Half-Life Calculator

What is a Half-Life Calculator?

A Half-Life Calculator is a free online tool that computes radioactive decay parameters using the exponential decay formula. Given any three values (initial quantity, remaining quantity, elapsed time, or half-life), it instantly calculates the fourth. It also converts between half-life, mean lifetime, and decay constant. Combine it with our Radioactive Decay Calculator and Exponential Decay Calculator for deeper analysis.

How to Use the Half-Life Calculator

Select what to calculate - Choose from remaining quantity, initial quantity, time elapsed, or half-life.
Enter the known values - Input any three of the four parameters. The missing field will be grayed out.
View results instantly - The calculated value appears in the result panel along with the formula used. Converted values for mean lifetime and decay constant are also displayed.

The Half-Life Formula

The exponential decay formula is: Nt = N0 × (1/2)^t/T

Where:

Nt = Remaining quantity after time t
N0 = Initial quantity
t = Elapsed time
T = Half-life (t_1/2)

Half-Life, Mean Lifetime, and Decay Constant

These three constants are mathematically related:

Half-Life (t_1/2) - Time for a quantity to reduce to half its initial value
Mean Lifetime (τ) - Average time before a particle decays: τ = t_1/2 / ln(2)
Decay Constant (λ) - Probability of decay per unit time: λ = 1 / τ

Applications of Half-Life

Half-life calculations are used in radiometric dating (carbon-14 dating), nuclear medicine, radiation safety, pharmacology (drug elimination), environmental science, and materials science. Understanding half-life helps scientists determine the age of artifacts, calculate safe radiation exposure times, and determine drug dosing intervals.

Common Half-Life Examples

Carbon-14: 5,730 years
Uranium-238: 4.5 billion years
Iodine-131: 8.02 days
Technetium-99m: 6.01 hours
Radon-222: 3.82 days

Frequently Asked Questions

What is half-life?

Half-life is the time required for a quantity to reduce to half of its initial value. It is most commonly used in the context of radioactive decay, where it describes how quickly unstable atoms undergo radioactive decay.

How does carbon-14 dating work?

Carbon-14 dating uses the half-life of carbon-14 (5,730 years) to determine the age of organic materials. By measuring the remaining carbon-14 in a sample and comparing it to the expected initial amount, scientists can calculate when the organism died.

What units does this calculator use?

The calculator accepts any consistent unit for time and quantity. The half-life and time should use the same time unit (years, days, hours, etc.). Quantity values can be any unit (grams, atoms, percentage, etc.).

Can I calculate the time for a substance to decay completely?

In theory, radioactive decay is exponential and never reaches zero completely. After 10 half-lives, less than 0.1% of the original substance remains, which is often considered negligible for practical purposes.

What is the difference between half-life and mean lifetime?

Half-life (t½) is the time for half the atoms to decay, while mean lifetime (τ) is the average time an atom exists before decaying. They are related by the formula: τ = t½ / ln(2). The mean lifetime is about 1.44 times longer than the half-life.

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