Half Life Calculator
Every half-life cuts what remains in half — type the starting amount, the half-life and either the wait or the target, and the survival curve answers.
Half Life Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Pure exponential survival — no branching chains
- Radiocarbon ages need calibration curves before use as dates
In short: 100 g of carbon-14 (half-life 5,730 years) left alone for 11,460 years: exactly 2 half-lives pass, so 25.000000 g remain — 25.000000% of the sample. The mean life is longer than the half-life: τ = 5,730/ln 2 = 8,266.642584 years, a factor of 1.442695 — the average atom outlives the headline number. Type 50 into the remaining box and blank the wait: one half-life, 5,730 years, solves back.
Formula
N(t) = N₀·2^(−t/t½) · t = t½·log₂(N₀/N) · τ = t½/ln 2
Decay is a fixed probability per tick of the clock, so multiplying it out gives a power of one half: after one half-life half remains, after two a quarter, after n of them 1/2ⁿ. The mean life — the average over all the atoms’ actual lifetimes — is the half-life divided by the natural logarithm of two, about 1.44 times longer. Elapsed time and half-life must share a unit; the fraction only cares about their ratio.
Worked Example
- Type the starting amount and the half-life (same unit for both).
- Fill the elapsed time to price what remains, or the remaining amount to price the wait.
- Leave exactly one of the two question boxes blank — that is the unknown.
- Read the survival card and the mean life.
Defaults: 100 g, t½ 5,730, wait 11,460 → 25.000000 g = 2 half-lives. Blank the wait and type 50 remaining: t solves to 5,730. Three half-lives from any start is 12.500000%.
Strengths & Limits Of This Model
Where this engine is strong
- Solves the wait or the remainder
- Mean life printed beside the half-life
Where it stops
- Single isotope — no decay-chain bookkeeping
- No statistical counting uncertainties
Practical Use Cases
Radiocarbon dating
the 5,730-year clock
Isotope logistics
shelf life of a stock vial
Teaching
exponential decay by powers of two
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Half Life Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does the unit not matter?
Because the curve answers to the ratio t/t½. A wait of 11,460 against a half-life of 5,730 is two half-lives whether both are years or both are microseconds — the survival fraction is 25% either way. Only when you convert the wait into a wall-clock date does the unit become real.
How is this different from the radioactive decay page?
Question. This page asks how much survives or how long the wait was — the survival road. The decay page asks how hot a sample is right now: it weighs the vial, counts the atoms and prices the activity in becquerel. Same exponential underneath, different ledger.
What is the mean life for?
It is the honest average of the atoms’ lifetimes. The half-life is a median — half die before it — but the survivors pull the average up to t½/ln 2, about 1.44 times the headline. Shielding and storage planning that budgets by the mean life does not undercount the long tail.
Does half of a half ever reach zero?
Never in the arithmetic — 2⁻ⁿ shrinks without touching zero — and never quite in nature, though past about ten half-lives the remainder is under a thousandth and most practical ledgers call it gone. The page prints the honest figure however small.
What does the half-life ledger card show?
The ratio and its logarithm: N₀/N for the default drive is 4.000000, the half-lives elapsed are 2.000000, and 2 raised to the matching exponent returns the survival fraction. The card prints all three so the powers-of-two ladder is visible — 1, 0.5, 0.25 — instead of a number arriving from nowhere.
Why does the remaining box refuse values above the start?
Because decay is one-way: no wait makes a sample grow. A remainder above the starting amount means the two boxes were swapped, or the daughter isotope got counted with the parent — decay chains grow at the bottom while the top runs down, and this page prices only the top. The refusal names the check instead of printing a nonsense age.
Can I date something with this alone?
The arithmetic yes, the answer no. Radiocarbon dates need calibration — the atmosphere’s carbon-14 fraction has wobbled over the centuries, so laboratories apply curve corrections to the raw count. Use the solved age as the arithmetic answer, then hand it to a calibration table before calling it a date.
Why refuse when both question boxes are filled?
Because they must agree or the inputs are contradictory: an elapsed time of 11,460 years and a remainder of 50 g from 100 g cannot both hold. The solver takes one unknown — blank the box you want priced.