Half-Life Calculator
Calculate radioactive decay, remaining quantity, or elapsed time using the half-life formula.
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Half-Life Formula
N(t) = N₀ × (1/2)^(t/t½) or equivalently N(t) = N₀ × e^(−λt) where λ = ln(2)/t½. Carbon-14 has a half-life of 5,730 years — used in radiocarbon dating. Iodine-131 (used in thyroid treatment) has a half-life of ~8 days.
What is the Half-Life Calculator?
The Half-Life Calculator measures the rate of exponential decay. It is widely used in nuclear physics to track radioactive isotope degradation, in pharmacology to measure drug clearance in the human body, and in radiocarbon dating.
How It Works (Formula)
The "Half-Life" ($t_{1/2}$) is the time it takes for a quantity to reduce to exactly half of its initial value. The calculator utilizes the standard exponential decay formula, incorporating the natural base $e$ and a negative decay constant ($\lambda$).
$$ N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} $$
The fundamental equation for determining exponential half-life decay.
How to Use It
You can solve for any missing variable. Simply input three known values (like Initial Quantity, Remaining Quantity, and Elapsed Time), and the tool will instantly calculate the specific Half-Life rate of your substance.