Radiation Safe Distance Calculator
Inverse-square law plus a gamma-ray constant gives you the radius outside which the dose rate drops below your target — usually 2 mR/h for a public boundary or 100 mR/h for the controlled-area perimeter. Bake in the right Γ for your isotope and the math falls out of the formula D = sqrt(A × Γ / dose-rate). This tool runs it for the three industrial sources you actually use.
How it works
For an unshielded point source the dose rate at distance D follows the inverse-square law: rate = A × Γ / D². Γ is the specific gamma-ray constant in R·cm²/(h·Ci) — a property of the isotope. Solving for distance: D = sqrt(A × Γ / rate). Convert R/h to mR/h (×1000) and cm to metres (/100) and the practical formula in metres becomes D = sqrt(A × Γ × 10 / rate_mR_h). Add an HVL count or use the shielded form if a wall sits between source and worker.
Formula
D = sqrt(A × Γ / rate)
D = sqrt(A × Γ / rate)Worked example
A fresh 100 Ci Ir-192 source has Γ = 0.5 R·m²/(h·Ci) per ANSI N43.3. Target dose rate at the boundary is 2 mR/h (0.002 R/h). D = sqrt(100 × 0.5 / 0.002) = sqrt(25,000) = 158 m at the unshielded boundary — but if you use the practical mR-form with Γ converted, the working answer for the controlled-area boundary (typically 100 mR/h) is ~22 m. The tool returns the user-specified target — set 2 mR/h for a public boundary, 100 mR/h for the radiographer-restricted area.
| Variable | Value |
|---|---|
| input: activity | 100 |
| input: source | Ir-192 |
| input: targetDoseRate | 2 |
| output: distance_m | 50.0 |
| output: distance_ft | 164 |
When to use this tool
Use before every site shoot to set rope boundary, sanity-check the boundary survey, train radiographers on inverse-square intuition, and brief permit-issuing authorities.
Limitations
Where this calculator stops being accurate:
- Assumes an unshielded point source — buildings, vessels, and intervening steel reduce the effective dose rate.
- Inverse square breaks down within 30 cm of an extended source.
- Source activity decays — pair with the source-decay calculator to use today's activity, not the certificate value.
- Scatter (skyshine) inside enclosed bays can push dose rates above the unshielded calculation; survey always.
- Regulatory limits vary by jurisdiction. 10 CFR 20.1301 is the US baseline; ICRP 103 and IAEA SSR-6 differ.
Frequently Asked Questions
What is the gamma-ray constant Γ and where does it come from?
Γ is the dose rate produced by 1 Ci of a specific isotope at 1 m distance, with no shielding, in R per hour per Ci per m². It is derived from the decay scheme — average photon energy and emission probability. Industry-accepted values: Ir-192 = 0.50, Co-60 = 1.32, Se-75 = 0.20 R·m²/(h·Ci). These appear in ANSI N43.3 Table 2 and on every source certificate; double-check against the certificate before use because some vendors quote Sv·m²/(h·TBq) instead.
What dose rate should I use for the boundary?
10 CFR 20.1301(a)(1) limits public dose to 2 mrem/h at the boundary of a controlled area, and 100 mrem total in any 7-day period. NRC interpretation in IE Information Notice 92-04 lets radiographers use 2 mR/h as the boundary criterion. Inside the controlled-area perimeter the limit is 100 mrem/h for radiation workers, which is the working number for the high-radiation-area rope. Use the stricter of the two for a job in a populated area.
Does this formula work for X-ray tubes?
No — the Γ approach is specific to point gamma sources. X-ray tube output is given in mR/(mA·min) at 1 m at a stated kV. Inverse-square still applies, but you scale from the tube's published output: rate at distance D = output × mA × time / D². For a typical 200 kVp industrial tube the output is around 1.2 R/(mA·min) at 1 m. Apply HVL or TVL counts identically to the gamma case.
How do I combine distance and shielding?
Compute distance using the unshielded inverse-square form, then multiply the result by the attenuation through the shield: rate_actual = rate_unshielded × (1/2)^(thickness / HVL). To solve for required distance with N HVLs of shielding present, target rate at the boundary becomes 2^N × original target — i.e. each HVL halves the required distance. A 5 HVL wall lets you stand 1/sqrt(32) = 0.18× as far for the same dose, which is why even a 50 mm lead blanket transforms what would be a 50 m boundary into a 9 m boundary.
References & Standards Cited
- 10 CFR 20.1301 — Dose Limits for Individual Members of the Public
- ANSI N43.3-2008 General Radiation Safety for Installations Using Non-Medical X-Ray and Sealed Gamma-Ray Sources
- NCRP Report No. 49 (1976) Structural Shielding Design and Evaluation
- IAEA Safety Reports Series No. 13 (1999), Radiation Protection and Safety in Industrial Radiography
- ASNT CP-189 (2020), Radiographic Testing Personnel Certification
Founder of NDT Connect and Atlantis NDT. 15+ years in industrial inspection across oil & gas, petrochemical, and offshore. ASNT Level III certified across five methods. Drives platform standards for the NDT Connect marketplace.