Calculators / Decay
Radioactive decay calculator
How much activity is left, how long until it falls to a given level, and what a source was worth on its calibration date. Half-lives come from the IAEA Live Chart of Nuclides (NUBASE2020); the arithmetic is the app’s own.
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The formula
A(t) = A₀ · e^(−λt), λ = ln 2 / T½ t = T½ · log₂(A₀ / A) time to fall from A₀ to A N = A / λ atoms behind an activity SA = λ · N_A / M specific activity (Bq/g)
Common sources
Fraction of the starting activity remaining after each interval, and the time to fall to 1 %.
| NUCLIDE | HALF-LIFE | 1 DAY | 30 DAYS | 1 YEAR | TO 1 % |
|---|---|---|---|---|---|
| F-18 | 1.829 h | 0.01125 % | < 10−6 % | < 10−6 % | 12.15 h |
| Tc-99m | 6.007 h | 6.271 % | < 10−6 % | < 10−6 % | 1.663 d |
| I-131 | 8.025 d | 91.73 % | 7.493 % | < 10−6 % | 53.32 d |
| Ir-192 | 73.83 d | 99.07 % | 75.45 % | 3.241 % | 1.343 yr |
| Co-60 | 5.271 yr | 99.96 % | 98.93 % | 87.68 % | 35.02 yr |
| Sr-90 | 28.91 yr | 99.99 % | 99.8 % | 97.63 % | 192.1 yr |
| Cs-137 | 30.08 yr | 99.99 % | 99.81 % | 97.72 % | 199.8 yr |
| Am-241 | 432.6 yr | 100 % | 99.99 % | 99.84 % | 2,874 yr |
| Ra-226 | 1,600 yr | 100 % | 100 % | 99.96 % | 10,630 yr |
Worked examples
From a calibration certificate. A Cs-137 check source was 10.0 mCi on 1 January 2010. On 28 September 2026, 16.74 years later:
A = 10.0 mCi × 2^(−16.74 / 30.08) = 6.799 mCi
Time to decay. I-131 waste held for decay until it is below 1 % of its starting activity:
t = 8.025 d × log₂(100) = 53.3 d
Assumptions
- A single nuclide. Where a daughter is itself radioactive and grows in (Sr-90 → Y-90, Ra-226 → Rn-222), use the decay chain calculator.
- A year is the Julian year of 365.25 days, the convention of the IAEA half-life data.
Sources
- Half-lives: IAEA Live Chart of Nuclides, NUBASE2020.
- Decay law: Lamarsh & Baratta, Introduction to Nuclear Engineering, §2.
Numbers on this page computed by the physics code of Nuclear Toolkit 1.4.1, the same code as the app. How it is checked.
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