☢️ Radioactive Decay Calculator

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. The number of radioactive atoms decreases exponentially over time according to the formula N = N₀ × e⁻λᵗ, where N₀ is the initial number of atoms, λ (lambda) is the decay constant, and t is elapsed time. The half-life (t₁/₂) is the time it takes for half of the atoms to decay, related to the decay constant by t₁/₂ = ln(2) / λ ≈ 0.693 / λ.

This calculator handles any radioactive isotope—whether you are working with Carbon-14 for archaeological dating, Iodine-131 for medical treatment, or Uranium-238 for geological analysis. Enter the initial amount, half-life, and elapsed time to find how much remains, or solve for any other unknown.

The calculator uses the exponential decay formula N = N₀ × e⁻λᵗ. The decay constant λ is derived from the half-life: λ = ln(2) / t₁/₂ ≈ 0.693147 / t₁/₂. After one half-life, 50% of the sample remains. After two half-lives, 25% remains. After three, 12.5%, and so on.

The table below lists half-lives of common isotopes:

Notice the enormous range: Technetium-99m decays in hours (ideal for medical scans where quick elimination is desired), while Uranium-238 lasts billions of years (useful for dating ancient rocks). The decay constant λ is inversely proportional to half-life: longer half-life means slower decay.

1. Enter the initial amount (N₀) of the radioactive substance.
2. Enter the half-life (t₁/₂) of the isotope.
3. Enter the elapsed time (t).
4. Click the Calculate button.
5. Review the remaining amount, decay constant, and percentage remaining.

What is half-life?

Half-life (t₁/₂) is the time required for half of the radioactive atoms in a sample to decay. After one half-life, 50% remains; after two, 25%; after three, 12.5%. Each isotope has a characteristic half-life that is constant regardless of temperature, pressure, or chemical environment.

How are half-life and decay constant related?

The decay constant λ = ln(2) / t₁/₂ ≈ 0.693147 / t₁/₂. A larger decay constant means faster decay and a shorter half-life. The two quantities are inversely proportional.

Can I solve for time instead of remaining amount?

Yes. If you know the initial amount, remaining amount, and half-life, you can rearrange the formula to find elapsed time: t = (−ln(N/N₀)) / λ. This is the basis of radiocarbon dating—measure the remaining C-14 ratio and calculate how long ago the organism died.

What units should I use?

Half-life and elapsed time must use the same time unit (both in years, days, hours, etc.). The initial amount can be in any unit (grams, moles, atoms, Bq). The remaining amount will be in the same unit as the initial amount.

Does temperature or pressure affect radioactive decay?

No. Unlike chemical reactions, radioactive decay is a nuclear process. It is unaffected by temperature, pressure, electric fields, magnetic fields, or chemical bonding. The half-life of an isotope is a fundamental constant of nature.

What is the difference between activity and amount?

Amount (N) is the number of radioactive atoms present at time t. Activity (A) is the rate of decay: A = λ × N, measured in Becquerels (1 Bq = 1 decay per second). Activity decreases over time at the same exponential rate as the amount.

Half-life and elapsed time must use the same time unit (both in years, or both in days, etc.). The calculator handles the conversion automatically. The initial amount N₀ can be in any unit—grams, moles, number of atoms, or Becquerels—and the remaining amount N will be in the same unit. For very long half-lives (like U-238), the remaining fraction changes extremely slowly: after 1 million years, a U-238 sample still has 99.98% of its original atoms. For medical isotopes (like I-131), decay is rapid: after 5 half-lives (about 40 days), only 3.1% of the original I-131 remains. The related concept of activity (A = λN) gives the number of decays per second, measured in Becquerels (Bq) or Curies (Ci).