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.

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)

Usage tips

  • 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.

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.
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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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