0.01
Sv
10
mSv
0.0012
Sv
0.5
chest x-rays
0.01
Sv
10
mSv
0.0012
Sv
0.5
chest x-rays
The Radiation Dose Calculator converts absorbed radiation dose (in Gray) to equivalent dose (in Sievert) using radiation weighting factors, and to effective dose using tissue weighting factors. These conversions are essential for radiation protection, medical physics, and occupational safety.
The absorbed dose D (Gray, Gy = J/kg) measures the energy deposited per unit mass of tissue by ionizing radiation, without regard to biological effect. The equivalent dose H (Sievert, Sv) accounts for the relative biological effectiveness (RBE) of different radiation types: H = D * wR, where wR is the radiation weighting factor. X-rays, gamma rays, and beta particles have wR = 1; protons wR = 2; alpha particles wR = 20 (much more biologically damaging per unit absorbed dose due to dense ionization).
The effective dose E (Sv) extends this to account for the varying sensitivity of different organs to radiation-induced cancer: E = sum(H_T * wT), where wT is the tissue weighting factor. The ICRP weighting factors reflect cancer risk: bone marrow, colon, lung, and stomach each have wT = 0.12 (most sensitive to radiation-induced cancer); skin and brain have wT = 0.01 (least sensitive).
Reference doses: annual background radiation ~2.4 mSv/year worldwide; chest X-ray ~0.02 mSv; CT scan of abdomen ~10 mSv; occupational limit ~20 mSv/year; probabilistic lethal dose (LD50) ~4-5 Gy whole-body gamma; deterministic effects threshold ~100 mSv acute dose for stochastic effects.
Radiation protection follows the ALARA principle (As Low As Reasonably Achievable). Time, distance, and shielding are the three tools for reducing radiation dose.
Equivalent dose: H = D * wR (Sv). Radiation weighting factors: gamma/X/beta wR=1, proton wR=2, alpha wR=20, thermal neutrons wR=2.5, fast neutrons wR=5-20 (energy dependent). Effective dose for one tissue: E = H * wT. Full effective dose requires summing over all exposed tissues: E = sum(D_T * wR * wT).
0.02 mSv = 1 chest X-ray. 2.4 mSv = annual background dose. 7 mSv = typical flight dose per year for pilots. 20 mSv/yr = occupational dose limit. 50-100 mSv = lowest dose showing statistically increased cancer risk. 1000 mSv (1 Sv) = nausea/early radiation sickness. 4-5 Gy whole-body = LD50 without treatment.
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0.01 Gy of alpha radiation to lung gives an equivalent dose of 200 mSv (wR=20), equivalent to 10,000 chest X-rays. The high wR for alpha particles explains why radon gas in homes (which irradiates lung with alpha emitters) is a significant lung cancer risk.
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1 mGy of gamma to lung-equivalent tissue gives 1 mSv equivalent dose, equal to ~50 chest X-rays or 15% of annual background dose. Regular occupational monitoring maintains doses well below regulatory limits.
Gray (Gy = J/kg) is the physical absorbed dose — how much energy is deposited. Sievert (Sv) is the equivalent or effective dose — corrected for biological damage potential of the radiation type and organ sensitivity. For gamma rays, 1 Gy = 1 Sv numerically.
A dimensionless factor (ICRP Publication 103) accounting for the biological effectiveness of different radiation types: gamma/X-ray/beta wR=1; proton wR=2; alpha wR=20; thermal neutrons wR=2.5; 1 MeV neutrons wR=10; high-energy heavy ions wR=20.
A dimensionless factor reflecting the contribution of each organ to whole-body cancer risk from radiation. Defined by ICRP so that sum of wT = 1. Bone marrow, lung, colon, stomach each have wT=0.12; gonads wT=0.08; thyroid, bladder, liver wT=0.04; bone surface, brain, skin wT=0.01.
The natural radiation dose everyone receives: cosmic rays (~0.4 mSv/yr), terrestrial gamma (~0.5 mSv/yr), radon inhalation (~1.3 mSv/yr), internal (40K, 14C, ~0.3 mSv/yr). Average worldwide: ~2.4 mSv/yr. Varies 5-fold by location.
The LNT model assumes cancer risk is proportional to dose with no safe threshold: any dose carries some (very small) risk. It is used for radiation protection policy even though it is controversial at low doses (below ~100 mSv). Alternative models include hormesis (low doses beneficial) and threshold models.
Deterministic effects have a threshold dose below which they do not occur and severity increases with dose (radiation burns, radiation sickness, cataracts). Stochastic effects (cancer, hereditary effects) have no threshold — probability increases with dose but severity does not.
ICRP recommended limits: 20 mSv/yr effective dose averaged over 5 years, with no single year exceeding 50 mSv. Eye lens: 20 mSv/yr (tightened 2011). Skin: 500 mSv/yr. Public dose limit: 1 mSv/yr.
Gamma and X-rays are attenuated by dense materials (lead, concrete) exponentially: I = I0 * e^(-mu*x), where mu is the linear attenuation coefficient. A 10 cm lead shield (mu ~ 50 cm^-1 for Co-60 gammas) reduces intensity by e^(-5) ~ 0.007 = 99.3% attenuation.
From internal contamination, ingested or inhaled radionuclides deliver dose over time as they decay inside the body. The committed effective dose integrates this over 50 years (workers) or 70 years (public). It is used for assessing internal radiation hazards from nuclear incidents.
As Low As Reasonably Achievable — the fundamental principle of radiation protection. Exposures should be kept as low as practical, not just below regulatory limits. The three tools: time (minimize exposure duration), distance (intensity falls as 1/r^2), shielding (attenuate the beam).
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