Radioactive Isotope Half-Life Calculator

Using the half-life formula N=N0×(1/2)^(t/T), calculate any one of remaining amount, initial amount, elapsed time, or half-life from the other three.

Last updated: 2026-09-05

Half-lives of common radioactive isotopes

Isotope	Half-life	Main use / characteristics
Carbon-14 (¹⁴C)	approximately 5,730 years	Used in radiocarbon dating
Iodine-131 (¹³¹I)	approximately 8 days	Used in diagnosis and treatment of thyroid disorders (nuclear medicine)
Cobalt-60 (⁶⁰Co)	approximately 5.27 years	Used in cancer radiotherapy and industrial non-destructive testing
Uranium-235 (²³⁵U)	approximately 700 million years	Fissile material for nuclear power and nuclear weapons
Uranium-238 (²³⁸U)	approximately 4.47 billion years	Used in dating rocks and the Earth (uranium-lead dating)
Plutonium-239 (²³⁹Pu)	approximately 24,100 years	Fissile material for nuclear power and nuclear weapons
Potassium-40 (⁴⁰K)	approximately 1.25 billion years	Used in geological dating (potassium-argon dating)

What half-life calculation means

A half-life is the time it takes for a radioactive substance to decay until exactly half of it remains. Starting from that figure, this calculator finds whichever of four quantities you are missing: the remaining amount, the initial amount, the elapsed time or the half-life itself. Because decay follows the exponential relationship N = N0 × (1/2)^(t/T), the same equation can be rearranged for any of the four, and the result is more precise than an estimate on a pocket calculator.

You simply choose which value you want, and the tool works it out from the remaining three. That covers radiocarbon dating, where the elapsed time — the age of the sample — is derived from the surviving proportion, as well as the everyday task of estimating how much of a medical or industrial isotope will be left. The whole calculation happens in your browser and no figure you enter is sent to a server.

How to use the calculator

Choose the value to calculate Pick one of remaining amount, initial amount, elapsed time or half-life. The input box for whichever you choose is hidden automatically.
Enter the other three values Fill in the boxes that remain. Elapsed time and half-life must be expressed in the same unit, whether years, days or anything else.
Check that the units agree The amounts may be in grams, counts or any unit you like, but the initial and remaining amounts must both use the same one.
Read the result The answer appears in the result panel as you type. The table below also lists the half-lives of some familiar isotopes for reference.

Tips for getting more out of it

Always enter elapsed time and half-life in the same unit (e.g. both in "days" or both in "years"). Mismatched units will produce incorrect results.
In "remaining amount" mode, enter the initial amount, half-life, and elapsed time to find out how much of the substance remains undecayed at that point in time.
The "half-life" mode is useful when you want to work backward from experimental or observational data (a known remaining amount at a given time) to find a substance's characteristic half-life.
Refer to the "half-lives of common radioactive isotopes" table below to get a sense of the order of magnitude of half-lives for familiar isotopes, such as carbon-14 used in dating.

When half-life calculation is useful

Approximating a radiocarbon date

If you know the surviving proportion of carbon-14 in a site or a fossil, setting elapsed time as the value to calculate gives a rough figure for how long ago the organism died.

Estimating residual activity in nuclear medicine

For isotopes used clinically such as iodine-131 or cobalt-60, you can work out in advance how much activity remains a given time after administration or irradiation.

Checking homework in science and chemistry

Solve the textbook problem yourself, then confirm it here; any arithmetic slip shows up immediately.

Comparing how fast different isotopes decay

Keep the elapsed time fixed and vary only the half-life to see how differently isotopes behave. To review the properties of the elements themselves, the periodic table tool sits alongside this one.

Getting a feel for exponential decrease

Watching the amount halve at each half-life makes the pattern concrete. To see the same behaviour as a curve, the exponential function grapher is a useful companion.

Terms used in half-life calculation

Half-life: The time taken for a radioactive substance to decay to exactly half its amount. It is characteristic of each isotope and is known to stay constant regardless of temperature, pressure or other conditions.
Radioactive decay: The process by which an unstable nucleus emits radiation and becomes a more stable one. Because the probability of decay does not change over time, the amount in a population falls exponentially.
Decay constant: The constant λ giving the probability that a nucleus decays per unit time. It relates to the half-life T by T = ln(2) / λ, so a shorter half-life means a larger decay constant.
Radiocarbon dating: A method that estimates age from the surviving proportion of carbon-14 in a site or fossil, using the fact that it decreases according to its half-life of about 5,730 years after an organism dies.
Isotope: Atoms of the same element with different numbers of neutrons in the nucleus. Stability and half-life differ greatly between them, as with carbon-12 and carbon-14.
Activity: The number of decays occurring per unit time in a radioactive substance, measured in becquerels (Bq). As the remaining amount falls, the activity falls in proportion.

Frequently asked questions

A half-life is the time it takes for the nuclei in a radioactive substance to decay until the remaining amount is exactly half of what it started as. It's a value unique to each substance (isotope), and it's known to remain constant regardless of surrounding conditions such as temperature or pressure.

No. The remaining amount is halved each time a half-life elapses, but mathematically it never reaches zero. For example, after 10 half-lives the remaining amount is about 0.1% of the initial amount (1 divided by 2 to the 10th power), but while it gets ever closer to zero, it never mathematically reaches exact zero.

While an organism is alive, it continuously takes in carbon from the atmosphere, so the ratio of radioactive carbon-14 (¹⁴C) to stable carbon-12 in its body stays roughly constant. Once the organism dies, it stops taking in carbon, and its ¹⁴C decreases at a steady rate governed by its half-life (approximately 5,730 years). By measuring the remaining ratio of ¹⁴C in archaeological remains or fossils, we can estimate how much time has passed since death.

The length of a half-life is determined by how unstable (prone to decay) a given nucleus is, which depends on the ratio of protons to neutrons inside it. Some highly unstable isotopes have half-lives of only seconds to days, while others, such as uranium-238, have half-lives on the order of billions of years — comparable to the age of the Earth or the solar system.

Side Note — Why Radioactive Decay Makes Such a Reliable "Clock"

The main reason radioactive decay is trusted as a dating "clock" is that its half-life is completely unaffected by external conditions such as temperature, pressure, or chemical bonding state, and always proceeds at a constant rate. This is in stark contrast to ordinary chemical reactions, whose rates change greatly with temperature, and reflects a stability unique to physical processes occurring within the atomic nucleus.

Radiocarbon dating was developed in 1949 by the American chemist Willard Libby, an achievement for which he was awarded the Nobel Prize in Chemistry in 1960. His method revolutionized archaeology, making it possible to assign a direct numerical age to archaeological finds that had previously only been estimated relatively, based on stratigraphy or cultural characteristics.

Radiocarbon dating does have its limitations, however. Because atmospheric ¹⁴C concentration fluctuates slightly due to solar activity and nuclear testing, obtaining accurate dates requires calibration curves derived from sources such as dendrochronology. In addition, because ¹⁴C's half-life of roughly 5,730 years is relatively short, it isn't suitable for dating samples older than tens of thousands of years — for those, other isotopes with longer half-lives, such as the uranium series or potassium-argon dating, are used depending on the era in question.

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