Half-Life Calculator
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What Your Result Means
- Remaining Quantity: The amount of your original substance still present after the elapsed time.
- Decayed Amount: How much of the original has decayed or transformed away.
- Number of Half-Lives: How many complete (or partial) half-life cycles have passed. After 1 half-life, 50% remains; after 2 half-lives, 25% remains; after 3 half-lives, 12.5% remains, and so on.
- Percent Remaining: The percentage of the original quantity that is still undecayed.
How This Calculator Works
This calculator applies the radioactive decay formula: Remaining = Initial × (0.5)n, where n is the number of half-lives (elapsed time divided by half-life period). The formula models exponential decay, assuming a constant half-life and that each half-life period reduces the quantity by exactly half, regardless of the starting amount.
Quick Questions
What is a half-life?
Half-life is the time required for a quantity to reduce to half its original amount. It's a fundamental concept in radioactive decay, where atoms spontaneously transform into other atoms or elements at a predictable rate.
Can you use this for things other than radioactivity?
Yes. Half-life applies to any exponential decay process: medicine clearance in the blood, cooling of hot objects, depreciation of assets, and population decline. Anywhere a quantity shrinks by a constant percentage per time period fits this model.
What if the number of half-lives is not a whole number?
The formula handles fractional half-lives perfectly. For example, 0.5 half-lives means 70.7% remains (√0.5 ≈ 0.707), and 1.5 half-lives means 35.4% remains. The exponential decay curve is smooth and continuous.
How accurate is this calculator?
The math is exact for ideal exponential decay. However, real radioactive samples may deviate due to daughter products, environmental contamination, or instrument error. Always use this as an estimate and consult experimental data for critical applications.
Can I use carbon-14 dating with this?
Yes. Carbon-14 has a half-life of 5,730 years. Enter that as your half-life period and the elapsed time since the organism died. The calculator will show the remaining C-14, which can be measured and used to estimate age.
What about very small or very large half-lives?
This calculator handles any positive half-life value, from nanoseconds (atomic processes) to billions of years (uranium decay). Choose consistent time units to avoid confusion.
Sources
Method & review
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.