Half-life calculator

Radioactive decay and half-life.

Amount left

25

N = N₀ × (1/2)^(t / T½). 2 half-lives have passed.

Starting amount (N₀)
100
Amount left (N)
25
Fraction left
25%
Time elapsed (t)
11,460 years
Half-life (T½)
5,730 years
Decay constant (λ = ln 2 / T½)
0.000120968 per year
Mean lifetime (τ = T½ / ln 2)
8,266.64 years
Half-livesTime (years)Amount leftFraction left
001001 (100%)
15,730501/2 (50%)
211,460251/4 (25%)
317,19012.51/8 (12.5%)
422,9206.251/16 (6.25%)
528,6503.1251/32 (3.125%)
634,3801.56251/64 (1.563%)
740,1100.781251/128 (0.7813%)
845,8400.3906251/256 (0.3906%)
951,5700.1953131/512 (0.1953%)
1057,3000.09765631/1024 (0.09766%)

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How to use the half-life calculator

  1. Choose what to find: the amount left, the starting amount, the time that has passed or the half-life.
  2. Enter the other three values. Amounts can be in any unit (grams, atoms, becquerels, percent) as long as both use the same one, and the time and half-life share the unit you pick.
  3. Read the answer, the number of half-lives, the decay constant and mean lifetime, and the table of what remains after each half-life.

Half-lives of some isotopes

Isotope Half-life
Iodine-131 8.02 days
Cobalt-60 5.27 years
Radium-226 1,600 years
Carbon-14 5,730 years
Uranium-238 4.47 billion years

Not just radioactivity

Anything that decays by the same fraction in each equal time step follows the same law: the concentration of many medicines in the blood, the charge on a discharging capacitor, or the fall in a light signal through a fibre. The half-life is the time for any amount to halve, whatever the amount was at the start.