Half-Life Calculator

Calculate how much of a substance remains after a given time, and how long it takes to decay to a target amount. Example: 100 g with a 5 day half-life leaves 18.95 g after 12 days, and takes 16.61 days to fall to 10%.

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Initial amount

Half-life

time units

Elapsed time (same units)

Target remaining (optional)

How to use the Half-Life Calculator

Enter the starting amount and the half-life.
Enter the elapsed time in the same units as the half-life.
Optionally set a target percent to find the time needed.
Press Calculate.

Formula and method

N(t) = N0 x (1/2)^(t / T), where T is the half-life. Decay constant = ln 2 / T. Time to reach a fraction f = T x log2(1 / f).

Worked example: 100 g, half-life 5 days

Step	Result
Half-lives in 12 days	2.4
Fraction remaining (0.5^2.4)	0.18946
Amount remaining	18.95 g
Time to reach 10%	16.61 days

Fraction remaining after n half-lives

Half-lives	Fraction left	Percent
0	1/1	100.00%
1	1/2	50.00%
2	1/4	25.00%
3	1/8	12.50%
4	1/16	6.25%
5	1/32	3.13%
10	1/1024	0.0977%

Examples of half-lives

Carbon-14 has a half-life of about 5,730 years, iodine-131 about 8 days, and caffeine about 5 hours in adults. The formula is the same for each, only the half-life changes.

Frequently asked questions

What is half-life?

The time it takes for half of a substance to decay.

How do I calculate remaining amount?

Multiply the starting amount by 0.5 raised to elapsed time divided by half-life.

How many half-lives until almost gone?

After 7 half-lives less than 1% remains.

What is the decay constant?

ln 2 divided by the half-life.

Does it work for drugs?

Yes, for first-order elimination.

What is the half-life of carbon-14?

About 5,730 years.

Sources

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Effortless Math Team

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