What Is a Radioactive Decay Remaining Quantity Calculator?
Radioactive isotopes decay exponentially: over each half-life, exactly half of whatever remains disappears. This calculator applies the classic decay equation N = N₀ × (1/2)^(t ÷ t½) to find exactly how much of an isotope is left after any elapsed time, given its half-life.
The same formula works for remaining mass, remaining moles, or remaining radioactive activity — decay is proportional in all three, so the fraction remaining is identical either way.
How to Read Your Results
Quantity Remaining
This is how much of your original quantity is still present after the elapsed time, in the same units you entered for the initial quantity.
Percent Remaining
The remaining quantity expressed as a percentage of the starting amount — useful for comparing decay progress regardless of units.
Half-Lives Elapsed
How many full half-lives have passed, as a decimal. This is simply elapsed time divided by the half-life, both converted to the same units.
Amount Decayed
The portion of the original quantity that has already decayed away (N₀ minus the remaining quantity).
Real-World Example
Carbon-14, used in radiocarbon dating, has a half-life of 5,730 years. Starting with 100 g of carbon-14 and waiting 11,460 years (exactly two half-lives):
| Quantity | Value |
|---|---|
| Half-lives elapsed | 11,460 ÷ 5,730 = 2.0 |
| Fraction remaining | (1/2)² = 0.25 |
| Remaining quantity | 100 g × 0.25 = 25 g |
After exactly two half-lives, only 25% (25 g) of the original carbon-14 remains — this is the basic principle behind carbon dating of organic material.
Tips for Working With Decay Calculations
- Use the correct half-life for your specific isotope — half-lives vary enormously, from microseconds to billions of years.
- The formula works for any quantity proportional to the number of remaining atoms: mass, moles, or activity (counts per second).
- Decay never quite reaches zero mathematically — the remaining amount keeps halving indefinitely, though it becomes negligible after 7-10 half-lives.
- Double-check your time units — mixing up days and years is the most common source of error in decay calculations.
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Last updated: August 2026 · Reviewed by: Simple Calculator Tools Editorial Team