NumberTally Half-Life Calculator
Compute the remaining quantity with N = N₀(1/2)^(t/T) — or flip the formula around: solve for the elapsed time, the half-life, or the starting amount from the other three. Enter your values to see what remains, what decayed, and how long until any percentage is left. Results update instantly. Free, no sign-up.
Must be less than N₀ (decay).
Advanced options
Cosmetic only — T and t must use the same unit.
How Half-Life Decay Works
After one half-life, half of the substance remains; after two, a quarter; after three, an eighth. The decay never truly reaches zero — it just keeps halving. The formula N = N₀ × (1/2)^(t/T) captures this: the exponent t/T counts how many half-lives have passed, and each one multiplies the remainder by one half.
The formula rearranges cleanly, so any one variable can be solved from the other three: t = T·ln(N₀/N)/ln 2 finds the elapsed time, T = t·ln 2/ln(N₀/N) finds the half-life, and N₀ = N·2^(t/T) recovers the starting amount. This same curve describes drug elimination from the bloodstream, the cooling of caffeine's effect, and depreciation. Flip it around and you get exponential growth — the math is identical, only the direction changes.
Famous Half-Lives
Half-lives span an astonishing range: some atomic nuclei decay in fractions of a second, while uranium-238's half-life is 4.5 billion years — the basis of radiometric dating. Carbon-14 (5,730 years) dates archaeological finds, iodine-131 (8 days) is used in medicine, and caffeine's ~5-hour half-life is why that afternoon coffee still affects your sleep.
Frequently Asked Questions
What is a half-life?
The time needed for half of a quantity to decay or be eliminated. After each half-life, the remainder halves again.
Does everything disappear after two half-lives?
No — two half-lives leave one quarter (1/2 × 1/2). The amount approaches zero but mathematically never reaches it.
How do I find the time until only 10% is left?
Solve t = T × log₂(100/10) ≈ 3.32 half-lives. The table below computes this for common targets automatically.
Can I solve for the half-life or the elapsed time instead?
Yes — use the "Solve for" menu. Given the start and end amounts, t = T·ln(N₀/N)/ln 2 finds the time, and T = t·ln 2/ln(N₀/N) finds the half-life.
Do T and t need the same units?
Yes. If the half-life is in days, the elapsed time must be in days too — only the ratio t/T enters the formula.
Is decay exactly exponential in real life?
For radioactive decay it is exact at the atomic level. For drugs or caffeine it is a good approximation that varies between individuals.