Half-Life Calculator

Use this half-life calculator to determine the remaining amount or elapsed time for radioactive substances, drugs, or other materials that follow exponential decay.

Half-Life Calculator

Enter the initial amount, half-life, and other parameters, then click Calculate to see the result with step-by-step solution.

Result

What is Half-Life?

Half-life is the time required for a quantity of a substance (such as a radioactive isotope, a drug, or other material following exponential decay) to reduce to half of its initial value.

For radioactive substances, half-life is an intrinsic physical property that is not affected by external conditions like temperature or pressure. Each radioactive isotope has its specific half-life, ranging from microseconds to billions of years.

Half-Life Formula

Half-life calculations use the exponential decay formula:

N(t) = N₀ × e(-λt)

Where N(t) is the quantity at time t, N₀ is the initial quantity, λ is the decay constant, and t is the elapsed time.

λ = ln(2) / T1/2

The decay constant λ is related to the half-life T₁/₂ by: λ = ln(2) / T₁/₂

Applications of Half-Life

  • Radioactive Measurements: Used to measure the decay rate of radioactive materials, such as monitoring nuclear fuel in power plants.
  • Nuclear Medicine: Using radioactive isotopes in medical imaging and radiation therapy, such as iodine-131 for thyroid disorders.
  • Archaeology and Dating: Using radioactive isotopes like carbon-14 to determine the age of ancient organic materials.
  • Drug Metabolism: Calculating the rate at which drugs are metabolized in the body, helping determine dosing frequency and amount.

How to Use This Calculator

  1. Enter the initial amount (in any units).
  2. Enter the half-life value and select the time unit (years, days, hours, etc.).
  3. Choose the calculation type: Calculate Remaining Amount (enter time) or Calculate Elapsed Time (enter remaining amount).
  4. Click 'Calculate' to see the result and detailed step-by-step explanation.