Half-Life Calculator
Calculate how much of a substance remains after a given time, or how long decay takes.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
Amount remaining (g)
About this calculator
The calculator models exponential decay for a constant half-life. Enter the half-life and elapsed time in the same unit. It illustrates the mathematics only; it does not identify an isotope, assess exposure or determine whether a material is safe.
Worked example
calculated with the default values below
Initial amount 100 g · Half-life 5.27 time units · Elapsed time 10 time units Amount remaining 26.840190 g · Amount decayed 73.159810 g · Remaining 26.8402 % · Half-lives elapsed 1.898 · Decay constant (per input time unit) 0.131527 1 / time unit · Half-lives to reach 10% 3.322 half-lives
Method and assumptions
Formula basis and scope
Remaining amount = initial amount × 0.5^(elapsed time / half-life); decay constant = ln(2) / half-life.
Assumes a constant half-life and one exponential decay process. Time to 10% is displayed as a number of half-lives, not elapsed time in the input time unit. No decay-chain or variable-rate model is included.
Data sources
Disclaimer
These calculators give general conversion results. Rounding and the precision of the value you enter both affect the output, so treat displayed decimals as indicative rather than exact.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
N(t) = N_0×0.5^(t/t_½); λ = ln 2/t_½
- N_0
- Initial amount
- t
- Elapsed time
- t_½
- Half-life
- N(t)
- Remaining amount
- λ
- Decay constant
Elapsed time and half-life must use the same unit. The decay constant is per that input unit; 10% remains after 3.3219 half-lives. This is a mathematical model only.
Frequently asked questions
Why does the decay constant depend only on the half-life value?
The calculator derives the decay constant as the natural log of 2 divided by your half-life, so it ignores the initial amount and elapsed time entirely. With the default 5.27-year half-life the constant is about 0.1316 per period, and the time to drop to 10 percent is the same fixed 3.32 half-lives regardless of starting mass. That is why a ton and a gram of the same isotope follow the identical percentage curve.
Which time unit should I enter?
Use the same unit for half-life and elapsed time, such as years for both or days for both. The calculator returns decay constants per that input unit. It models the math only and does not identify an isotope or assess exposure or safety.