Radioactive Decay After One Half-Life
If a sample starts at 100 units and one half-life has passed, half of the material remains.
N(t) = 100 × (1/2)^1
Result: 50 units remain
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
- 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.
Tip: use consistent units for half-life and elapsed time, otherwise the decay calculation will be interpreted incorrectly.
Half-Life Examples
Two Half-Lives Later
After two half-lives, the remaining quantity is one quarter of the original amount.
N(t) = 80 × (1/2)^2
Result: 20 units remain
Finding Elapsed Time
If 25 units remain from an initial 100 units, the material has passed through two half-lives.
25 / 100 = 1/4 = (1/2)^2
Result: elapsed time = 2 half-lives
Drug Clearance Estimate
Half-life calculations are often used to estimate how much of a medication remains in the body after several hours or days.
Remaining amount = initial amount × e^(-λt)
Result: helps estimate dosing intervals
Half-Life Calculator FAQ
What does half-life mean?
Half-life is the time required for a quantity to decrease to half of its original value under exponential decay.
What materials use half-life calculations?
Half-life calculations are common for radioactive isotopes, medications, chemical decay, and other processes that follow exponential reduction.
Why does the amount never instantly reach zero?
Exponential decay continuously reduces the quantity by proportion, so the remaining amount approaches zero over time rather than dropping to zero all at once.
Can this calculator find time as well as remaining amount?
Yes. Depending on the selected mode, it can calculate either the remaining quantity after a given time or the elapsed time needed to reach a target remaining amount.