Radioactive Decay (Half-Life) Calculator

Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. The rate of decay is characterized by the half-life — the time it takes for half of the radioactive atoms to decay.

Decay formula: N(t) = N₀ × (1/2)^(t / t½)

Where:

• N(t) = amount remaining after time t
• N₀ = initial amount
• t = elapsed time
• t½ = half-life of the isotope

Decay constant: λ = ln(2) / t½ ≈ 0.693 / t½

Activity formula: A(t) = A₀ × e^(-λt)

Activity is measured in becquerels (Bq) or curies (Ci). 1 Ci = 3.7 × 10¹⁰ Bq.

Common isotope half-lives:

Practical example: If you start with 100 grams of Iodine-131 (half-life = 8.02 days):

• After 8.02 days: 50 g remains
• After 16.04 days: 25 g remains
• After 24.06 days: 12.5 g remains
• After 80.2 days (~10 half-lives): only 0.098 g remains

Number of half-lives: n = t / t½

After n half-lives, the fraction remaining is (1/2)^n.

Tip: After about 10 half-lives, less than 0.1% of the original material remains. This is often used as a practical threshold for when a radioactive source is considered “decayed away.”