Half-Life Calculator
Radioactive decay — N(t) = N₀ × (½)^(t/t½)
Remaining (N)
25.000000
% Remaining
25.0000%
Amount Decayed
75.000000
Half-lives elapsed
2.000
Decay constant λ
0.00012097
What is the Half-Life Calculator?
Half-life is the time it takes for half of a substance to decay or break down. It's used in nuclear physics, radiocarbon dating, pharmacology (how fast a drug clears your system), and even finance. This calculator works for any exponential decay situation where you know the half-life. CalciHub's version lets you calculate the remaining quantity after a given time, or figure out how long it'll take to reach a certain level.
How Does It Work?
Every half-life period, the amount of substance drops by half. This follows an exponential decay curve, not a straight line. The formula accounts for how many half-life cycles fit into the time period you're looking at.
N(t) = N₀ × (1/2)^(t / t½)
• N(t) = Remaining quantity at time t
• N₀ = Initial quantity
• t = Time elapsed
• t½ = Half-life (in the same time unit as t)
How to Use CalciHub's Half-Life Calculator
1. Enter the initial quantity of the substance.
2. Enter the half-life value and its time unit (seconds, minutes, hours, years, etc.).
3. Enter the total elapsed time in the same unit.
4. Click Calculate to get the remaining amount.
Tip: Make sure your elapsed time and half-life are in the same units. Mixing hours and days without converting will give wrong results.
A Quick Example
A medical imaging technician is working with Technetium-99m, a radioactive tracer with a half-life of 6 hours. They start with 400 mg and need to know how much remains after 24 hours.
• N₀ = 400 mg
• t½ = 6 hours
• t = 24 hours
• Number of half-lives = 24 / 6 = 4
• N(t) = 400 × (1/2)^4 = 400 × 0.0625 = 25 mg
After 24 hours, only 25 mg of the original 400 mg remains, that's four halvings, which explains why short-half-life isotopes are preferred in medical imaging: they decay quickly and limit the patient's radiation exposure.
Frequently Asked Questions
No. After one half-life, half remains. After two, a quarter remains. The decay is exponential, so the substance technically never reaches exactly zero — it just gets smaller and smaller.
Yes. In pharmacology, drug half-life describes how quickly your body eliminates a medication. After about 5 half-lives, roughly 97% of the drug has cleared from your system — which is why doctors use that as a rule of thumb for washout periods.
It comes down to the stability of the nucleus. Some isotopes are only mildly unstable and decay slowly (uranium-238 has a half-life of 4.5 billion years). Others are extremely unstable and decay almost instantly.
Yes. Half-life is a fixed property of the substance, not the quantity. Whether you start with 1 gram or 1,000 grams of the same isotope, the half-life stays the same.
A common rule of thumb is ten half-lives, which leaves under a tenth of a percent of the original. Strictly it never reaches zero, so safety is judged against a threshold rather than complete disappearance. What counts as safe depends on the isotope and how it is contained.
Before you rely on this result
These apply idealised relationships and assume every input is in consistent units. Real systems include effects the formula omits, so treat the result as the textbook answer rather than a measurement.
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