Half-Life Calculator

Instantly calculate the half-life of a substance based on its decay rate. Visualize the exponential decay process.

Enter the decay rate (e.g., 0.1 for 10% per time period):

Decay rate should be between 0 and 1 (exclusive).

Half-Life:

Exponential Decay Chart

Understanding Half-Life

Half-life is the time required for a quantity to reduce to half of its initial value. In radioactive decay, it's the time it takes for half of the radioactive atoms in a sample to decay.

The formula to calculate half-life (t_1/2) from the decay rate (λ) is:

t_1/2 = ln(2) / λ ≈ 0.693 / λ

In our calculator, we use the decay rate as a fractional decrease per time period, so the formula is adapted to:

Half-life = log(0.5) / log(1 - Decay Rate)

This calculator is useful in various fields like nuclear physics, medicine (pharmacokinetics), and environmental science to understand decay processes.

Example Usage:

Medical Isotopes: Determine how long a radioactive tracer remains effective in a patient's body.
Carbon Dating: Estimate the age of ancient artifacts by measuring the remaining carbon-14.
Nuclear Waste: Understand how long nuclear waste remains hazardous.

Sources: Wikipedia - Half-life, Britannica - Half-life