Radiation Dose Calculator
Estimate the gamma radiation dose rate received by a worker near a radioactive source, accounting for distance, exposure time, isotope type, and shielding. Used in health physics and radiation safety planning.
About this calculator
The dose rate from a point gamma source decreases with the square of distance (inverse-square law) and is reduced by shielding materials. The formula implemented here is: Dose = (A × t × Γ) / (d² × S), where A is the source activity in Curies, t is the exposure time in hours, d is the distance in metres, S is the shielding attenuation factor (1 = no shielding), and Γ is an isotope-specific dose rate constant (R·m²/Ci·hr): approximately 0.33 for Co-60, 0.10 for Cs-137, and 0.08 for I-131. The dose rate constant Γ encapsulates the energy and abundance of gamma rays emitted per disintegration. Shielding factor S > 1 represents attenuation; for example, a 10 cm lead shield around a Cs-137 source might give S ≈ 100, reducing dose by a factor of 100. Regulatory occupational limits are typically 20 mSv/year (ICRP), and this tool helps workers plan time, distance, and shielding to stay within safe limits.
How to use
A radiation worker stands 2 m from a 0.5 Ci Cs-137 source for 3 hours with a shielding factor of 2. Enter: Activity = 0.5 Ci, Distance = 2 m, Exposure Time = 3 hours, Isotope = Cs-137 (Γ = 0.10), Shielding Factor = 2. Calculation: Dose = (0.5 × 3 × 0.10) / (2² × 2) = (0.15) / (4 × 2) = 0.15 / 8 = 0.01875 R ≈ 18.75 mR. This is well below the occupational limit, but if the worker repeated this exposure daily for a year it would accumulate to roughly 6.84 R/year — underscoring the importance of minimising time and maximising distance and shielding.
Frequently asked questions
How does distance affect radiation dose rate from a gamma source?
Radiation dose rate from a point source follows the inverse-square law: doubling the distance reduces the dose rate by a factor of four, and tripling it reduces it by nine. This is because gamma rays spread out over an ever-increasing spherical surface area as they travel outward, so the intensity per unit area falls as 1/d². In practical radiation safety, increasing distance is one of the three cardinal protective principles alongside time reduction and shielding. Even moving from 1 m to 3 m away from a source reduces dose by 89%, making distance the most cost-effective protection strategy when physical shielding is unavailable.
What shielding factor should I use for lead or concrete against Co-60 gamma rays?
Co-60 emits two high-energy gamma rays at 1.17 MeV and 1.33 MeV, making it one of the more penetrating isotopes to shield. For lead, the tenth-value layer (TVL — thickness reducing dose by 90%) is approximately 4–5 cm; 10 cm of lead corresponds to roughly two TVLs, giving a shielding factor of about 100. For ordinary concrete (density ≈ 2.3 g/cm³), the TVL is about 21 cm, so 42 cm of concrete also gives a factor of ~100. Enter the calculated attenuation factor as the shielding input to the calculator. Always refer to NCRP, IAEA, or vendor-specific shielding data for regulatory compliance work.
What are the annual occupational radiation dose limits and how do I check compliance?
The International Commission on Radiological Protection (ICRP) recommends a whole-body occupational limit of 20 mSv per year averaged over five years, with no single year exceeding 50 mSv. In the United States, the NRC enforces a 50 mSv (5 rem) annual limit for radiation workers. To check compliance, sum all estimated dose contributions from each work task over the year using the calculator. If the projected total approaches the annual limit, implement additional shielding, reduce time near sources, or increase working distance. Personal dosimeters (TLDs or OSLDs) provide legally binding dose records and should always be cross-referenced with calculator estimates.