Half-life calculator
Choose the unknown, fill in the other three values and read the answer. Time and half-life share one unit that you pick below. The amounts can be in any unit, as long as the starting and remaining amounts use the same one.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose the unknown: amount remaining, starting amount, elapsed time or half-life.
- Fill in the other values and pick the time unit.
- Read the answer and the extra lines: half-lives elapsed, percent remaining and the decay constant.
How it works
Each half-life halves the amount, so after t the fraction left is (1/2)^(t/T½). Solving for time gives t = T½ × log₂(N₀/N), and for half-life T½ = t × ln 2 ÷ ln(N₀/N).
Worked example
Starting from 100 units with a half-life of 5 years, after 15 years there are 100 × (1/2)³ = 12.5 units left. Carbon-14 with a half-life of about 5,730 years falls to 25 percent after 11,460 years.
Tips
- Time and half-life must use the same unit; the unit selector applies to both.
- The half-life of a real isotope is a measured value; look it up in a reliable source.
Frequently asked questions
What is the half-life formula?
N = N₀ × (1/2)^(t ÷ T½). After one half-life half remains, after two a quarter, after three an eighth. Equivalently N = N₀ × e^(−λt) with λ = ln 2 ÷ T½.
How do I find the time for a given amount to decay?
Choose Elapsed time and enter the starting amount, the remaining amount and the half-life. The time is T½ × log₂(N₀ ÷ N). For example, 80 falling to 10 is three halvings, so 3 half-lives.
Can I use it for things other than radioactivity?
Yes, any process that decays exponentially with a constant relative rate fits: a drug cleared from the body, a chemical reaction of first order, or a charge draining from a capacitor if you use the time constant carefully.
Why does the decay constant depend on the unit?
The constant λ is a rate per unit of time, so it is shown per the unit you pick. A 5-year half-life gives 0.1386 per year; the same decay in days gives a much smaller number per day.