Reaction Time Calculator

Background.

In a first-order reaction the rate at any moment is proportional to how much reactant is left. Double the concentration and the reaction runs twice as fast; as the reactant is used up, it slows in step. The result is exponential decay, and it has one property that makes timing unusually clean: the reaction always takes the same time to use up the same fraction of what remains, however much you started with. Halving takes as long from 1 mol/L to 0.5 as from 0.02 to 0.01.

That fixed halving time is the half-life, ln 2 ÷ k, and it is the clearest sign that a process is first order. Radioactive decay is the textbook case. Many decompositions in solution and in the gas phase follow the same law, and so does the elimination of most drugs from the bloodstream, which is why dosing intervals are planned around half-lives. Reactions between two species can behave as first order too when one is present in such excess that its concentration barely changes; hydrolysis in water is the usual example.

The page answers the practical question of how long to wait. Give it the rate constant and the starting and target concentrations and it returns the time, along with the half-life. Because only the ratio of the two concentrations enters the formula, their units cancel: mol/L, partial pressure or absorbance all work, provided both values use the same one.

The rate constant is the input to treat with care. It is constant only at a fixed temperature and can change sharply as the temperature moves, so a value measured at 25 °C will not predict a run at 40 °C. Getting close to completion is slow as well: 99% conversion takes about 6.6 half-lives.

What is reaction time calculator?

Reaction time here means the time a first-order reaction needs to bring a reactant from its initial concentration [A]₀ down to a chosen lower concentration [A]ₜ. It comes from the integrated first-order rate law, [A]ₜ = [A]₀ × e^(−kt), solved for t. The half-life reported alongside is the special case where the target is half the starting value. Neither has anything to do with human reflex reaction time; both describe how quickly a chemical or physical decay proceeds.

How to use this calculator.

1. 01Enter the First-order rate constant k in s⁻¹. If your source quotes it per minute or per hour, convert it, or read the results in that same time unit, because time comes out in the reciprocal of k's unit.
2. 02Enter the Initial concentration and the Target concentration in one consistent unit; any unit works, since only their ratio matters.
3. 03Keep the target below the starting value. To time a given conversion, set the target to the amount left: 90% conversion from 1 mol/L means a target of 0.1.
4. 04Read the time to target and the half-life. Dividing the first by the second tells you how many half-lives the reaction has to run.

The formula.

For an irreversible first-order reaction, d[A]/dt = −k[A]. Integrating from time zero gives ln([A]₀ ÷ [A]ₜ) = kt, so the time to reach the target is t = ln([A]₀ ÷ [A]ₜ) ÷ k. Setting [A]ₜ to half of [A]₀ turns the logarithm into ln 2, about 0.693, which gives the half-life t½ = ln 2 ÷ k. The rate constant k has units of reciprocal time and holds only at constant temperature. Time scales inversely with k, so halving the rate constant doubles every time on the page, but only logarithmically with the concentration ratio: going from one fifth remaining to one tenth adds just ln 2 ÷ k, one more half-life. Zero-order, second-order, reversible and multi-step reactions follow different integrated laws and are not covered.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Chemistry 2e, 2019. Chapters 4, 9, and 12. Retrieved 2026-08-06.
2. [2]IUPAC. Gold Book current 2026. First-order reaction and rate constant. Retrieved 2026-08-06.
3. [3]OpenStax, Rice University. University Physics, 2016. Volume 1 mechanics and Volume 2 thermodynamics. Retrieved 2026-08-06.