Interactive Radioactive Decay Calculator
Use this tool to calculate remaining material, time to reach a target amount, or estimate half-life from measurements.
Assumes simple exponential decay with a constant half-life and no external production or removal processes.
What Is Radioactive Decay?
Radioactive decay is the natural process where unstable atomic nuclei lose energy by emitting radiation. Over time, the number of undecayed nuclei decreases in a predictable way. This behavior follows an exponential law, which is why half-life calculations are so useful in physics, chemistry, geology, medicine, and environmental science.
Instead of decaying at a fixed linear rate, radioactive materials decay by a constant fraction per unit time. That means each half-life cuts the amount in half, regardless of how much is present at the start of that interval.
The Core Formulas
The calculator uses the standard decay relationships below:
N(t) = N₀ × e-λt
λ = ln(2) / T½
- N₀: initial amount
- N(t): remaining amount after time t
- T½: half-life
- λ: decay constant
How to Use This Radioactive Decay Calculator
1) Find remaining amount
Choose Find remaining amount after elapsed time. Enter initial amount, half-life, and elapsed time. You’ll get:
- Remaining amount
- Total amount decayed
- Percent remaining
- Decay constant
2) Find time to target amount
Choose Find time needed to reach a target amount. Enter initial amount, half-life, and desired remaining amount. The tool returns the required elapsed time and equivalent number of half-lives.
3) Estimate half-life from measurements
Choose Estimate half-life from measurements. Enter initial amount, measured final amount, and elapsed time. The tool computes the implied half-life and decay constant.
Worked Examples
Example A: Carbon-14 dating idea
If you start with 100 units of Carbon-14 and wait two half-lives, you will have 25 units left. This is true for any isotope: two half-lives always means 25% remains.
Example B: Medical isotope planning
Suppose a tracer has a half-life of 6 hours and you need to know when it drops from 80 MBq to 20 MBq. Since 20 is one-quarter of 80, that is two half-lives, so the required time is 12 hours.
Common Use Cases
- Radiometric dating: estimating ages of archaeological or geological samples.
- Nuclear medicine: timing doses for imaging and therapy.
- Radiation safety: estimating when activity falls below thresholds.
- Laboratory planning: scheduling experiments around isotope decay.
Important Notes and Assumptions
This calculator models ideal single-isotope exponential decay. Real-world systems can be more complex due to:
- Decay chains (daughter isotopes that are also radioactive)
- Mixed isotope samples with different half-lives
- Measurement uncertainty and detector limits
- Chemical/physical loss unrelated to nuclear decay
For safety-critical or regulatory applications, use validated professional software and verified measurements.
Quick FAQ
Does half-life depend on the starting amount?
No. Half-life is an intrinsic property of the isotope.
Can I use any units?
Yes, as long as your time units are consistent. If half-life is in years, elapsed time must also be in years.
Why can’t target amount be zero?
In ideal exponential decay, the amount approaches zero asymptotically and never reaches exactly zero in finite time.