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Half-Life Calculator

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Enter a starting amount, half-life, and elapsed time to find how much of a substance remains.

Half-Life Calculator

Live
Amount remaining
78.51
Number of half-lives elapsed
0.349
Percent remaining
78.51%
Enter half-life and time in the same unit (both in years, both in days, etc.) for a correct result.

The formula

N = N₀ × (1/2)^(t / half-life) where N₀ = starting amount, t = time elapsed
Example

100g of carbon-14 (half-life 5,730 years) after 2,000 years: N = 100 × (0.5)^(2000/5730) = 78.51g remaining.

Step-by-step guide

  1. Enter the starting amount of the substance.
  2. Enter the half-life and the elapsed time, using the same unit for both.
  3. Read the remaining amount, half-lives elapsed, and percent remaining.

Why decay never quite reaches zero

Each half-life reduces the remaining amount by exactly half, but half of any positive number is still a positive number - mathematically, the decay curve approaches zero but never technically reaches it, no matter how much time passes. In practice, after about 10 half-lives, less than 0.1% of the original substance remains, which is typically treated as negligible for real-world purposes, but the exponential formula itself never outputs a true zero.

Common mistakes

Mixing time units - entering half-life in years but elapsed time in days (or vice versa) produces a meaningless result. Both must use the same unit.
Assuming decay is linear (losing a fixed amount per year) rather than exponential (losing a fixed percentage per half-life) - these produce very different curves over time.

Frequently asked questions

What is half-life used for beyond radioactivity?

The same exponential decay formula applies to drug elimination from the body (pharmacokinetics), caffeine metabolism, and any process where a quantity decreases by a consistent proportion over consistent time intervals.

How is carbon dating related to this formula?

Carbon-14 dating works in reverse of this calculator - scientists measure the remaining percentage of carbon-14 in a sample, then solve this same formula backward to estimate how much time has elapsed since the organism died.

Does the substance's amount affect its half-life?

No - half-life is a fixed property of the specific substance or isotope, independent of the starting quantity. A gram and a kilogram of the same isotope both take the same amount of time to reduce by half.

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