Radioactive Decay Calculator
Free radioactive decay calculator. Enter the initial amount, half-life and elapsed time to find the quantity remaining, fraction left and number of half-lives.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Radioactive Decay Calculator Works
Radioactive decay follows a predictable exponential pattern. This calculator takes the initial quantity (N₀), the half-life, and the elapsed time (t), then returns how much remains, the fraction left, and the number of half-lives that have passed.
The Formula
The amount remaining after time t is:
N = N₀ × (½)^(t / half-life)
This is equivalent to the exponential form using the decay constant λ:
N = N₀ × e^(−λt), where λ = ln(2) / half-life
Make sure the half-life and the elapsed time are expressed in the same units (both in years, both in days, and so on).
Worked Example
Carbon-14 has a half-life of 5,730 years. Starting with 100 grams, how much remains after 11,460 years?
- Half-lives elapsed = 11,460 ÷ 5,730 = 2
- Fraction remaining = (½)² = 0.25
- N = 100 × 0.25 = 25 grams
So after two half-lives, 25 grams of the original 100 grams of carbon-14 remain.
Decay by Number of Half-Lives
| Half-lives elapsed | Fraction remaining | Percent remaining |
|---|---|---|
| 0 | 1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.125% |
Where Decay Calculations Are Used
- Radiometric dating — carbon-14 for organic remains, uranium-lead for rocks.
- Nuclear medicine — timing doses of short-lived tracers like technetium-99m.
- Radiation safety — estimating how long a source remains hazardous.
- Physics coursework — practicing exponential decay and logarithms.
Frequently asked questions
How do you calculate radioactive decay?+
Use N = N₀ × (1/2)^(t / half-life), where N₀ is the starting amount, t is the elapsed time and the half-life is the time for half the sample to decay. Equivalently, N = N₀ × e^(−λt) with the decay constant λ = ln(2) / half-life. The result N is how much radioactive material remains.
What is a half-life?+
A half-life is the time it takes for half of a radioactive sample to decay. After one half-life, 50 percent remains; after two, 25 percent; after three, 12.5 percent, and so on. Each isotope has a fixed half-life ranging from fractions of a second to billions of years, and it does not depend on the amount present.
What is the decay constant?+
The decay constant λ is the probability per unit time that a single nucleus decays. It is related to the half-life by λ = ln(2) / half-life, where ln(2) is about 0.693. A larger decay constant means a shorter half-life and faster decay. It appears in the exponential form N = N₀ × e^(−λt).
How much of a sample remains after 3 half-lives?+
After each half-life the amount halves, so after three half-lives you have (1/2)³ = 1/8, or 12.5 percent of the original sample. The number of half-lives elapsed is simply the total time divided by the half-life, and it does not have to be a whole number.
Does temperature or pressure affect radioactive decay?+
For ordinary radioactive decay the rate is essentially constant and is not affected by temperature, pressure or chemical state, because it is governed by the nucleus, not the electron cloud. This is what makes techniques like carbon dating reliable, since the half-life stays fixed over the conditions found on Earth.