What Is a First-Order Half-Life?
The half-life (t½) is the time required for the concentration of a reactant to fall to half its original value. For a first-order reaction, this half-life is constant throughout the reaction and depends only on the rate constant k — not on how much reactant you start with. This makes first-order kinetics especially predictable and is why it describes radioactive decay, many drug-elimination processes, and a wide range of chemical decompositions.
How to Use This Calculator
Enter the first-order rate constant k in reciprocal seconds (1/s) and the calculator returns the half-life in seconds. If your rate constant is in other units (1/min, 1/hr), the resulting half-life will be in the matching time unit (minutes, hours), since the formula is unit-agnostic as long as you stay consistent.
The Formula Explained
Starting from the integrated first-order rate law, \ln([A]/[A]_0) = -kt, set [A] = \tfrac{1}{2}[A]_0. Solving gives:
The natural log of 2 (≈ 0.693) appears because we are halving the concentration. Notice the initial concentration cancels entirely — a defining feature of first-order behavior.
Worked Example
Suppose a reaction has a rate constant k = 0.0693\ 1/s. Then
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