Half-Life (First Order) Calculator Formula

Understand the math behind the half-life (first order) calculator. Each variable explained with a worked example.

Use the Half-Life (First Order) Calculator

Formulas Used

Half-Life (t½)

half_life = log(2) / rate_constant

Half-Life

half_life_min = log(2) / rate_constant / 60

Variables

VariableDescriptionDefault
rate_constantRate Constant (k)(1/s)0.05

How It Works

First-Order Half-Life

For a first-order reaction, the half-life is the time required for the concentration to decrease to half of its initial value. Uniquely for first-order kinetics, the half-life is independent of initial concentration.

Formula

t½ = ln(2) / k = 0.693 / k

where k is the first-order rate constant. This formula applies to radioactive decay, drug metabolism, and many chemical decomposition reactions.

Worked Example

A first-order reaction with rate constant k = 0.05 s⁻¹.

rate_constant = 0.05
  1. 01t½ = ln(2) / 0.05
  2. 02t½ = 0.6931 / 0.05 = 13.86 s
  3. 03In minutes: 13.86 / 60 = 0.231 min

Ready to run the numbers?

Open Half-Life (First Order) Calculator