Half-Life Calculator
Use the half-life formula N(t) = N₀ × (½)t/t½ to solve for any variable in a radioactive decay problem. Choose what you want to calculate, fill in the known values, and click Calculate.
Solve for:
In any unit (g, kg, atoms, %). Must match N₀ units.
Common isotope half-lives:
Results
Remaining (N)
Initial (N₀)
Elapsed Time (t)
Half-Life (t½)
What Is Radioactive Decay and Half-Life?
Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. The half-life (t½) is the time it takes for half of a given quantity of a radioactive substance to decay. It is a constant characteristic of each radioactive isotope — it does not depend on temperature, pressure, or the amount of substance present.
The governing formula is:
N(t) = N₀ × (½)t / t½
where N(t) is the remaining quantity after time t, N₀ is the initial quantity, and t½ is the half-life. An equivalent form uses the decay constant λ = ln(2) / t½:
N(t) = N₀ × e−λt
Common Half-Life Examples
- Carbon-14 (¹⁴C): 5,730 years. Used in radiocarbon dating of organic materials up to ~50,000 years old.
- Iodine-131 (¹³¹I): 8.02 days. Used in thyroid cancer treatment; short half-life limits radiation exposure.
- Uranium-238 (²³⁸U): 4.47 billion years. Used in uranium-lead dating to determine the age of rocks and meteorites.
- Strontium-90 (⁹⁰Sr): 28.8 years. A fission product and environmental concern from nuclear fallout.
- Radium-226 (²²⁶Ra): 1,600 years. Historically important; discovered by Marie Curie.
How to Use This Calculator
- Select what you want to solve for (remaining amount, initial amount, elapsed time, or half-life).
- Enter values for the three known quantities. Use the unit dropdowns for time fields.
- Both time values (elapsed time and half-life) must use the same unit. The calculator automatically converts them to a common unit before solving.
- Click Calculate to see the result. The detail section shows the decay fraction and number of half-lives elapsed.
Half-Life and Significant Figures
When working with half-life problems in chemistry or physics classes, pay attention to significant figures in your answer. Our Significant Figures Calculator can help you round a result to the correct number of sig figs. For calculations involving moles and chemical amounts, the Molar Mass Calculator provides molar masses of radioactive compounds.
Frequently Asked Questions
Can I use different units for elapsed time and half-life?
Yes — select any time unit from the dropdowns for each field. The calculator normalizes both to the same base unit (seconds) internally before computing, then displays the result in the unit you selected for the solved-for quantity.
What is the decay constant (λ)?
The decay constant λ is related to half-life by λ = ln(2) / t½ ≈ 0.693 / t½. It represents the probability per unit time that a given nucleus will decay. The activity (disintegrations per second) of a sample equals λ × N.
Does half-life change with temperature or pressure?
No. Unlike chemical reaction rates, the half-life of a radioactive isotope is determined by nuclear forces and is essentially constant under any conditions you would encounter in a lab. It does not depend on chemical bonding, temperature, or pressure.
How is radiocarbon dating related to half-life?
Living organisms continuously absorb Carbon-14 (produced in the atmosphere by cosmic ray bombardment of nitrogen). When an organism dies, it stops absorbing C-14, and the remaining amount decays with a half-life of 5,730 years. By measuring the current ratio of C-14 to C-12, scientists can estimate when the organism died — up to about 50,000 years ago.
What happens after many half-lives?
After each half-life, half of the remaining amount decays. After 10 half-lives, only (½)¹⁰ ≈ 0.098% of the original amount remains. In nuclear medicine and radiation safety, materials are often considered safe after 10 half-lives, by which point less than 0.1% of the radioactive isotope remains.
