Half-Life Calculator
Calculate radioactive or drug half-life. Solve for remaining quantity, initial amount, time elapsed, or half-life period using the exponential decay formula.
Solve for: Remaining
About Half-Life Decay
Half-life is the time required for a quantity to reduce to half of its initial value. This concept is commonly used in nuclear physics to describe radioactive decay, as well as in pharmacology to describe how drugs are metabolized by the body.
The Half-Life Formula
The general equation for exponential decay is:
N(t) = N₀(1/2)^(t / t½)
- N(t): Quantity remaining after time t.
- N₀: Initial quantity.
- t: Time elapsed.
- t½: Half-life of the substance.
Uses in Pharmacology
In medicine, half-life describes the time it takes for the concentration of a drug in the body to be reduced by 50%. This helps determine dosing schedules. For example, if a drug has a half-life of 8 hours, you might need to take it 3 times a day to maintain stable levels.
Uses in Radiocarbon Dating
Carbon-14 dating uses the half-life principle to determine the age of organic materials. Since the half-life of Carbon-14 is known (approx 5,730 years), measuring the remaining amount allows scientists to calculate how much time has passed since the organism died.
? Frequently Asked Questions
Yes! The calculator is unit-agnostic. As long as you keep your units consistent (e.g., if Half-Life is in hours, Time Elapsed must be in hours), the math works perfectly.
This is mathematically impossible for decay. The calculator will show an error. However, this formula works in reverse for exponential growth (doubling time) if you invert the logic, but this tool specifically calculates decay.
Technically, it never reaches exactly zero, but after 5 half-lives, roughly 97% of the substance is gone. After 10 half-lives, 99.9% is gone, which is often considered negligible.