Radioactive Decay Calculator
Estimate the activity and specific activity of a radioactive sample from its mass, molar mass, and half-life. The calculator follows the standard decay-constant relationship and works well for chemistry and nuclear-science exercises.
Activity Result
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Quick Answer: Activity is calculated with A = (m / M) x N_A x ln(2) / t1/2. Specific activity removes the sample mass and uses a = (N_A / M) x ln(2) / t1/2.
How to Calculate Radioactive Activity
- Enter the sample mass: Use the amount of radioactive material you actually want to evaluate.
- Enter the molar mass: This identifies how many atoms are present in each gram of the isotope.
- Supply the half-life: Shorter half-lives produce larger decay constants and therefore higher activities for the same mass.
- Read both outputs: The page reports total activity for the sample and specific activity per gram of material.
Radioactive Decay Calculator Formula
A = (m / M) x N_A x ln(2) / t1/2 ; a = (N_A / M) x ln(2) / t1/2
| Variable | Meaning | Unit |
|---|---|---|
| A | Activity | Bq |
| a | Specific activity | Bq/g |
| m | Sample mass | g |
| M | Molar mass | g/mol |
| t1/2 | Half-life | time |
Worked Examples
Example 1 - Iodine-131 sample
- Mass: 1 mg
- Molar mass: 131 g/mol
- Half-life: 8.02 days
Result: Activity = 4.60 TBq; Specific activity = 4.60 PBq/g
A short half-life makes I-131 highly active even in a small sample.
Example 2 - Cobalt-60 sample
- Mass: 2 mg
- Molar mass: 59.93 g/mol
- Half-life: 5.27 years
Result: Activity = 83.8 GBq
The much longer half-life reduces activity compared with short-lived medical isotopes.
Example 3 - Technetium-99m sample
- Mass: 0.05 mg
- Molar mass: 99 g/mol
- Half-life: 6 hours
Result: Activity = 9.76 TBq
Very short half-lives can generate extremely large activities from tiny masses.
Radioactivity Interpretation Table
| Range | Meaning | Action |
|---|---|---|
| Short half-life | Large decay constant and high activity for a given mass. | Check units carefully because small mass changes can shift the result a lot. |
| Long half-life | Lower activity for the same sample mass. | Do not confuse long-lived isotopes with zero risk; activity is only one part of the picture. |
| High specific activity | Each gram of the isotope produces strong radiation output. | Use the result as a physics or chemistry estimate, not a handling instruction. |
Frequently Asked Questions
Radioactive decay is the spontaneous transformation of an unstable nucleus into a more stable state while releasing particles or electromagnetic radiation.
Activity is the number of nuclear disintegrations per unit time. In SI units it is measured in becquerels, where 1 Bq equals 1 decay per second.
Specific activity is the activity per unit mass of radioactive material, usually expressed in becquerels per gram.
The decay constant is ln(2) divided by half-life, so a shorter half-life means more atoms decay each second and the activity rises sharply.
No. Activity alone is not a safety decision tool. Shielding, isotope type, exposure path, and regulations also matter.
Note: This calculator is for educational use only and does not replace radiation-safety training, labeling requirements, or regulatory guidance.
References
Last reviewed: March 14, 2026