First-Order Reaction Half-Life Calculator

The half-life (t₁/₂) is the time required for the concentration of a reactant to drop to half its initial value.

Half-life formulas by reaction order:

Zero-order reaction ([A]t = [A]₀ − kt):

t₁/₂ = [A]₀ / (2k)

Half-life depends on initial concentration — it gets shorter as the reaction proceeds.

First-order reaction ([A]t = [A]₀ × e^(-kt)):

t₁/₂ = ln(2) / k = 0.6931 / k

Half-life is constant and independent of initial concentration. This is why radioactive decay and many drug clearance rates use first-order kinetics.

Second-order reaction (1/[A]t = 1/[A]₀ + kt):

t₁/₂ = 1 / (k × [A]₀)

Half-life increases as the reaction proceeds (reactant gets depleted).

Time to reach a certain fraction:

First-order: t = (1/k) × ln([A]₀/[A]t) = (t₁/₂/0.693) × ln([A]₀/[A]t)

Units of k:

• Zero-order: M/s (or mol/L/s)
• First-order: s⁻¹ (1/time)
• Second-order: M⁻¹s⁻¹ (or L/mol/s)

Biological half-lives (first-order):