If you need to estimate how much of a radioactive substance remains after a given amount of time, this radionuclide decay calculator gives you quick, transparent results. Enter an initial amount, a half-life, and elapsed time, and it will compute remaining quantity, decayed quantity, decay constant, and optional activity.
Interactive Radionuclide Decay Calculator
Use any unit (atoms, grams, moles, MBq-equivalent quantity) as long as you keep it consistent.
If provided, the calculator also returns remaining activity A(t).
How to use this calculator
- Enter the initial amount of radionuclide.
- Enter the half-life and select its unit.
- Enter the elapsed time and unit.
- Optionally enter initial activity in becquerels (Bq).
- Click Calculate Decay to get all key outputs.
Decay equation used
Radioactive decay follows an exponential law. This calculator uses two equivalent forms:
N(t) = N0 e-λt
N(t) = N0 (1/2)t / T1/2
What each symbol means
- N0: Initial amount at time zero.
- N(t): Amount remaining after time t.
- T1/2: Half-life.
- λ: Decay constant, computed as
λ = ln(2) / T1/2. - A(t): Activity at time t, where
A(t) = A0 e-λt.
Worked examples
Example 1: Iodine-131 in nuclear medicine
I-131 has a physical half-life of about 8 days. If a sample starts at 100 units and 24 days pass, then 3 half-lives have elapsed. Remaining fraction is (1/2)3 = 1/8, so only 12.5 units remain.
Example 2: Cesium-137 in environmental monitoring
Cs-137 has a half-life around 30.17 years. Over one decade, roughly one-third of activity is lost, while about two-thirds remains. Because the half-life is long, decay is slow over short intervals.
Common radionuclides and approximate half-lives
| Radionuclide | Half-life | Typical context |
|---|---|---|
| Carbon-14 | 5,730 years | Archaeological dating |
| Iodine-131 | 8.02 days | Thyroid treatment and imaging |
| Technetium-99m | 6.01 hours | Diagnostic nuclear medicine |
| Cesium-137 | 30.17 years | Environmental and contamination studies |
| Cobalt-60 | 5.27 years | Industrial and therapeutic sources |
Activity, dose, and practical interpretation
Activity (Bq) describes how many decays happen per second, not directly how much biological harm occurs. Dose depends on radiation type, energy, pathway, exposure geometry, shielding, and tissue sensitivity. This calculator handles the decay physics only.
Unit reminder
- 1 Bq = 1 decay per second
- 1 Ci = 3.7 × 1010 Bq
Assumptions and limitations
- Assumes a single radionuclide with constant half-life.
- Does not model decay chains (parent-daughter buildup).
- Does not include biological clearance (important in internal dosimetry).
- Does not account for shielding, geometry, or detector response.
Quick FAQ
Can I use grams instead of atoms?
Yes. The decay fraction is unitless, so any amount unit works as long as you stay consistent from input to interpretation.
What if time is zero?
The calculator returns the original amount unchanged, because no decay interval has elapsed.
Why are some values shown in scientific notation?
Very large or very small values are displayed in scientific notation to preserve readability and precision.
Safety note
This tool is for educational and planning purposes only. For regulated work involving radioactive material, follow your institution’s radiation safety procedures and consult qualified health physics professionals.