Calculators / Counting
MDA calculator: Currie critical level and detection limit
The minimum detectable activity is the smallest true activity a measurement will detect with 95 % confidence, fixed before the count. The critical level is the decision threshold applied after it. They are different numbers, and confusing them is the classic error.
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The formulas (Currie 1968, paired blank, k = 1.645)
L_C = k·√(2B) = 2.33·√B decision threshold (counts) L_D = k² + 2k·√(2B) = 2.71 + 4.65·√B detection limit (counts) MDA = L_D / (ε · p · t) Bq MDC = MDA / sample size Bq/kg, Bq/L
Worked example
A 1 kg soil sample counted for 3600 s on a detector with 3 % full-energy efficiency at 662 keV (p = 0.851 for Cs-137); the blank gives 900 counts in the peak region.
- L_C
- 69.8 counts
- L_D
- 142 counts
- MDA
- 1.55 Bq · 41.8 pCi
- MDC
- 1.55 Bq/kg
A net count above 69.8 is reported as detected. An activity at the MDA gives a net count that exceeds LC 95 % of the time.
How background sets the limit
| BACKGROUND B | L_C | L_D | MDA |
|---|---|---|---|
| 10 | 7.36 | 17.4 | 0.19 Bq |
| 100 | 23.3 | 49.2 | 0.536 Bq |
| 1,000 | 73.6 | 150 | 1.63 Bq |
| 10,000 | 233 | 468 | 5.09 Bq |
Assumptions
- Sample and blank counted for the same live time; Poisson statistics; α = β = 5 %.
- No decay correction during the count and no systematic uncertainty in ε — apply those separately where they matter.
Sources
- Currie, L. A. (1968), Anal. Chem. 40, 586.
- MARLAP Manual, Chapter 20.
- Emission probability: IAEA decay_rads (ENSDF).
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.