Watch how much is left after decay.
Enter a starting amount, the half-life, and how much time has passed to see exactly what remains, how many half-lives elapsed, and the full decay curve.
Your numbers
What this means
The decay curve
Amount after each half-life
| Half-lives | Elapsed time | Remaining | % remaining |
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Half-life, explained
What Is Half-Life?
Half-life is the time required for a quantity to reduce to half its initial value. It is most commonly associated with radioactive decay but applies to any exponential decay process, drug metabolism, chemical reactions, and even depreciation. The formula is N(t) = N₀ × (1/2)^(t/t½).
How to Calculate Remaining Amount
To find the remaining amount after time t: divide elapsed time by the half-life to get the number of half-lives (n = t / t½), then multiply the initial amount by (1/2)^n. For example, 100g with a 5-year half-life after 15 years: n = 3, remaining = 100 × (1/2)³ = 12.5g.
Half-Life in Medicine
In pharmacology, half-life determines how often you need to take medication. A drug with a 4-hour half-life needs more frequent dosing than one with a 24-hour half-life. Doctors use half-life to calculate when a drug reaches steady state (about 5 half-lives) and when it is effectively eliminated from the body.
Radioactive Decay Applications
Carbon-14 has a half-life of 5,730 years, enabling radiocarbon dating of archaeological artifacts. Uranium-238 (4.5 billion years) dates geological formations. Medical isotopes like Technetium-99m (6 hours) are used in imaging because they decay quickly, minimizing radiation exposure.
Common questions
Does the substance ever fully decay to zero?
Mathematically, exponential decay never reaches zero, it approaches it asymptotically. Practically, after about 10 half-lives, less than 0.1% remains, which is often considered negligible.
Can half-life change?
For radioactive decay, half-life is a fixed physical constant unaffected by temperature, pressure, or chemical state. For biological or chemical processes, half-life can vary with conditions like temperature, pH, or enzyme activity.
What is the difference between half-life and decay constant?
The decay constant (λ) is related to half-life by t½ = ln(2) / λ ≈ 0.693 / λ. The decay constant represents the probability of decay per unit time, while half-life is the time for half the material to decay.
How many half-lives until a substance is considered safe?
A common guideline is 10 half-lives, after which about 99.9% has decayed. For medication, 5 half-lives (about 97% eliminated) is the standard rule for clearance from the body.
Estimates only. This models ideal exponential decay; real biological or chemical processes can vary with temperature, pH and other conditions.