Half-Life Calculator

Radioactive decay and any other first-order process: find the amount left, the time elapsed, the starting amount or the half-life itself.

N = N₀ × (½)^(t ÷ t½)
Solve for
N
Amount remaining
25g
1 sig figs: 30
≡
Same value in
25 units
25 mg · 25 atoms · 25 Bq
  1. Rearrange: N = N₀ × 0.5^(t ÷ t½)
  2. Substitute: N₀ = 100 g, t = 11460 yr, t½ = 5730 yr (converted to SI units first).
  3. Result: N = 25 g, rounded to 1 significant figures because the least precise input has 1.

N and N₀ just need the same unit (grams, atoms, counts per minute, percent).

Step through the half-lives

Start with 64 undecayed nuclei. Each step is one half-life: every nucleus has a 50 % chance of decaying, so on average half of what is left goes.

After 0 half-lives: 64 of 64 left = (½)0 = 100.0 %.

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Why the curve never quite reaches zero

Decay removes a fixed fraction of whatever is left, not a fixed amount, so each half-life takes a smaller bite than the one before. Like a decay curve, some science is easier to watch than to read about: ahaboo’s narrated photosynthesis explainer lets you zoom into a leaf and follow sunlight becoming stored energy.

Half-lives of common isotopes

Values from the NNDC (Brookhaven National Laboratory) nuclear data tables, rounded.

IsotopeHalf-life
Carbon-145,730 years
Uranium-2384.47 billion years
Potassium-401.25 billion years
Plutonium-23924,110 years
Radium-2261,600 years
Caesium-13730.1 years
Tritium (H-3)12.3 years
Cobalt-605.27 years
Iodine-1318.02 days
Radon-2223.82 days
Technetium-99m6.01 hours
Fluorine-18109.8 minutes

Frequently asked questions

What is the half-life formula?
N = N₀ × (½)^(t ÷ t½). N is the amount remaining after time t, N₀ the starting amount and t½ the half-life. Equivalent forms use the decay constant λ = ln 2 ÷ t½: N = N₀e^(−λt).
How do I find the half-life from data?
t½ = t × ln(0.5) ÷ ln(N ÷ N₀). If 100 g decays to 12.5 g in 24 days, N ÷ N₀ = 0.125 = (½)³, so three half-lives passed and t½ = 8 days.
How does carbon dating use half-life?
Living things keep a constant ratio of carbon-14 to carbon-12. After death C-14 decays with a 5,730-year half-life. Measuring the fraction left gives the time since death: 25 % remaining means two half-lives, about 11,460 years.
Does anything ever fully decay?
Mathematically the amount halves forever and never reaches zero. In practice, after about 10 half-lives less than 0.1 % remains and individual atoms decay at random, so the smooth curve stops being useful.
Is half-life only for radioactivity?
No. Any first-order process has a constant half-life: drug elimination from the body, some chemical reactions, and capacitor discharge (via the time constant) all follow the same equation.