Reaction Rate Calculator
The reaction rate calculator computes concentration at any time and half-life for zero, first, and second order chemical reactions using integrated rate laws. Understanding reaction kinetics is fundamental to designing chemical reactors, predicting drug metabolism, analyzing radioactive decay, modeling environmental pollutant degradation, and optimizing industrial chemical processes. The integrated rate law gives the concentration as a function of time without needing to solve differential equations, making it immediately useful for laboratory and engineering applications. Enter the reaction order, initial concentration, rate constant, and time to find the concentration remaining.
Integrated rate law formulas
Zero order: [A] = [A0] - k*t; t(1/2) = [A0]/(2k)
First order: [A] = [A0]*exp(-k*t); t(1/2) = ln(2)/k
Second order: 1/[A] = 1/[A0] + k*t; t(1/2) = 1/(k*[A0])
Examples of reaction orders
- Zero order: surface-catalyzed reactions, some enzyme reactions (saturated), photolysis at fixed light intensity.
- First order: radioactive decay, many unimolecular reactions, drug elimination from body.
- Second order: bimolecular reactions, gas-phase dimerization, many solution reactions.
Reaction rate: frequently asked questions
What is a reaction rate?
Reaction rate is the change in concentration of reactants or products per unit time. It is expressed in M/s (mol/L/s) or similar units. For aA + bB to products: rate = -1/a * d[A]/dt = -1/b * d[B]/dt. The negative sign for reactants indicates their concentration decreases over time.
What is a rate law?
The rate law relates reaction rate to reactant concentrations: rate = k * [A]^m * [B]^n, where k is the rate constant, [A] and [B] are concentrations, and m, n are partial reaction orders determined experimentally. The overall reaction order is m + n. The rate law cannot be determined from the balanced equation alone.
What is a first-order reaction?
For a first-order reaction, rate = k*[A]. The integrated rate law is [A] = [A0]*exp(-k*t), and the half-life is t_1/2 = ln(2)/k, independent of initial concentration. Examples: radioactive decay, many unimolecular reactions, some enzyme-catalyzed reactions at low substrate concentrations.
What is the half-life of a reaction?
The half-life (t_1/2) is the time for the reactant concentration to fall to half its initial value. For zero order: t_1/2 = [A0]/(2k). For first order: t_1/2 = ln(2)/k (constant, independent of [A0]). For second order: t_1/2 = 1/(k*[A0]) (depends on initial concentration).
How do I determine reaction order experimentally?
Method of initial rates: measure rate at different initial concentrations. If doubling [A] doubles rate, reaction is first order in A. If it quadruples, it is second order. Alternatively, plot [A] vs t (zero order: linear), ln([A]) vs t (first order: linear), or 1/[A] vs t (second order: linear). The plot that is linear determines the order.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.