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.
Last updated: September 2026
Formula below · 2 sources (nrc.gov, Wikipedia) · Updated Sep 2026
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About this calculator
For a point gamma source the exposure rate at distance d is Γ × A / d², where A is the activity in curies and Γ is the isotope's specific gamma-ray constant in R·m²/(Ci·h): cobalt-60 1.32, cesium-137 0.33, iridium-192 about 0.5–0.59 (0.59 used, the conservative end), radium-226 0.825. The total dose over the exposure time t, reduced by any shield, is Dose (mrem) = Γ × A × t / (d² × S) × 1,000, taking 1 R of gamma exposure ≈ 1 rem (10 mSv) of dose, and S is the shielding reduction factor (1 with no shield, 2 per half-value layer, 10 per tenth-value layer). The inverse-square law assumes a point source and distances much larger than the source; it ignores air attenuation and scatter from nearby objects, both of which matter little at a few metres.
How to use
A radiation worker stands 2 m from a 0.5 Ci Cs-137 source for 3 hours behind a shield that halves the dose (factor 2). Dose = 0.33 × 0.5 × 3 / (2² × 2) × 1,000 = 0.495 / 8 × 1,000 = 61.9 mrem (0.62 mSv). Repeated daily for 250 working days it would reach about 15,500 mrem, three times the 5,000 mrem annual limit — which is why time, distance and shielding all matter. The defaults (100 Ci of Co-60 at 2 m for 8 h, no shield) give 264,000 mrem (2.6 Sv), a dangerous acute dose.
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. Broad-beam tenth-value layers (NCRP Report 49) are about 4.0 cm of lead, 6.9 cm of steel and 20.6 cm of concrete; for Cs-137 they are 2.1 cm, 5.3 cm and 15.7 cm. The reduction factor for a shield of thickness x is 10^(x / TVL): 8 cm of lead in front of Co-60 gives 10^(8/4.0) = 100. Enter that number as the shielding factor.
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.
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