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About This Calculator
Half-life describes the time required for a quantity to reduce to half its initial value, a concept critical in nuclear physics, pharmacology, and chemistry. This calculator determines remaining quantity after a given time, the number of half-lives elapsed, or the initial amount from current measurements. Medical professionals use half-life calculations daily to determine proper drug dosing intervals and clearance times.
Quick Tips
- 1 After 7 half-lives, less than 1% of the original substance remains.
- 2 Drug half-life determines dosing frequency — shorter half-life means more doses.
- 3 Radioactive half-lives range from fractions of a second to billions of years.
Example Calculation
500mg dose of medication with a 6-hour half-life, after 18 hours.
Remaining: 62.5mg | After 3 half-lives: 500 > 250 > 125 > 62.5mg | 87.5% eliminated
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.
Frequently Asked Questions
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.
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.
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.
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.