Radioactive Decay Calculator

Atoms, Becquerel, grams, or any consistent unit.
In any time unit (same as elapsed time).
Chemistry

Calculate the remaining activity, number of nuclei, or mass of a radioactive sample after a given time.

Formula

N(t) = N₀ × e^(−λt); λ = ln(2)/t½
  • Uses the continuous decay law: N(t) = N₀ × e^(−λt).
  • Carbon-14 half-life: 5,730 years (used in radiocarbon dating).
  • Uranium-235: 703.8 million years; Radium-226: 1,600 years.
  • 1 Becquerel = 1 decay per second.

Carbon-14 decay after 2 half-lives (11,460 years)

Inputs
  • Initial Amount (N₀): 1000
  • Half-Life (t½): 5730
  • Elapsed Time: 11460

N = 1000 × e^(−0.693/5730 × 11460) = 1000 × 0.25 = 250 atoms.

Frequently asked questions

What is radiocarbon dating?
Uses C-14 decay (t½ = 5,730 yr) to date organic materials up to ~50,000 years old.
What is the difference between N(t) = N₀(½)^n and N₀e^−λt?
They are mathematically equivalent — the first uses discrete half-lives, the second uses continuous decay.