The half-life calculator computes remaining amount after radioactive decay using N = N₀ × (½)^(t/t½). Enter initial amount, half-life, and elapsed time. Works with any units for amount — grams, moles, atoms, or activity units.
Half-Life Calculator
How to Use the Half-Life Calculator
The half-life calculator uses N(t) = N₀ × (½)^(t/t½) to find remaining radioactive material after any elapsed time.
Common Isotopes
Use the preset buttons for common isotopes: Carbon-14 (5730 yr, archaeological dating), Iodine-131 (8 days, medical treatment), Technetium-99m (6 hours, diagnostic imaging), Radium-226 (1600 yr, historical applications).
Example: Carbon Dating
A wood sample has 40% of its original C-14 remaining. How old is it? t = t½ × log₂(N₀/N) = 5730 × log₂(1/0.4) = 5730 × 1.322 = 7,574 years old.
Mixed Time Units
Half-life and elapsed time can use different units (e.g., half-life in years, elapsed in days). The calculator converts to the same base unit before computing.
FAQ
What is the half-life formula?
The radioactive decay formula is N(t) = N₀ × (½)^(t/t½), where N₀ is the initial amount, t is elapsed time, t½ is the half-life, and N(t) is the remaining amount. Equivalently, N(t) = N₀ × e^(-λt) where λ = ln(2)/t½ is the decay constant.
What are some common half-lives?
Carbon-14: 5,730 years (used for dating organic material). Uranium-238: 4.47 billion years. Radium-226: 1,600 years. Iodine-131: 8.02 days (used in thyroid treatments). Technetium-99m: 6.01 hours (medical imaging). Polonium-214: 1.64 × 10⁻⁴ seconds.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
How is half-life used in carbon dating?
Carbon-14 forms in the atmosphere at a roughly constant rate and is absorbed by living organisms. When an organism dies, C-14 decays with a 5,730-year half-life. By measuring the ratio of C-14 to C-12, we can estimate how many half-lives have passed — and thus the age of the sample up to ~50,000 years.