Half-Life Calculator
Exponential decay, made concrete.
Half-Life Calculator
N(t) = N₀ × (1/2)^(t / t½)
Calculated instantly
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What This Calculator Does
The Half-Life Calculator projects exponential decay: how much of a substance remains after a chosen time, how much has decayed, and how many half-lives have elapsed. The units are yours to choose, as long as the half-life and elapsed time match.
How It Works
Every half-life reduces the remaining amount by half. The number of half-lives is elapsed time divided by the half-life, and the remaining fraction is one half raised to that power. Because the exponent is continuous, the formula also works for fractional half-lives.
Example
Start with 100 units of a substance with a 5-day half-life and wait 10 days. Two half-lives have passed, so 100 × (1/2)² = 25 units remain and 75 have decayed. Waiting 15 days would leave 12.5 units.
Formula
N(t) = N₀ × (1/2)^(t / t½)n = t / t½Decayed = N₀ − N(t)Reading the Results
Amount remaining
The quantity left after the elapsed time, in whatever unit you entered as the initial amount. It approaches zero without ever reaching it.
Half-lives elapsed
The exponent that drives the decay. Each whole number halves the amount again, so the first few half-lives remove most of the material.
Sources and References
IUPAC — Compendium of Chemical Terminology (Gold Book)
Definition of half-life
Defines half-life as the time for the concentration or amount to fall to half its initial value.
NIST — Guide for the Use of the International System of Units (SP 811)
Units for time and activity
Clarifies the unit conventions used for decay rates and elapsed time.
References identify the method or data behind this calculator. Where a standard or tariff changes, the current edition applies, and the assumptions stated above take precedence over a remembered figure.
Frequently Asked Questions
Does the amount ever reach zero?
Mathematically no. Exponential decay approaches zero asymptotically. In practice, once only a few atoms remain, the statistical model gives way to individual random events.
What is the difference between half-life and mean life?
Mean life is the average lifetime of an atom, equal to the half-life divided by the natural logarithm of 2, about 1.44 times longer. Half-life is the more commonly reported figure.
Can I use this for drug clearance or carbon dating?
Yes, both follow first-order exponential decay. Carbon dating uses a half-life of about 5,700 years for carbon-14; drug clearance uses a biological half-life that assumes first-order elimination.
Why does the calculator not ask for a decay constant?
The half-life already encodes it: the decay constant is ln(2) divided by the half-life. Entering either one is enough, and half-life is the form most data sources report.