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