Science calculator

Half-life and decay.

Enter any three of initial quantity, remaining quantity, elapsed time and half-life. Use particle count, amount or activity consistently.

Remaining quantity NSolved
N = N₀(½)^(t/T½)
Fraction remaining
Quantity decayed
N=N0(12)tT1/2

Assumptions

  • One radionuclide with a constant decay probability and a fixed half-life.
  • No new nuclei are produced and no daughter activity is added.
  • Initial and remaining entries use the same kind of quantity and compatible units.
  • For activity, any background count rate has already been removed and detector response is unchanged.

How it works

After each half-life, half of the undecayed nuclei remain. Three half-lives therefore leave one eighth of the initial quantity.

Activity is proportional to the number of undecayed nuclei for a single isotope, so it follows the same fractional law. It can be used in place of N when units are kept consistent.

Leave one field blank to solve it. The logarithmic rearrangements for elapsed time and half-life assume 0 < N ≤ N₀.