Half Life Calculator
Calculate remaining amount, elapsed time, or half-life.
Exponential decay in four directions: find what is left, how long it took, the half-life itself, or the original amount. Any consistent amount unit works because the model depends only on the ratio N/N₀.
Decay constant and half-life are linked by λ = ln 2 / t½ ≈ 0.693 / t½.
How to Use the Half Life Calculator
1
Choose the unknown. Select remaining amount, elapsed time, half-life, or initial amount.
2
Enter the known values. Type the amounts in any consistent unit and the times with their unit — seconds through years.
3
Read the decay profile. The result reports the answer plus the number of half-lives elapsed, percent remaining, decay constant, and mean lifetime.
What is the Half Life Calculator?
The half life calculator works with the exponential decay relationship N = N0(1/2)^(t/t½) to find the remaining amount of a substance, the time elapsed, or the half-life itself. It applies to radioactive isotopes, first-order chemical reactions, and drug elimination alike.
Half-life problems reward setting up the ratio N/N0 correctly before touching logarithms. The calculator shows the number of half-lives elapsed as an intermediate value, making the exponential structure visible instead of hiding it inside one formula.
Common Uses
- Find remaining mass of a radioactive isotope
- Calculate elapsed time from a decay ratio
- Determine half-life from two measurements
- Model first-order reaction kinetics
How to Solve It by Hand
Manual calculation is still important: identify the known variables, convert units before substitution, apply the equation, and check whether the result is chemically reasonable. The most common mistakes are inconsistent units, constants rounded too early, and skipping the interpretation step.
Practice Prompt
Try changing the default values and ask the lower-right chemistry chat why the result increased or decreased. That turns the calculator from a number machine into a study loop.
N = N₀(1/2)^(t/t½), where N₀ is the starting amount, N is what remains after time t, and t½ is the half-life. Rearranged, the elapsed time is t = t½ × log₂(N₀/N).
λ = ln 2 / t½, roughly 0.693 divided by the half-life. The mean lifetime τ is 1/λ, which is longer than the half-life by a factor of 1/ln 2 ≈ 1.44.
One half-life leaves 50 percent, two leave 25 percent, three leave 12.5 percent, and ten leave under 0.1 percent. The fraction remaining is always (1/2)ⁿ regardless of the starting amount.
No. The model depends only on the ratio N/N₀, so grams, atom counts, becquerels, or concentration all work as long as you use the same unit for both values.
Yes. Any first-order process follows the same exponential law, including first-order reaction kinetics and first-order drug elimination in pharmacokinetics.