How to Find Units for k (Rate Constant)

Updated 6 November 2026 · Standard formula, shown below

This guide explains how to determine the units of the rate constant k for a chemical reaction. You will learn the general formula that works for any overall reaction order, see it applied to common orders, and avoid the unit mistakes that often appear in homework and exams. No prior knowledge beyond basic algebra and reaction order is needed.

What You’ll Need

The rate law for your reaction (or at least the overall order).
The units of concentration used in the rate law (usually mol/L, written as M).
The unit of time used in the rate (usually seconds, s).

Step-by-Step

Write the general rate law. For a reaction with overall order n, the rate law is: rate = k [A]ⁿ. Here, [A] is the concentration of a reactant (or product, depending on the rate expression) and n is the sum of the exponents in the rate law.
Identify the units of rate. Rate is always expressed as a change in concentration over time. So, rate has units of concentration/time, e.g., M/s (moles per liter per second).
Write the units of the concentration term. The concentration term [A]ⁿ has units of Mⁿ (molarity raised to the power n).
Set up the equation with units. Replace rate and concentration with their units in the rate law: (M/s) = k × (Mⁿ).
Solve for the units of k. Divide both sides by Mⁿ to isolate k: k = (M/s) / Mⁿ = M^1-n · s^-1.
Simplify the exponent. The general formula for the units of k is: M^1-n s^-1, where n is the overall order of the reaction.
Plug in the order. For a specific reaction, substitute the known overall order n into the formula. For example, if the reaction is second order (n=2), the units become M^1-2 s^-1 = M^-1 s^-1.
Convert to other units if needed. If concentrations are given in different units (e.g., atm for gases, or mmol/L), replace M with that unit. For time, use the unit given (s, min, hr). The same exponent logic applies.

Common Mistakes

Using the wrong order. Make sure you use the overall order (sum of all exponents in the rate law), not just the order with respect to one reactant.
Forgetting the time unit. Rate always has a time component (s^-1, min^-1). Do not drop it.
Mixing up M and mol/L. M is shorthand for mol/L. If you write out mol/L, the algebra still works, but be consistent.
Confusing rate constant with rate. The rate constant k does not change with concentration, but its units do change with reaction order.
Sign errors in the exponent. For n=3, 1-n = -2, giving M^-2 s^-1. Double-check your subtraction.

Tips

Memorize the common ones: Zero order: M s^-1 (or M/min). First order: s^-1 (or min^-1). Second order: M^-1 s^-1. Third order: M^-2 s^-1.
Use dimensional analysis. Always write units in the rate law and cancel them algebraically. This catches most mistakes.
Check the overall order. If you have a rate law like rate = k[A][B]², the overall order is 1+2=3, so k units are M^-2 s^-1.
For gas-phase reactions, if concentrations are in atm, replace M with atm. For example, first order: atm⁰ s^-1 = s^-1 (still just s^-1).

Troubleshooting

If you get a fractional exponent, that’s okay. For example, if the overall order is 1.5, the units are M^-0.5 s^-1. Just keep the exponent as a decimal or fraction.
If you see a rate law with negative orders, the overall order might be negative. For instance, if rate = k[A]^-1, then n = -1, so units are M^1-(-1) s^-1 = M² s^-1. This is rare but possible.
If your teacher uses different units for concentration (e.g., mmol/L), replace M with that unit. The exponent logic remains the same.
If you are given the rate constant and asked for the order, work backwards: compare the units of k to the general formula M^1-n s^-1. For example, if k has units M^-2 s^-1, then 1-n = -2, so n = 3 (third order).
If you are unsure about the overall order, sum the exponents in the rate law. If you don’t have the rate law, you cannot find the units of k.

Frequently Asked Questions

Why do the units of k change with reaction order?

Because the rate law must always give rate in M/s. If the concentration term has units of Mⁿ, then k must have units that cancel out the extra M’s to leave M/s. The exponent n changes, so the units of k adjust.

What are the units of k for a first-order reaction?

For n=1, the formula gives M⁰ s^-1 = s^-1. So k has units of 1/time (e.g., s^-1, min^-1).

Can k have units of M/s?

Yes, that happens for a zero-order reaction (n=0). Then k = M¹ s^-1 = M/s, which is the same as the rate.

Does the unit of time affect the numerical value of k?

Yes. If you change from seconds to minutes, the numerical value of k changes, but the units change accordingly (e.g., s^-1 to min^-1). Always keep track of the time unit.

What if the reaction is second order in A and first order in B?

Then the overall order is 2+1=3, so k has units M^-2 s^-1. The individual orders don’t matter, only the sum.

How do I find the units of k from a graph?

If you plot concentration vs. time and get a straight line for a certain order, you can use the slope to find k. The units of the slope will match the units of k for that order. For example, a first-order plot of ln[A] vs. time has a slope with units s^-1.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.