Half-Life Calculator
Choose what you want to find: the amount left after a time, the time needed to fall to a given amount, the half-life from two measurements, or the starting amount from what remains. The calculator also gives the decay constant, the mean lifetime, the share lost per unit of time and a table of the amount left after each half-life. The unit of time is up to you. Everything runs in your browser.
| Half-lives | Time (years) | Amount left | Fraction |
|---|---|---|---|
| 0 | 0 | 100 | 1 |
| 1 | 5730 | 50 | 1/2 |
| 2 | 11460 | 25 | 1/4 |
| 3 | 17190 | 12.5 | 1/8 |
| 4 | 22920 | 6.25 | 1/16 |
| 5 | 28650 | 3.125 | 1/32 |
| 6 | 34380 | 1.5625 | 1/64 |
| 7 | 40110 | 0.78125 | 1/128 |
| 8 | 45840 | 0.390625 | 1/256 |
| 9 | 51570 | 0.195313 | 1/512 |
| 10 | 57300 | 0.0976563 | 1/1,024 |
The half-life is the time for a quantity to fall to half its value, and after t the amount left is the starting amount times one half to the power of t divided by the half-life. The decay constant is the natural log of 2 divided by the half-life, and the mean lifetime is the half-life divided by the natural log of 2, about 1.4427 half-lives. The same maths covers radioactive decay and any quantity that falls by a fixed share per unit of time. The presets are example values. Real decay of a single atom is random, and the formula describes large numbers of atoms. The unit box only labels the results. Everything is worked out in your browser.
Related Tools
[5 suggestions]Doubling Time and Rule of 72 Calculator
Find how many years it takes money or any quantity to double, triple or reach any multiple, compare with the rule of 72, and find the rate you need.
Math & MoneyLogarithm Calculator
Calculate a logarithm to any base, plus the common, binary and natural logs, antilogarithms and the change of base working.
Student ToolsScientific Notation Converter
Convert a number to scientific, engineering, E and standard notation, round to significant figures and see the SI prefix, with every digit kept exact.
Student ToolsCompound Interest Calculator
See how a starting amount and monthly deposits grow with compound interest, year by year, with the effective annual rate.
Math & MoneyCAGR Calculator
Find the compound annual growth rate between two values, the value after growing at a rate, or the time to reach a target, with the doubling time and rule of 72.
Math & MoneyAbout the Half-Life Calculator
A half-life is the time it takes for a quantity to fall to half its value. After a time t, the amount left is the starting amount times one half to the power of t divided by the half-life, so after 3 half-lives one eighth remains and after 10 half-lives 1/1,024 remains, about 0.1%. The decay constant, lambda, is the natural logarithm of 2 divided by the half-life, and the mean lifetime is the half-life divided by the natural logarithm of 2, about 1.4427 half-lives. To find the time to reach a final amount, the calculator uses half-life times the natural log of the ratio of start to end, divided by the natural log of 2, and to find a half-life from two measurements it inverts the same formula. For example, with a half-life of 5,730 years, the figure for carbon-14, 50,000 years leaves about 0.2362% of the original. The same relationship applies to radioactive decay, the elimination of a drug from the body when it follows first-order kinetics, and any other quantity that falls by a fixed share per unit of time. The preset half-lives are examples, and real values depend on the substance and the person. Decay of a single atom is random, and the formula describes the average over many atoms.
What is a half-life?▾
It is the time it takes for a quantity to fall to half of its value. After one half-life half remains, after two a quarter, after three an eighth, and so on, whatever the starting amount.
How do I calculate the amount left after a time?▾
Multiply the starting amount by one half raised to the power of the time divided by the half-life. With a half-life of 10 days, 100 grams leaves 25 grams after 20 days.
How do I find a half-life from two measurements?▾
Multiply the elapsed time by the natural log of 2 and divide by the natural log of the starting amount over the amount left. If 100 falls to 25 in 20 days, the half-life is 10 days.
What is the decay constant?▾
It is the natural log of 2 divided by the half-life, the fraction of the quantity that decays per unit of time in the continuous form of the equation. The mean lifetime is its reciprocal.
Is my data uploaded?▾
No. The calculation runs in your browser and nothing you enter is sent anywhere.