Half-Life Calculator
Find how much of a substance remains after a given time using its half-life.
Example
Start with 100 mg of a substance whose half-life is 5 hours. After 10 hours:
half-lives = 10 / 5 = 2
remaining = 100 x (1/2)^2 = 100 x 0.25 = 25 mg
percent = 25%
How it works
Enter the initial amount, the half-life, and the elapsed time (using the same time unit for both). The remaining quantity is N0 x (1/2)^(time / half-life).
Good to know
This Half-Life Calculator works out how much of a decaying substance is left after a stretch of time, using the exponential decay law remaining = N0 x (1/2)^(time / half-life). You enter three numbers — the starting amount, the half-life, and how much time has passed — and it instantly returns the remaining amount, the percent remaining, the amount that has decayed, and how many half-lives have elapsed. It's handy for chemistry and physics students, pharmacology and nursing learners modeling drug clearance, and anyone curious about radioactive isotopes, carbon dating, or any quantity that halves on a fixed schedule.
Reach for it whenever something shrinks by a constant fraction over equal time intervals rather than by a fixed amount. The single most important rule is unit consistency: the half-life and the elapsed time must be expressed in the same unit. If a drug's half-life is 6 hours, enter the elapsed time in hours too; mixing hours with days will silently give a wrong answer because the tool only divides the two numbers, it doesn't convert between units.
To read the result, focus on the "Half-lives elapsed" figure — it's the elapsed time divided by the half-life, and it tells the whole story. One half-life leaves 50%, two leave 25%, three leave 12.5%, and so on; non-whole values are perfectly valid and just land between those marks. Notice that the percent remaining never changes if you alter only the initial amount, because the fraction left depends solely on time and half-life — the starting quantity merely scales the absolute number.
- Tip: to find a "how long until X% is left" answer, this tool runs forward (amount from time), so adjust the elapsed time up or down until the percent remaining matches your target, or solve time = half-life x log2(N0 / remaining) by hand. Also remember this is a smooth mathematical model — for biological half-lives, actual clearance varies by individual, so treat the output as an estimate, not medical guidance.
Frequently asked questions
What time unit should I use?
Any unit works as long as the half-life and the elapsed time use the same one. If the half-life is in hours, enter the elapsed time in hours too.
Why is the percent remaining independent of the initial amount?
The fraction remaining is (1/2)^(time/half-life), which only depends on time and half-life. The initial amount just scales the absolute quantity, not the percentage.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the formula for half-life decay?
The remaining amount equals the initial amount multiplied by (1/2) raised to the power of (elapsed time divided by half-life). In symbols: N = N0 x (1/2)^(t / t_half). This same formula underlies radioactive decay, drug elimination, and other constant-fraction decay processes.
How many half-lives until a substance is essentially gone?
There is no exact zero in exponential decay, but after about 5 half-lives roughly 3% remains and after 10 half-lives less than 0.1% remains. Many fields treat 5 to 7 half-lives as the point where a substance is considered effectively cleared.
How do I calculate the half-life if I know the decay constant?
The half-life equals the natural log of 2 (about 0.693) divided by the decay constant, written t_half = 0.693 / k. Conversely, the decay constant equals 0.693 divided by the half-life.
Can I use this calculator for drug dosage in the body?
You can use it to estimate how much of a drug remains based on its elimination half-life, entering the dose as the initial amount and using consistent time units. Real clearance varies with metabolism, organ function, and other factors, so results are estimates and not a substitute for professional medical advice.
What is the difference between half-life and mean lifetime?
Half-life is the time for a quantity to fall to 50%, while mean lifetime (tau) is the average time a particle survives before decaying. They are related by mean lifetime = half-life / 0.693, so the mean lifetime is always longer than the half-life.
Does a larger starting amount decay faster?
No. A larger initial amount means more absolute substance decays, but the fraction remaining after a given time is identical regardless of how much you start with. The percentage depends only on the elapsed time and the half-life.
How do I find the elapsed time if I know how much is left?
Rearrange the formula to time = half-life x log base 2 of (initial amount / remaining amount). For example, if 25% remains, log2(100/25) equals 2, so two half-lives have passed.
Is half-life the same for chemical reactions and radioactive decay?
The concept of a constant fractional decrease applies to first-order processes such as radioactive decay and many drug eliminations, where half-life is constant. For reactions that are not first-order, the half-life changes as concentration changes, so this constant half-life model would not apply.
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