Half-Life Calculator
Calculate the half-life of a radioactive substance or drug from initial and final amounts over time. Free physics calculator with decay curves and step-by-step results.
About This Calculator
The Half-Life Calculator determines the half-life of a substance given the initial amount, final amount, and elapsed time. This is essential for radioactive decay analysis, pharmacokinetics, and nuclear physics.
Half-life is calculated using the exponential decay formula: t1/2 = t x ln(2) / ln(N0/N). The calculator also computes the decay constant lambda = ln(2)/t1/2 and the remaining fraction as a percentage.
Applications of Half-Life
Half-life is used across multiple disciplines: nuclear physics for radioactive isotope characterization, pharmacology for drug clearance rates, environmental science for pollutant persistence, and archaeology for radiocarbon dating.
Frequently Asked Questions
What is half-life?
Half-life (t1/2) is the time required for a quantity to reduce to half its initial value. It is used in nuclear physics, chemistry, and pharmacology to describe exponential decay processes.
How do you calculate half-life?
t1/2 = t x ln(2) / ln(N0/N), where N0 is the initial amount, N is the final amount, and t is the elapsed time. This formula is derived from the exponential decay law N = N0 x (1/2)^(t/t1/2).
What is the half-life of common isotopes?
Carbon-14: 5,730 years, Uranium-238: 4.47 billion years, Iodine-131: 8 days, Technetium-99m: 6 hours, Radon-222: 3.8 days, Cobalt-60: 5.27 years.
What is the decay constant?
The decay constant lambda = ln(2)/t1/2 represents the probability of decay per unit time. It is directly related to half-life: a shorter half-life means a larger decay constant.
How is half-life used in medicine?
In nuclear medicine, half-life determines how long radioactive tracers remain active for imaging (e.g., ^9^9ᵐTc, 6h) and how quickly radiation exposure decreases. In pharmacology, drug half-life determines dosing intervals.