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Chemistry Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

Half-Life Calculator

You can calculate radioactive decay with the half-life formula: find the remaining or initial amount, the elapsed time or the half-life itself, with half-lives elapsed and the decay constant shown.

Runs in your browserFree · No sign-up · No watermark
HALF-LIFE → AMOUNTRuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
HALF-LIFE → AMOUNT
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Chemistry Tools

About Half-Life Calculator

A half-life is the time it takes for half of a sample to decay. Because the process is exponential, every half-life removes the same fraction rather than the same amount: after one half-life 50 percent remains, after two 25 percent, and after ten about 0.1 percent.

This calculator works in all four directions. Enter the known values and it solves for the remaining amount, the initial amount, the elapsed time or the half-life, showing the number of half-lives, the fraction remaining, the decay constant and the substituted formula. Time can be entered in seconds, minutes, hours, days or years.

What this tool does

The details that matter when you use Half-Life Calculator for real work.

  • Four solve modes

    Find the remaining amount, the initial amount, the elapsed time or the half-life, with only the fields that mode needs on screen.

  • Half-lives and fraction remaining

    Every result reports how many half-lives have passed and what fraction of the original amount is left, as a percentage.

  • Decay constant and mean lifetime

    The summary shows λ = ln 2 / t½ in reciprocal time units and the mean lifetime t½ / ln 2 next to the main answer.

  • Time units with conversion

    Half-life and elapsed time can each be entered in seconds, minutes, hours, days or years, and the result can be requested in any of them.

  • Formula with substituted values

    The working panel writes out N(t) = N₀ × (1/2)^(t/t½), or its rearrangement, with your numbers substituted.

  • Range validation

    Zero or negative times, a half-life of zero and decay directions that would need growth are reported with clear messages instead of a broken number.

How to use Half-Life Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Choose what to find

    Pick remaining amount, initial amount, elapsed time or half-life from the mode buttons.

  2. 02

    Enter the known values

    Type the amounts and time values you have, choosing a unit for each time field; amounts use any consistent unit.

  3. 03

    Pick a result unit

    When solving for time or half-life, choose the unit you want the answer in; the calculator converts internally.

  4. 04

    Read the result

    The headline shows the requested value, and the summary gives half-lives elapsed, fraction remaining, decay constant and mean lifetime.

  5. 05

    Check the working

    The formula panel substitutes your numbers into the rearranged equation so each step can be followed by hand.

How this tool works

Works with
HALF-LIFE → AMOUNT
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • Models exponential decay with a constant half-life; mixtures of isotopes, biological clearance and non-exponential processes are not handled separately.
  • Decay only: solving for time or half-life requires a remaining amount strictly smaller than the initial amount.
  • One year is taken as 365.25 days and results are rounded to four significant figures; no uncertainty analysis is included.

Privacy and file handling

The amounts and times you enter are used only for the arithmetic in this browser tab. Nothing is uploaded, stored or logged, and the calculator makes no network request.

Read the full privacy policy

Half-Life Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
What is a half-life?
A half-life is the time needed for half of the atoms in a radioactive sample to decay, or more generally for an exponentially decaying quantity to fall to half its value. It is a property of the isotope or process, not of the sample size.
What is the half-life formula?
Remaining amount is N(t) = N₀ × (1/2)^(t/t½), where N₀ is the initial amount, t is the elapsed time and t½ is the half-life. Rearranging gives N₀ = N(t) × 2^(t/t½), t = t½ × log₂(N₀/N(t)) and t½ = t × ln 2 / ln(N₀/N(t)).
How do I convert a half-life to a decay constant?
The decay constant is λ = ln 2 / t½. It has reciprocal time units, so a half-life in years gives a decay constant per year. The mean lifetime is the reciprocal of λ, which equals t½ / ln 2 and is about 1.44 half-lives.
Can the half-life and the elapsed time use different units?
Yes. Both are converted to seconds internally, so a half-life in years can be combined with an elapsed time in days and the answer still comes out correctly. One year is taken as 365.25 days.
Why must the remaining amount be smaller than the initial amount?
This calculator models decay, where the amount decreases. If the remaining amount equals the initial amount, the decay time is infinite; if it is larger, the quantity is growing, which needs a different model such as doubling time or a growth rate.
Does it work for carbon dating?
Yes, as ordinary exponential decay: carbon-14 has a half-life of about 5,730 years and the same formula gives the remaining fraction after a given time. Radiocarbon dating also assumes a constant atmospheric ratio and a closed sample, which the calculator cannot verify.
Why is the remaining fraction not exactly 50 percent after one half-life?
It is 50 percent before rounding; the displayed percentage is rounded to a few decimal places, so a value very close to 50 can appear as 50 or 49.99 depending on the amounts entered. The exponential model itself is exact.

Background reading

Format guides that explain the trade-offs behind Half-Life Calculator.