Gamma dose rate, activity & shielding calculator

How this calculator works

A small radioactive source that emits gamma rays behaves, from far enough away, like a point: its photons spread out evenly in every direction. That makes three things predictable. The dose rate is proportional to the activity (twice the curies, twice the dose rate). It falls with the square of the distance. And each slab of shielding removes a fixed fraction of what reaches it. Put together with a per-isotope constant, those rules give the dose rate anywhere around the source — or, run backwards, the activity that explains a meter reading, the distance to a boundary, or the thickness of lead, steel or concrete needed to reach a target.

Pick what you want to solve for, choose an isotope (or enter your own constant), and fill in the other values. Every input has its own unit selector, so you can mix curies and becquerels, meters and feet, or mR/h and µSv/h freely. The link button copies a URL that reproduces your exact inputs.

Gamma constants used

Values are exposure-rate constants for an unshielded point source, in R·m²/(Ci·h). Multiply by 10 for R·cm²/(mCi·h). Published tables disagree by 5–20 % depending on which x-rays and weak lines they include, so treat results as estimates.

Shielding data used

Broad-beam half-value and tenth-value layers (cm) from NCRP Report No. 49. Isotopes not listed have no broad-beam values in that table; for them, pick “Custom HVL” and enter a value from your own reference.

The formula

Ẋ = Γ · A · T / d²

T = 10^(−x / TVL)     or     T = 2^(−x / HVL)

A = Ẋ · d² / (Γ · T)          d = √(Γ · A · T / Ẋ)
x = TVL · log₁₀(Γ · A / (Ẋ · d²))

Ẋ is the exposure rate (R/h), Γ the specific gamma-ray constant (R·m²/(Ci·h)), A the activity (Ci), d the distance (m), x the shield thickness and T its transmission. Air-kerma rate is Ẋ × 8.764 mGy/R (2.58 × 10⁻⁴ C/kg × 33.97 J/C, ICRU 85). Dose-equivalent units use the photon convention 1 R ≈ 1 rem.

The point-source model holds once you are at least about three times the source's largest dimension away. It ignores air attenuation (under 1 % per meter for photons above ~100 keV), scatter from walls and floors, and self-shielding inside the source.

Worked example

Portable gauge source rod. A nuclear moisture–density gauge typically holds about 8 mCi of Cs-137. With the rod extended and nothing in the way, at 1 m: Ẋ = 0.33 × 0.008 / 1² = 2.64 mR/h (roughly 26.4 µSv/h). Step back to 3 m and it falls ninefold to 0.293 mR/h. Put 2 cm of lead between you and the rod and the 1 m figure becomes 0.295 mR/h (transmission 11.2 %).

Radiography boundary. How far from a 100 Ci Ir-192 radiography source, with no collimator, does the exposure rate drop to 2 mR/h (the familiar 10 CFR 20 “2 mrem in any one hour” figure)? d = √(0.48 × 100 / 0.002) ≈ 155 m. That is why radiographers use collimators and shielded exposure devices.

Frequently asked questions

What is a specific gamma-ray constant?

It is the exposure rate one unit of activity produces at one unit of distance from an unshielded point source, for example 0.33 R/h at 1 m from 1 Ci of Cs-137. It bundles the photon energies, their yields per decay and how strongly air absorbs them into one number per nuclide.

How much does the dose rate drop when I double the distance?

For a point source it falls to one quarter (the inverse-square law). Tripling the distance cuts it to one ninth. This is why distance is usually the cheapest and most effective protection.

Why does the calculator give R/h and also mSv/h?

The equation produces exposure rate in roentgens per hour. Air-kerma rate (Gy/h) follows exactly from 1 R = 8.76 mGy in air. For photons, radiation-protection practice treats 1 R as about 1 rem (10 mSv); that conversion is an approximation and is labeled as such.

What is the difference between HVL and TVL?

A half-value layer (HVL) is the thickness of shielding that halves the dose rate; a tenth-value layer (TVL) cuts it to one tenth. One TVL is about 3.3 HVLs. Broad-beam values, used here, already include photons scattered inside a thick shield.

How much lead do I need to shield Cs-137?

With the broad-beam values used here (HVL 0.65 cm, TVL 2.1 cm of lead), each 2.1 cm of lead cuts the Cs-137 dose rate by a factor of ten. Choose "Shield thickness" in the calculator to solve for the exact thickness for your target dose rate.

Can I use this to decide whether an area is safe?

No. This is an educational estimate for a bare point source. Real sources have encapsulation, self-absorption and scatter from nearby surfaces. Use a calibrated survey meter and follow your radiation safety program.

Sources

1. Unger, L. M. & Trubey, D. K. (1982). Specific Gamma-Ray Dose Constants for Nuclides Important to Dosimetry and Radiological Assessment. ORNL/RSIC-45/R1, Oak Ridge National Laboratory. www.osti.gov
2. U.S. Department of Health, Education, and Welfare (1970). Radiological Health Handbook, revised edition. Public Health Service, Bureau of Radiological Health.
3. Cember, H. & Johnson, T. E. (2009). Introduction to Health Physics, 4th edition. McGraw-Hill. (Chapters on external radiation safety and shielding.)
4. NCRP Report No. 49 (1976). Structural Shielding Design and Evaluation for Medical Use of X Rays and Gamma Rays of Energies up to 10 MeV. National Council on Radiation Protection and Measurements. (Broad-beam half-value and tenth-value layers for gamma sources.)
5. ICRU Report 85 (2011). Fundamental Quantities and Units for Ionizing Radiation. (Mean energy per ion pair in dry air, W/e = 33.97 J/C.)
6. National Nuclear Data Center, Brookhaven National Laboratory. NuDat 3 (ENSDF evaluated half-lives and photon emission data). www.nndc.bnl.gov
7. Hubbell, J. H. & Seltzer, S. M. (2004). Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients (version 1.4). NIST Standard Reference Database 126. www.nist.gov
8. U.S. Nuclear Regulatory Commission. 10 CFR 20.1004, Units of radiation dose. www.nrc.gov