Radiation Dose Calculator
Compute radiation dose using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Equivalent Dose (Sv) = Absorbed Dose (Gy) x Radiation Weighting Factor
The equivalent dose accounts for biological damage by multiplying the absorbed dose by a radiation weighting factor specific to the type of radiation. Different radiation types cause different levels of biological damage per unit of energy deposited.
Worked Examples
Example 1: Medical CT Scan Dose
Problem:A CT scan delivers an absorbed dose of 10 mGy of X-rays. Calculate the equivalent dose.
Solution:Radiation type: X-rays (wR = 1)\nEquivalent dose = 10 mGy x 1 = 10 mSv\nThis equals 1000 mrem
Result:Equivalent dose = 10 mSv (within diagnostic range)
Example 2: Alpha Particle Exposure
Problem:A worker receives 0.5 mGy absorbed dose from alpha particles. Calculate equivalent dose.
Solution:Radiation type: Alpha (wR = 20)\nEquivalent dose = 0.5 mGy x 20 = 10 mSv\nSame biological effect as 10 mGy of gamma
Result:Equivalent dose = 10 mSv (within annual occupational limit)
Frequently Asked Questions
What is the difference between absorbed dose and equivalent dose?
Absorbed dose (measured in Gray or Gy) is the amount of radiation energy deposited per unit mass of tissue. Equivalent dose (measured in Sievert or Sv) accounts for the biological effectiveness of different radiation types by multiplying absorbed dose by a radiation weighting factor. For gamma and beta radiation, the weighting factor is 1, so absorbed and equivalent doses are numerically equal. For alpha particles, the weighting factor is 20, meaning 1 Gy of alpha radiation is equivalent to 20 Sv in biological damage.
What are safe radiation dose limits?
The general public limit is 1 mSv per year above natural background, while occupational workers are limited to 20 mSv per year averaged over 5 years (ICRP recommendations). Natural background radiation averages about 2.4 mSv per year globally. A chest X-ray delivers about 0.02 mSv, a CT scan about 2-10 mSv, and a transatlantic flight about 0.08 mSv. Acute doses above 250 mSv can cause measurable blood changes, and doses above 1,000 mSv cause radiation sickness.
How does the inverse square law apply to radiation?
The radiation dose rate decreases with the square of the distance from a point source. If you double your distance from a source, the dose rate drops to one-quarter. This is because radiation spreads out over a sphere whose area increases with the square of the radius. The formula is D2 = D1 x (d1/d2)^2, where D is dose rate and d is distance. This principle is one of the three key radiation protection methods: time, distance, and shielding.
What are radiation weighting factors?
Radiation weighting factors (wR) account for the different biological damage caused by different types of radiation. Gamma rays, X-rays, and beta particles have wR = 1 because they are sparsely ionizing. Protons have wR = 2. Alpha particles and heavy ions have wR = 20 because they deposit energy densely along their path, causing more DNA damage per unit of absorbed dose. Neutron weighting factors range from 5 to 20 depending on their energy, with fast neutrons being more damaging.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy