Half-Life CalculatorFree online science calculator — instant results, no sign-up
Calculate the remaining amount of a substance after radioactive or chemical decay.
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About the Half-Life Calculator
The Half-Life Calculator estimates how many grams of a substance remain after radioactive decay or chemical decay that follows a constant half-life. Enter the initial amount in grams, the half-life in years, and the elapsed time in years to find the remaining amount, percent remaining, and number of half-lives elapsed.
- Initial amount (g)
- The starting mass of the substance before decay, measured in grams, with a default of 100 g.
- Half-life (years)
- The time required for half of the remaining substance to decay, measured in years, with a default of 5.27 years.
- Elapsed time (years)
- The time since the initial amount was measured, expressed in years, with a default of 10 years.
Formula and method
n = t / T; m = m₀ × (1/2)^(t/T); P = 100 × (1/2)^(t/T). With the default inputs: n = 10 / 5.27 ≈ 1.898; m = 100 × (1/2)^(10/5.27) ≈ 26.8402 g; P ≈ 26.84%.
- m₀Initial mass of the substance, in grams.
- THalf-life of the substance, in years.
- tElapsed time, in years.
- nNumber of half-lives elapsed, a dimensionless quantity.
- mMass of the original substance remaining, in grams.
- PPercentage of the initial substance remaining.
Divide elapsed time by half-life to obtain the number of half-lives elapsed. Raise one-half to that power to obtain the remaining fraction, then multiply by the initial mass for grams remaining and by 100 for percent remaining. Retain full precision during calculation and round only the displayed results.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Initial amount100 g
- Half-life5.27 years
- Elapsed time10 years
Results
- Remaining amount26.8402 g
- Percent remaining26.84%
- Half-lives elapsed1.898
How to use the Half-Life Calculator
- 1Enter the initial amount in grams; use 100 for the default example.
- 2Enter a positive half-life in years; use 5.27 for the default example.
- 3Enter a nonnegative elapsed time in years; use 10 for the default example.
- 4Run the calculation to apply exponential decay over the elapsed time.
- 5Read the results: Remaining amount = 26.8402 g; Percent remaining = 26.84%; Half-lives elapsed = 1.898.
Reading your result
Remaining amount is the mass of the original, undecayed substance still present, not necessarily the total mass of the sample including decay products. Percent remaining expresses that mass as a percentage of the initial amount. Half-lives elapsed counts how many half-life intervals fit into the elapsed time, including fractional intervals. For the default inputs, 26.8402 g remains from 100 g after 10 years, equivalent to 26.84%, with 1.898 half-lives elapsed.
Limitations
The model assumes a constant half-life and first-order exponential decay, with no replenishment or additional removal of the original substance. It applies to chemical decay only when those assumptions hold; many chemical reactions do not have a constant half-life. Initial mass and elapsed time must be nonnegative, and half-life must be greater than zero. The tool does not model daughter-product buildup, decay chains, or mixtures with different half-lives, and it does not determine radiation dose or safety. Results are idealized estimates whose accuracy depends on the input data; displayed decimal places do not imply measurement precision.
Common questions
Why does the default example leave slightly more than one-quarter of the substance?+
The default elapsed time of 10 years is slightly less than two half-lives when the half-life is 5.27 years. Only 1.898 half-lives have elapsed, so 26.84% remains rather than exactly one-quarter.
Can this calculator handle a fractional number of half-lives?+
Yes. The exponential formula works continuously, so elapsed time does not need to be a whole-number multiple of the half-life. The default calculation uses 10 / 5.27 without rounding that ratio before computing the remaining mass.
Can I enter a half-life given in days or seconds?+
Convert both the half-life and elapsed time to years before entering them because this page labels both inputs in years. The ratio t / T is valid only when the two times use the same unit.
Does the amount that decays disappear from the sample?+
Not necessarily. The result tracks only the original substance: radioactive decay produces daughter nuclides, and chemical decay produces other substances. Those products may remain in the sample, but this calculator does not track their masses.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.