Reaction Half-Life Calculator (Zero, First, Second Order)
Half-life and remaining concentration for zero-, first- and second-order reactions from the rate constant and initial concentration — with time to any percentage conversion and how t½ changes with concentration.
How it works
zero: t½ = [A]₀/2k, [A] = [A]₀ − kt; first: t½ = ln 2/k, [A] = [A]₀e^(−kt); second: t½ = 1/(k[A]₀), 1/[A] = 1/[A]₀ + kt
How the half-life responds to concentration is the fingerprint of the rate law: constant for first order (radioactive decay, most drug elimination), shrinking for zero order (enzyme-saturated or surface-catalysed reactions), growing for second order (dimerisations, many gas-phase reactions). Measure successive half-lives in one run and you can read off the order without a full kinetic fit. Rate-constant units differ by order, which is the easy way to check you have the right one.
Worked example
First order, k = 0.0231 s⁻¹, 0.5 M: t½ = 30 s; after 60 s (two half-lives) 0.125 M remains, and 90% conversion takes 99.7 s.
Frequently asked questions
What about pseudo-first order?
A second-order reaction with one reagent in large excess behaves as first order with k′ = k[B]; its half-life is constant at fixed [B].
How many half-lives to “complete”?
For first order 7 half-lives leave under 1%, 10 leave 0.1% — the reaction never strictly finishes.
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This calculator is for educational purposes. Double-check important results before acting on them.