Half Life Calculator
This half life calculator handles radioactive decay three ways: it'll find what's left of a sample, the half-life of an isotope, or how much time has passed. The half life formula it runs is N(t) = N0 × 0.5^(t/T½), and you'll watch the decay curve redraw the moment you type a number. Tap a preset for carbon-14, iodine-131, radium-226, or uranium-235, and you won't have to look up a half-life by hand. Every answer shows the equation with your numbers filled in, so you can check the working and learn how decay math fits together.
- Solve 3 ways
- Isotope presets
- Live decay curve
- Percent remaining
- Formula shown
Last updated June 18, 2026 Method: N(t) = N0 × 0.5^(t/T½) Reviewed by the Calcowa science team
Enter positive values to see the decay result.
N(t) = 100 × 0.5^(20/10) = 25 units
What is half-life?
Half-life is the time it takes for half of a radioactive sample to decay. It's written T½, and it stays the same no matter how much you start with. Begin with 100 atoms of an isotope whose half-life is 10 years, and after 10 years you'll have about 50, after 20 years about 25, after 30 years about 12.5, and so on.
That steady halving is what makes decay so handy for dating and dosing. Because the fraction left depends only on how many half-lives have gone by, you can read the clock backwards: measure what's left, count the half-lives, and you've got the elapsed time. The same idea isn't limited to atoms, since drugs and signals fade the same exponential way.
The half life formula explained
The half life formula for the amount remaining is N(t) = N0 × 0.5^(t/T½). The exponent t/T½ is just the number of half-lives that have passed, and raising one-half to that power tells you the surviving fraction. Two half-lives means 0.5² = 0.25, so a quarter is left.
You can flip that equation to chase a different unknown. To find the half-life from a measured drop, use T½ = t × ln2 / ln(N0/Nt). To find how long decay has run, use t = T½ × log₂(N0/Nt). It's the same relationship rearranged, and this calculator switches between the three forms based on what you've picked to solve for. If you want a refresher on raising numbers to a power, the exponent calculator breaks that step down.
N(t) = N0 × 0.5^(t/T½)
T½ = t × ln2 / ln(N0/Nt)
t = T½ × log₂(N0/Nt)
How to calculate the remaining amount
To find what's left after radioactive decay, divide the elapsed time by the half-life, then apply that count as a power of one-half. Here's the full sequence:
- 1
Note the starting amountWrite down N0, the quantity you began with, whether that means atoms, grams, or a dose.
- 2
Get the half-lifeUse the isotope's half-life T½, keeping it in the same kind of time unit as your elapsed time.
- 3
Count the half-livesDivide the elapsed time t by the half-life T½. That ratio is how many half-lives have passed.
- 4
Raise one-half to that powerCompute 0.5 to the power of t/T½. That's the fraction of the sample still left.
- 5
Multiply by the startMultiply N0 by that fraction to get the remaining amount N(t).
How to find the half-life from a measurement
If you know how much you started with, how much is left, and how long it took, you can solve for the half-life itself with T½ = t × ln2 / ln(N0/Nt). Say 100 units fall to 25 over 20 years. Then N0/Nt is 4, ln(4) is about 1.386, and T½ = 20 × 0.693 / 1.386, which lands on 10 years. Switch the tool to its Half-life mode and it does that division for you.
T½ = 20 × ln2 / ln(100/25) = 10 years
because two halvings turn 100 into 25
Radioactive decay and carbon dating
The biggest payoff of half-life math is dating things. Living matter holds a steady level of carbon-14, but once it dies the C-14 starts to decay with a half-life of 5,730 years. Measure how much is left, count the half-lives, and you've got an age. That's radiocarbon dating in a nutshell.
Medicine leans on the same curve. Iodine-131, with its 8-day half-life, fades fast enough to be useful for thyroid scans without lingering. Geologists stretch the idea across uranium-235's 703.8-million-year half-life to date rocks. For the chemistry side of measuring a sample's strength, our molarity calculator pairs well, and you'll find more tools in the chemistry hub.
Decay reference table
This table shows the fraction and percent of a sample left after each half-life, from 0 up to 10. When your elapsed time is a whole number of half-lives, the calculator highlights the matching row below, so you can read the percent remaining at a glance.
| Half-lives | Fraction left | Percent left |
|---|---|---|
| 0 | 1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.125% |
| 6 | 1/64 | 1.5625% |
| 7 | 1/128 | 0.78125% |
| 8 | 1/256 | 0.390625% |
| 9 | 1/512 | 0.195313% |
| 10 | 1/1024 | 0.097656% |
Frequently asked questions
Is half-life the same as average lifetime?
No. The half-life is the time for half the sample to decay, while the average (mean) lifetime is a bit longer, equal to the half-life divided by ln2 (about 1.443 times the half-life). They describe the same decay, just two different reference points along the curve.
The core half life formula for what's left after time t is N(t) = N0 × 0.5^(t/T½), where N0 is the starting amount and T½ is the half-life. Rearranged, you can solve for the half-life with T½ = t × ln2 / ln(N0/Nt), or for elapsed time with t = T½ × log2(N0/Nt). The calculator runs all three forms for you.
Measure how much you started with (N0) and how much is left (Nt) after a known time t, then plug them into T½ = t × ln2 / ln(N0/Nt). For example, if 100 units drop to 25 over 20 years, that's T½ = 20 × ln2 / ln(4), which works out to 10 years. Pick the Half-life mode in the tool and it'll do that division for you.
Carbon-14 has a half-life of about 5,730 years. That's the value radiocarbon dating leans on. Tap the C-14 preset chip and the tool fills in 5730 years, so you can work out how old a sample is from how much C-14 it still holds.
Strictly, it never reaches exactly zero, because each half-life only cuts the amount in half. After 10 half-lives you're down to roughly 0.1% of the start, and most people treat that as effectively gone. The decay table on this page shows the fraction left at every step from 0 to 10.
Each atom has the same fixed chance of decaying in any given moment, so the more atoms you've got, the more decays happen per second. As the count drops, the decay rate drops with it. That self-slowing pattern is what gives you a curve instead of a straight line, and it's why the formula uses a power of one-half.
Yes. The same math describes how a drug clears from the body or how a medical isotope like I-131 fades. Enter the dose as N0, the drug's half-life as T½, and the time since the dose as t, and you'll see how much is left. It's an estimate, not medical advice, so don't use it for dosing decisions.
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Need a quick decay answer?
Try the half life calculator above, or browse every tool in the chemistry hub.