1st-Order Reaction Half-Life Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
A 1st-order reaction half-life is calculated with t½ = ln(2) ÷ k, where k is the reaction rate constant. For a rate constant of 0.05 s⁻¹, the half-life is about 13.86 seconds.
Explanation
In chemical kinetics, a reaction's order describes how its rate depends on reactant concentration. For a 1st-order reaction (the rate is directly proportional to the concentration of a single reactant), the half-life has a remarkable property: it's constant, independent of the starting concentration. This behavior is directly visible in the formula t½ = ln(2) ÷ k, where the initial concentration appears nowhere — unlike 0-order reactions (where the half-life depends directly on the starting concentration) or 2nd-order reactions (where it depends on it inversely). This is exactly the same property already found in our radioactive decay calculator and our drug half-life calculator: all three phenomena (1st-order chemical reaction, radioactive decay, 1st-order pharmacological elimination) share the same exponential decay math, where a constant fraction of the remaining amount disappears at regular time intervals, regardless of the starting amount. The rate constant k characterizes the reaction's inherent speed: the higher it is, the faster the reaction and the shorter its half-life, the two quantities moving in strictly opposite directions.
Example: a rate constant of 0.05 s⁻¹
Inputs
Rate constant (k): 0.05 s⁻¹.
Calculation
t½ = ln(2) ÷ 0.05 = 0.693147 ÷ 0.05 ≈ 13.8629 s.
Result
This reaction has a half-life of about 13.86 seconds.
Frequently asked questions
Why doesn't a 1st-order reaction's half-life depend on the starting concentration?
Because in a 1st-order reaction, the reactant's rate of disappearance is always proportional to the amount remaining at that instant: whether a lot or a little reactant remains, the same fraction disappears per unit time. It's this constant proportionality that makes the time needed to halve the remaining amount always the same, regardless of the starting amount — a property that doesn't hold for 0-order or 2nd-order reactions.
How do you know if a reaction is actually 1st order?
A reaction's order is determined experimentally, generally by measuring how its initial rate varies as reactant concentration changes, or by checking that the measured half-life stays actually constant at different starting concentrations. This formula only applies to confirmed 1st-order reactions: applying it to a reaction of a different order would give an incorrect result.
What's the difference between the rate constant k and the half-life?
The rate constant k is an intrinsic property of the reaction under given conditions (temperature, solvent), generally determined experimentally or theoretically; the half-life t½ is a derived quantity, more intuitive to interpret (the time needed for half the reactant to have reacted), but it contains exactly the same information as k for a 1st-order reaction, the two being related by this simple formula.