Radiation Background Statistics Simulator

Detector Setup

True background rate 30 cpm

Counting window 10 s

Anomaly threshold 3σ

Live Readout

Verdict

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Count in window

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Expected (λ)

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σ = √λ

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z-score

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Windows seen

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False "spikes"

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A "false spike" is a window that crossed your threshold even though the true rate never changed — pure Poisson fluctuation.

How it works

Radioactive decay events arrive independently at random instants, so the count observed in any fixed window follows a Poisson distribution. For a true mean count λ (background rate × window length), the count's own standard deviation is not a free parameter — it is fixed by the physics at σ = √λ. A single 10-second reading of a 30 cpm source has λ = 5 counts and σ ≈ 2.2, so a reading of 10 counts (a "100% spike" over the mean) is only about z = (10−5)/2.2 ≈ 2.3σ away — well inside the range normal statistical noise produces regularly.

λ = rate × window
σ = √λ
z = (observed − λ) / σ
flag "anomaly" only if |z| ≥ threshold

True background rate — the real, unchanging count rate of the source (counts per minute). This never itself spikes; only the counts in a short window appear to.
Counting window — how long each measurement integrates. A longer window raises λ, and because σ grows only as √λ, the relative noise (σ/λ) shrinks — a real anomaly becomes easier to tell from noise.
Anomaly threshold — how many σ a reading must deviate before it's flagged. A low threshold (1-2σ) flags harmless fluctuation constantly; a proper radiological anomaly claim requires ≥3σ and, ideally, a repeat measurement.

Real-world relevance: claimed "anomalous radiation" at alleged sighting sites is almost always a single short, low-count reading interpreted without this statistics — a Geiger counter briefly reading 2-3x background is the expected, routine behavior of any Poisson process, not evidence of an exotic source. Health physicists always ask for counting time and repeat trials before calling anything an anomaly.

Normal window Flagged "spike" ±σ / ±threshold·σ band