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Half-Life Calculator

Find how much of a substance remains after a number of half-lives.

How it is calculated

The remaining amount follows N = N₀ × 0.5^(t / T), where N₀ is the starting amount, T is the half-life and t is the elapsed time. The decayed share is (1 − 0.5^(t / T)) × 100 percent.

The half-life and the elapsed time must be in the same unit (both days, both years, and so on); the tool does not convert. The half-life has to be greater than zero and the time cannot be negative. The starting amount can be in any unit (grams, becquerels, mg of a drug), and the remaining amount is returned in that same unit with two decimals.

Worked example

Start with 200 units of a substance with a half-life of 8 hours and wait 20 hours. The number of half-lives is 20 / 8 = 2.5. The fraction left is 0.5^2.5 ≈ 0.1768. Remaining: 200 × 0.1768 = 35.36. The decayed share is (1 − 0.1768) × 100 = 82.32%.

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Common mistakes

  • Entering the half-life in years and the elapsed time in days (or the reverse). The ratio t/T is only meaningful when both share a unit.
  • Assuming half the substance disappears each half-life of the original amount. It is half of what is left, so after two half-lives 25% remains, not 0%.
  • Confusing half-life with the mean lifetime, which is longer by a factor of about 1.44.
  • Entering the amount already decayed as the starting amount.

About this calculator

This calculator applies the half-life decay formula — the amount remaining equals the starting amount times 0.5 raised to the power of (elapsed time divided by half-life) — to find how much of a substance is left after a given time, and what percentage has decayed. Half-life is the time it takes for exactly half of a quantity to decay, and because decay is exponential rather than linear, the amount never technically reaches zero, only gets closer and closer to it.

The concept is central to nuclear physics and radiometric dating, where the known half-life of an isotope (like carbon-14's roughly 5,730 years) lets scientists estimate the age of fossils and artifacts from how much of the isotope remains. It's equally important in medicine and pharmacology, where a drug's half-life in the body determines dosing intervals, and in nuclear medicine, where it determines how long a radioactive tracer or waste stays significantly radioactive.

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Comments (1)

  • Editorial team

    A quick sanity check: after exactly one half-life the answer should be half your starting amount, and after three it should be an eighth. The remaining amount comes out in whatever unit you typed for the initial amount, and the elapsed time and half-life must share one unit, so convert days to hours first if needed. This assumes a single, simple decay process. Which substance or process are you modelling? Tell us what you would like to see covered.

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