Half-Life Calculator
This calculator solves the exponential decay law N = N0 times one half raised to t over T. Give it any three of the starting amount, remaining amount, half-life and elapsed time and it finds the fourth, then reports the decay constant and how many half-lives have passed. Every field shares whatever unit you choose, so it works for grams, atom counts, becquerels or a plain percentage.
How to use the half-life calculator
- Open the 'Solve for' menu and pick the unknown: initial amount, remaining amount, half-life or elapsed time.
- The chosen value drops out of the inputs, leaving three number fields to fill in.
- Enter the half-life and elapsed time in one shared time unit, such as years, minutes or seconds.
- Enter the initial and remaining amounts in one shared quantity unit; the two just have to match each other.
- Read the highlighted answer along with the decay constant and the number of half-lives elapsed.
- Click Copy to grab N0, N, half-life, time and the decay constant as plain text.
Examples
Carbon-14 remaining after one half-life
Solve for remaining: N0 = 100, half-life = 5730 yr, time = 5730 yr
Remaining = 50, decay constant = 0.000120968 per yr, 1 half-life elapsed
Radiocarbon age from remaining C-14
Solve for elapsed time: N0 = 100, remaining = 25, half-life = 5730 yr
Time = 11460 yr, 2 half-lives elapsed
Measure a half-life from a decay run
Solve for half-life: N0 = 1000, remaining = 125, time = 30 min
Half-life = 10 min, decay constant = 0.069314718 per min, 3 half-lives
Frequently asked questions
What is the half-life formula?
The amount remaining is N = N0 times one half raised to the power of time divided by half-life, written N = N0 * (1/2)^(t/T). The calculator rearranges this same equation to solve for whichever of the four quantities you leave blank.
What is the decay constant it reports?
The decay constant lambda equals the natural log of 2 divided by the half-life, lambda = ln(2)/T. It is the fractional decay rate per unit time, so a half-life of 5730 years gives lambda near 0.000120968 per year.
Does it work with any units?
Yes. There are no built-in units at all. As long as the half-life and elapsed time share one time unit, and the initial and remaining amounts share one quantity unit, the answer comes out in those same units.
How does it find an elapsed time or a half-life?
It inverts the decay law with logarithms: t = T times log base 2 of N0 over N, and T = t times ln(2) divided by ln(N0 over N). That is why the remaining amount must be a positive number smaller than the initial amount for those two modes.
Can I use it for non-radioactive decay?
Yes. Any quantity that halves over a fixed period follows the same law: a drug clearing the bloodstream, a capacitor discharging, or a reverberation fading. Substitute your own half-life and the math is identical.
What inputs are rejected?
Amounts and times cannot be negative, the half-life must be greater than zero, and when solving for time or half-life the remaining amount must be strictly less than the initial amount. Otherwise the tool shows a short message instead of a number.
How many half-lives until almost nothing is left?
After 10 half-lives about 0.098 percent remains, and after 20 half-lives under one part per million. Each half-life removes half of what is left, so the curve keeps shrinking but never reaches exactly zero.
Does this model radioactive dating accurately?
The exponential math is exact, but real dating also depends on calibration curves, contamination and measurement error. Treat the number as the ideal decay age, not a lab-grade date with its uncertainty.
Is my data private?
Yes. The calculation runs entirely in your browser with JavaScript. Nothing you type is uploaded, logged or sent to a server.
Learn more
- Radioactive decay, half-life and carbon dating
How exponential decay works, what a half-life really measures, and how carbon-14 turns leftover atoms into an age estimate.
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