About the Half-Life Calculator
A half-life calculator works out how much of a quantity remains after a given time, given the time it takes to halve. Exponential decay describes radioactive isotopes, drug clearance from the body, carbon dating, and any process where a fixed proportion is lost per unit time.
The formula
N(t) = N₀ · (1/2)^(t / t½)N₀ is the starting quantity, t the elapsed time, and t½ the half-life. The exponent counts how many half-lives have passed, and each one halves what remains.
How to use this calculator
- 1Enter your Initial Quantity. The field starts at
1000, which you can overwrite. - 2Enter your Half-Life (any time unit). The field starts at
5730, which you can overwrite. - 3Enter your Elapsed Time (same unit). The field starts at
11460, which you can overwrite. - 4Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Initial Quantity | 1000 |
| Half-Life (any time unit) | 5730 |
| Elapsed Time (same unit) | 11460 |
Result
Remaining Quantity: 250.0000
Decayed Amount: 750.0000
Percent Remaining: 25.0000%
Number of Half-Lives: 2.00
Decay Constant (λ): 1.2097e-4
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Decay is proportional, not linear, which is the key idea. After one half-life half remains, after two a quarter, after three an eighth. It never reaches exactly zero mathematically, but after ten half-lives less than a thousandth is left, which is why clinicians treat a drug as cleared after roughly five half-lives.
Half-lives span an extraordinary range and that range is what makes them useful. Carbon-14 halves every 5,730 years, which suits archaeological dating up to about 50,000 years. Iodine-131 halves in eight days, making it usable in medicine without leaving long-lived contamination. Uranium-238 takes 4.5 billion years, which is how the age of the Earth was determined.
Things worth knowing
- Elapsed time and half-life must be in the same units. Mixing years with days is the most common error.
- The fraction remaining after n half-lives is (1/2)ⁿ, regardless of the starting amount.
- The decay constant λ relates to half-life as λ = ln 2 / t½ ≈ 0.693 / t½.
- Drug half-life determines dosing intervals; steady state is reached after about five half-lives of regular dosing.
- Carbon dating becomes unreliable past roughly ten half-lives, when too little carbon-14 remains to measure.
Frequently asked questions
What does half-life mean?+
The time for half of a quantity to decay or be eliminated. It is constant for a given substance regardless of how much you start with — a defining property of exponential decay.
How much remains after several half-lives?+
Half after one, a quarter after two, an eighth after three, and so on. After ten half-lives roughly 0.1 percent remains, which is why that is often treated as effectively complete.
How does carbon dating use half-life?+
Living things absorb carbon-14 at a known rate and stop at death. Measuring how much remains against its 5,730-year half-life gives the time since death, reliably up to about 50,000 years.
Does half-life apply to medicines?+
Yes, and it drives dosing schedules. A drug with a six-hour half-life needs more frequent dosing than one with a 24-hour half-life to maintain a therapeutic level in the bloodstream.