Half-Life Calculator

The Formula

The radioactive decay formula describes how a quantity of a radioactive substance decreases over time. The half-life (t₁₂⁄₂) is the time required for the quantity to reduce to half its initial value. After each half-life, exactly half of the remaining atoms decay, producing an exponential decay curve. This same formula applies to any process that follows first-order kinetics, including drug elimination from the body and capacitor discharge.

Variable Definitions

How to Use This Calculator

1. 1

   Select which variable you want to solve for using the dropdown menu.

2. 2

   Enter values for the three known variables (the field for the unknown variable will be hidden).

3. 3

   All values must be positive numbers. The remaining quantity must be less than the initial quantity when solving for half-life or time elapsed.

4. 4

   Review the detailed results, including the number of half-lives elapsed and the percentage remaining.

5. 5

   Explore the decay progression table and the SVG decay curve in the panel below the results.

The half-life is the time required for a quantity to reduce to half its initial value

Understanding the Concept

Radioactive decay is a random process at the atomic level, but for large numbers of atoms, it follows a precise exponential law. The half-life is independent of the starting amount: after one half-life, half of the original atoms remain; after two half-lives, one-quarter remain; after three, one-eighth; and so on. This means the quantity never reaches zero — it asymptotically approaches it. The number of half-lives elapsed (n = t / t₁₂⁄₂) determines the fraction remaining: (1/2)^n. This concept extends beyond radioactivity to carbon dating, pharmacokinetics (drug half-life), nuclear medicine, environmental science, and any system exhibiting first-order exponential decay.

Frequently Asked Questions

Sources & References