Calcyx
Physics

Radioactive Decay / Half-Life Calculator

Calculate remaining radioactive material, decay fraction, and activity from initial amount, half-life, and elapsed time.

Starting quantity of radioactive material (in atoms, grams, or any unit).

Time required for half of the material to decay (use any time unit).

Time passed since the start (use the same unit as half-life).

Decay Summary

Remaining Amount

25

Decayed Amount

75

Fraction Remaining

25%

Fraction Decayed

75%

Half-Lives Passed

2

Decay Constant (λ)

0.138629 per time unit

Activity (A)

3.47 Bq

Use consistent time units for half-life and elapsed time (e.g., both in years, days, or seconds).

Uses the exponential decay formula: N(t) = N₀ × (0.5)^(t/t½)

Activity is calculated as A = λ × N, where λ is the decay constant. The result is in Becquerels (decays per second) if N represents number of atoms.

Radioactive Decay / Half-Life Calculator Guide

Overview

The Radioactive Decay Calculator helps you understand how radioactive materials diminish over time based on their half-life. Whether you're studying nuclear physics, carbon dating, or medical isotopes, this tool calculates the remaining amount, fraction decayed, decay constant, and activity from three simple inputs: initial amount, half-life, and elapsed time. By using the exponential decay equation, it provides accurate insights into how radioactive substances behave across any timeframe.

Inputs & Usage

You need to provide three values: the initial amount of radioactive material (N₀), the half-life (t½) which is characteristic of each isotope, and the elapsed time (t) since the measurement began. The initial amount can be expressed inany convenient unit—grams, atoms, or moles—as long as you stay consistent. The half-life and elapsed time must share the same time unit, whether years, days, or seconds. Once entered, the calculator immediately shows how much material remains and how much has decayed.

How It Works

The calculator applies the exponential decay formula: , which describes first-order decay kinetics typical of radioactive processes. The decay constant is derived from the half-life using , approximately 0.693 divided by the half-life. Activity, measured in Becquerels (decays per second), is calculated as , showing the current rate of nuclear transformations.

Interpreting the Results

The remaining amount tells you how much of the original substance is still present, while the decayed amount shows what has transformed into daughter products. The fraction decayed and fraction remaining give you percentage-based insights. The number of half-lives passed helps contextualize the timeline—after one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on. Activity indicates how "hot" the sample is in terms of decay events per second, which is crucial for safety and dosimetry calculations.

Example

Imagine you start with 1000 grams of a radioactive isotope that has a half-life of 5 years. After 10 years (two half-lives), the calculator shows that 250 grams remain, 750 grams have decayed, and 75% of the material has transformed. The decay constant would be approximately 0.1386 per year, and the activity depends on the number scale (atoms vs. mass units). Thisexample mirrors scenarios in carbon-14 dating or tracking medical tracers.

Limitations

This calculator assumes first-order decay kinetics and constant environmental conditions. It does not account for nuclear reactions induced by external radiation, chain reactions, or complex decay series with multiple daughter isotopes. Use it for idealized single-isotope scenarios where the half-life remains stable throughout the observation period.