Counting Statistics counting_uncertainty_calc
Net Count Rate & Propagated Poisson Uncertainty
Propagates Poisson counting statistics for sample and background measurements, computing 1σ (68.3%) and 2σ (95.4%) confidence limits and coefficient of variation (%CV).
R_n = R_g − R_b; σ_Rn = √[(R_g / t_g) + (R_b / t_b)]
RADCALC HEALTH PHYSICS & NUCLEAR ENGINEERING WORKSHEET
Net Count Rate & Propagated Poisson Uncertainty (Counting Uncertainty)
Domain: Counting Statistics & Detection Limits · Tool ID:
counting_uncertainty_calc · Engine: 100% Local Browser WASM R_n = R_g − R_b; σ_Rn = √[(R_g / t_g) + (R_b / t_b)]
Operational Notes:
Guided Stepper Workflow All Input Parameters & Solver
1
What do you want to calculate?
Select your target output variable. The stepper will guide you through only the required inputs.
2
Start from a Field Scenario Preset (Optional)
Pre-fill realistic health physics values, then refine individual parameters or jump straight to the result.
All Parameters Entered
Review Inputs & Calculated Result
Solved Output Live WASM Readout
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Entered Input Parameters (Tap any row to edit)
Calculated Result & Visual Analysis
Nominal Solved Value Updated automatically
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Enter parameters on the left to calculate.
CLIENT-SIDE 3D SIMULATION Net Count Rate & Propagated Poisson Uncertainty 3D Transport Field
Interactive 3D Geometry & Particle Transport
WebGPU / WebGL2 Ready
3D Hardware Acceleration & Browser Compatibility Status Inspect Requirements ↓
Checking Browser 3D Capabilities… Probing WebGPU adapter, WebGL 2.0, and WebGL 1.0 contexts locally.
Geometry & Field Diagram
Interactive Model
Sensitivity Curve
Normalized Base-Unit & WebMCP Tool Payload counting_uncertainty_calc
1. Input & Solved Parameter Ledger
| Role | Symbol | Parameter Name | Entered / Display Value | Normalized Base Unit | Definition |
|---|
2. ISO 11929 / MARSSIM Counting Lab QA
Governing Equation & Parameters
Net Rate = Gross Rate − Background Rate; Standard Error (1σ) = √[(Gross / tg²) + (Bkg / tb²)]
| Symbol | Parameter | Default Unit | Definition |
|---|---|---|---|
| R_g | Gross Sample Count Rate | cpm | Total observed count rate including sample and ambient background in cpm. |
| N_g | Gross Counts Observed | counts | Total raw counts accumulated during the sample counting period. |
| t_g | Sample Count Time | min | Duration of sample measurement in minutes. |
| R_b | Background Count Rate | cpm | Independent ambient background count rate in cpm. |
| N_b | Background Counts Observed | counts | Total raw background counts accumulated. |
| t_b | Background Count Time | min | Duration of dedicated background measurement in minutes. |
| R_n | Net Sample Count Rate | cpm | Net sample count rate corrected for background in cpm. |
| σ_Rn | Standard Uncertainty (1σ) | cpm | Propagated Poisson standard error at 68.3% confidence in cpm. |
Health Physics Notes & Related Calculators
Operational Guidance & Physics Assumptions
- Radioactive decay obeys Poisson statistics where variance equals total count: σ_N = √N.
- Uncertainties in gross and background count rates add in quadrature: σ_Rn² = σ_Rg² + σ_Rb².
- Optimal time allocation rule: t_g / t_b = √(R_g / R_b) minimizes total combined counting time for a target precision.
More in Counting Statistics & Detection Limits (2)
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