Half-Life Calculator
Enter three of starting amount, remaining amount, elapsed time and half-life to solve for the fourth.
Use any consistent unit (grams, atoms, activity in Bq) for N0 and N, and any consistent time unit (seconds, years, etc.) for t and half-life -- just keep the two time values in the same unit.
N = N0 × (1/2)^(t / half-life), solved for N = 25.0000.
Exponential Decay and Half-Life
Half-life describes exponential decay: N = N0 × (1/2)^(t / half-life). Every time exactly one half-life passes, whatever amount remains is cut in half again -- not a fixed amount, a fixed fraction. That's what makes decay curves flatten out over time instead of reaching zero in a straight line.
This equation solves in any direction: given a starting and remaining amount, you can find how much time has passed; given a starting amount and a half-life, you can find how much remains after any elapsed time.
Worked example
80 g of a radioactive isotope with a 5.27-year half-life is left to decay for 15.3 years. How much remains?
N = 80 × (1/2)^(15.3 / 5.27) = 80 × (1/2)^2.903 = 10.6938 g remaining -- about 2.9 half-lives have passed, just short of a full third halving.
Common mistake
Treating half-life like linear decay -- assuming 3 half-lives removes 3/2 = 150% (more than everything). Each half-life only removes half of what's currently left, so 3 half-lives leaves (1/2)³ = 1/8 of the original, not a negative or over-100% amount.
Keep going
- Half-life describes how a radioactive isotope's quantity decays over time; the atomic mass calculator uses that same isotope data (mass and abundance) to find an element's average atomic weight. Atomic Mass Calculator
Frequently Asked Questions
What is half-life?
The time it takes for exactly half of a radioactive (or otherwise first-order-decaying) sample to decay or react away. It's constant for a given isotope or process -- unlike simple linear decay, the same fraction (1/2) always decays in the same time span, no matter how much is left.
Why does the same fraction decay every half-life, not the same amount?
Because decay is proportional to how much is currently present -- more material decays faster in absolute terms, less decays slower, but the RATE relative to the current amount stays constant. Starting with 100 g, you lose 50 g in one half-life; starting with 50 g, you lose 25 g in the next -- half each time, not a fixed 50 g every time.
What's the formula behind this calculator?
N = N0 × (1/2)^(t / half-life), where N0 is the starting amount, N is the remaining amount after time t, and half-life is the isotope's or process's characteristic half-life. This calculator solves that same equation for whichever of the four values you're missing.
Do the units of N0 and N matter?
Only that they match each other -- grams, number of atoms, or radioactive activity in becquerels all work, as long as N0 and N use the same unit. Similarly, t and half-life just need to share the same time unit (both seconds, both years, etc.).
Is this only for radioactive decay?
No -- the same first-order-decay math applies to some drug elimination and other exponential decay processes, though this calculator's default framing and examples are radioactive-decay chemistry, not medical dosing.
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