadruple means the reaction is second order in A (since 2^m = 4 gives m = 2); watching the rate merely double means first order (2^1 = 2); and watching the rate stay the same means zero order in A (2^0 = 1). The same comparison, done for pairs of experiments where only [B] changes, gives the order n with respect to B.

The Advanced Tools tab on this page automates and generalizes that comparison. Instead of requiring perfectly paired experiments where only one concentration changes at a time, it takes the natural log of the rate law — turning ln(rate) = ln k + m·ln[A] + n·ln[B] into an ordinary linear regression — and fits m, n, and k simultaneously from any set of experiments by least squares. This works even with imperfect, real-world lab data where every concentration varies a little between runs, and the R² value it reports tells you how well the fitted rate law actually explains your measurements.

How to Use This Calculator

On the Standard Solver tab, first choose whether your reaction depends on one reactant or two, then enter the reaction orders m (and n) — most textbook problems state these directly, or you can find them first using the Advanced Tools tab. Pick what you want to solve for: the rate constant k, the reaction rate, or the concentration of A. Fill in the other values, and the calculator converts everything to consistent internal units, solves the rearranged rate law, and converts the answer back into your chosen concentration and time units — automatically building the correct compound unit label for k based on the overall reaction order.

The Advanced Tools tab is for determining the rate law itself from experimental data. Enter each experiment's starting concentration(s) and its measured initial rate as a row — at least two rows for a single reactant, or three for two reactants, though more experiments give a far more reliable fit — and the calculator returns the fitted reaction orders, the rate constant, and an R² goodness-of-fit value, all with full step-by-step working.

Worked Example: Finding k from a Known Rate Law

A reaction follows the rate law rate = k[A]²[B]. In one experiment, [A] = 0.100 M and [B] = 0.100 M, and the measured initial rate is 5.00 × 10⁻³ M/s. What is k?

Apply k = rate / ([A]² × [B]) = 0.00500 / (0.100² × 0.100) = 0.00500 / 0.00100 = 5.00 M⁻²s⁻¹.

The units follow directly from the overall order (m + n = 2 + 1 = 3): k = M^(1−3)·s⁻¹ = M⁻²s⁻¹, exactly matching the third-order pattern described above.

Worked Example: Finding the Rate Law from Experimental Data (Advanced Tools)

Three experiments are run on the same reaction A + B → products, each with a different starting concentration of A and/or B, and the initial rate is measured each time: (1) [A] = 0.100 M, [B] = 0.100 M, rate = 5.00 × 10⁻³ M/s; (2) [A] = 0.200 M, [B] = 0.100 M, rate = 2.00 × 10⁻² M/s; (3) [A] = 0.100 M, [B] = 0.200 M, rate = 1.00 × 10⁻² M/s.

Comparing experiments 1 and 2, [A] doubled while [B] stayed fixed, and the rate rose from 0.00500 to 0.0200 — a factor of exactly 4, so 2^m = 4 gives m = 2 (second order in A). Comparing experiments 1 and 3, [B] doubled while [A] stayed fixed, and the rate rose from 0.00500 to 0.0100 — a factor of exactly 2, so 2^n = 2 gives n = 1 (first order in B).

With m = 2 and n = 1 established, k = rate / ([A]²[B]) = 0.00500 / (0.100² × 0.100) = 5.00 M⁻²s⁻¹, using experiment 1 (and the other two experiments give the same value, confirming the fit). This is exactly the data used as this calculator's default Advanced Tools example, and the least-squares regression it runs recovers the same m = 2, n = 1, and k = 5.00 M⁻²s⁻¹ with R² = 1.000, since the data was designed to fit the rate law perfectly.

Reaction Order vs Stoichiometric Coefficient — A Common Mix-Up

It's tempting to assume the exponents in a rate law simply match the coefficients in the balanced chemical equation, but this is one of the most common mistakes in introductory kinetics. The balanced equation only describes the overall stoichiometry of the reaction — how much of each reactant is consumed and how much product forms — while the rate law describes the mechanism, specifically which species are actually involved in the slow, rate-determining step.

For an elementary reaction (one that happens in a single molecular step, exactly as written), the orders do match the coefficients. But most real reactions proceed through several steps, and the overall rate is controlled only by the slowest of those steps. A reactant with a large coefficient in the balanced equation might not even appear in the rate law at all (zero order) if it isn't involved in the rate-determining step, while a species added as a catalyst — appearing nowhere in the overall balanced equation — can still show up in the rate law. This is exactly why reaction orders must always be determined experimentally, using a method like the method of initial rates, rather than read off the balanced equation.

Common Mistakes to Avoid

A handful of small errors account for most incorrect answers when working with rate constants and rate laws by hand.

• Assuming reaction orders match the balanced equation's coefficients — as explained above, they usually have to be measured experimentally instead.
• Mixing up the differential rate law (rate = k[A]^m[B]^n, used on this page's Standard Solver) with an integrated rate law (which links concentration to time, used by the dedicated zero-, first-, and second-order reaction rate calculators) — they answer different questions and use k in different ways.
• Forgetting that k's units depend on the overall reaction order — quoting a bare number for k without units (or with the wrong units) makes it meaningless, since M/s, s⁻¹, and M⁻¹s⁻¹ are all completely different quantities.
• Comparing initial rates from experiments where more than one concentration changed at once — the classic paired comparison used in the method of initial rates only isolates one reactant's order when every other concentration is held perfectly constant between the two experiments being compared; this calculator's Advanced Tools regression handles the more general case where concentrations vary together.
• Confusing the rate constant k with the equilibrium constant K — they're related for reversible reactions (K = kforward/kreverse) but describe fundamentally different things: k describes how fast a reaction proceeds, while K describes where it ends up at equilibrium.

Limitations to Keep in Mind

This calculator assumes a simple power-law rate law of the form rate = k[A]^m[B]^n holds across the concentration range you're working with. Some real reactions — especially those involving catalysts, enzymes, or multi-step mechanisms with a pre-equilibrium — follow more complicated rate expressions (such as Michaelis-Menten kinetics) that don't reduce to a clean power law at all concentrations. For those systems, a dedicated model (like the site's Enzyme Kinetics calculator) is the right tool rather than a simple power-law fit. As with any experimental fit, always check the R² value from the Advanced Tools regression, and be cautious about extrapolating a fitted rate law far outside the concentration range your data actually covers.

Quick Reference: Every Formula on This Page

rate = k[A]^m[B]^n — the general differential rate law used in the Standard Solver. k = rate / ([A]^m[B]^n) — rearranged to solve for the rate constant. Units of k for overall order p = m + n: M^(1−p)·time⁻¹ (for example M/s at p = 0, s⁻¹ at p = 1, M⁻¹s⁻¹ at p = 2, M⁻²s⁻¹ at p = 3). ln(rate) = ln k + m·ln[A] + n·ln[B] — the linear form used by the Advanced Tools method-of-initial-rates regression.