Half-Life Calculator: Decay Over Time

Last reviewed: November 2026

A half-life calculator shows how much of a substance remains after a given time. Enter the starting amount, the half-life with its unit, and the elapsed time to get the remaining amount, the percent remaining, and how many half-lives have passed.

Half-life governs everything from carbon dating to how long a painkiller stays in your system. The key insight is that decay is proportional: each half-life removes half of whatever is currently there, so the amount falls fast at first and then ever more slowly, never quite reaching zero. This free tool handles the unit conversions for you, so a half-life in hours and an elapsed time in days still give the right answer.

How to use the half-life calculator

1. Enter the initial amount (grams, milligrams, becquerels, any unit).
2. Enter the half-life and pick its unit: seconds, minutes, hours, days, or years.
3. Enter the elapsed time and pick its unit (it can differ from the half-life unit).
4. Click Calculate to see the remaining amount, percent remaining, and half-lives elapsed.

Half-life formula

N0 is the starting amount, T is the half-life, t is the elapsed time, and N is what remains. The exponent t/T counts how many half-lives have passed, including fractions. Because each half-life multiplies the amount by one-half, the curve drops steeply at first: the first half-life removes 50% of the original, but the tenth half-life removes only about 0.1%. Related forms use the decay constant: N = N0 x e^(-0.693 x t / T).

Worked examples

Example 1: 80 g of iodine-131 after 24 days

Iodine-131 has a half-life of 8 days. Half-lives elapsed = 24 / 8 = 3. Remaining = 80 x (1/2)^3 = 80 x 0.125 = 10 g. Percent remaining = 12.5%.

Example 2: 200 mg of a drug after 18 hours

The drug's half-life is 6 hours. Half-lives elapsed = 18 / 6 = 3. Remaining = 200 x (1/2)^3 = 200 x 0.125 = 25 mg. Percent remaining = 12.5%: after three half-lives, seven-eighths of the dose is gone.

Common half-lives reference table

Substance	Half-life	Use
Iodine-131	8 days	Thyroid treatment and diagnosis
Technetium-99m	6 hours	Medical imaging scans
Carbon-14	5,730 years	Archaeological dating
Uranium-238	4.5 billion years	Geological dating
Caffeine (in the body)	~5 hours	Drug elimination timing
Radon-222	3.8 days	Indoor air safety

Tips for accurate half-life results

• Use the half-life for the right isotope or drug: different forms of the same element decay at wildly different rates.
• Remember the result is the amount remaining, not the amount decayed. Subtract from the start to get the decayed portion.
• For fractional half-lives (like 2.5), the formula still works: just raise one-half to 2.5.
• In medicine, five half-lives (about 97% eliminated) is the rule of thumb for a drug being effectively cleared.

Common half-life mistakes to avoid

• Linear thinking: the amount does not fall by the same grams each period. The drop shrinks as the amount shrinks.
• Mixing units: a half-life in hours with a time in days must be converted first. This calculator converts for you, but check when doing it by hand.
• "After two half-lives nothing is left": wrong, 25% remains. Decay approaches zero but never reaches it mathematically.
• Confusing half-life with lifetime: the average (mean) lifetime is the half-life divided by 0.693, about 44% longer.

Frequently asked questions

What is half-life in simple terms?

Half-life is the time it takes for half of a substance to decay or be eliminated. After one half-life, 50% remains; after two, 25%; after three, 12.5%. It is a fixed property of the substance, independent of the starting amount.

How do you calculate the remaining amount after n half-lives?

Multiply the starting amount by one-half raised to the number of half-lives: N = N0 x (1/2)^n. For 3 half-lives, multiply by 0.125; for 2, by 0.25.

Does the starting amount change the half-life?

No. Half-life is constant for a given substance under given conditions. Starting with 1000 g or 1 g, the time to lose half is identical, which is exactly what makes the calculation so useful.

How many half-lives until a drug is out of your system?

About five half-lives removes roughly 97% of a drug, which medicine treats as effectively eliminated. Ten half-lives leaves only about 0.1%.

What is the difference between half-life and decay constant?

They describe the same decay two ways. The decay constant (lambda) is the fraction decaying per unit time, and half-life = 0.693 / lambda. This calculator works directly with half-life, so no conversion is needed.

How old is a sample with 25% of its carbon-14 left?

Carbon-14 has a half-life of 5,730 years. Having 25% left means two half-lives have passed, because (1/2) x (1/2) = 1/4. The sample is 2 x 5,730 = 11,460 years old.

What are the decay constant and mean lifetime?

The decay constant is lambda = 0.693 / half-life. For iodine-131, with a half-life of 8 days, lambda = 0.693 / 8 = 0.0866 per day. The mean lifetime is tau = half-life / 0.693, which for iodine-131 is 8 / 0.693 = 11.5 days, about 44% longer than the half-life.

Related calculators

• Scientific Calculator: evaluate exponentials and logarithms by hand.
• Exponent Calculator: work out powers such as (1/2)^3 = 0.125.
• Logarithm Calculator: solve for elapsed time or half-life from the fraction remaining.

Sources

• OpenStax: Chemistry 2e textbook, nuclear chemistry and radioactive decay chapter
• U.S. NRC: Nuclear Regulatory Commission, radioactive decay and half-life reference

Key takeaways

• Bookmark this tool for quick recalculations whenever your inputs change.
• N = N0 x (1/2)^(t/T): remaining amount from starting amount, time, and half-life.
• 50%, 25%, 12.5% remain after 1, 2, 3 half-lives; five half-lives clears ~97%.
• Half-life never depends on the starting amount.
• Keep time units consistent, or let the calculator convert them for you.