Equivalent Dose Calculator

Absorbed dose (D) is the physical energy deposited per unit mass, measured in grays (Gy). Equivalent dose (H) is the product of absorbed dose and the radiation weighting factor (w_R), expressed in sieverts (Sv). While D is a purely physical quantity, H accounts for the biological effectiveness of different radiation types—for example, 1 Gy of alpha particles is biologically more damaging than 1 Gy of gamma rays, so H is higher for alpha due to w_R = 20. Equivalent dose is used for organ-specific risk assessments, whereas effective dose further weighs by tissue sensitivity.

According to ICRP 103 (2007), the w_R values are: X-rays, gamma rays, and beta particles = 1; protons (≥2 MeV) = 2; neutrons are energy-dependent (ranging from 2.5 to 20, with a continuous function); alpha particles, fission fragments, and heavy nuclei = 20. For most diagnostic and occupational exposures (X-rays and gamma), w_R = 1, so 1 Gy = 1 Sv. For neutron and alpha exposures, the equivalent dose is significantly higher than the absorbed dose.

Alpha particles are massive, highly ionizing, and deposit their energy in a very short range (only a few cells deep in tissue). This dense ionization causes more complex and less repairable DNA damage (double-strand breaks) per unit energy deposited, leading to a higher probability of cancer or cell death. In contrast, gamma rays deposit energy sparsely over a longer path, with mostly single-strand breaks that are more easily repaired. The w_R of 20 reflects this increased biological effectiveness, which is validated by epidemiological studies of radon exposure and animal experiments.

The total equivalent dose to an organ is the sum of the individual equivalent doses from each radiation type: H_total = Σ (w_{R,i} × D_i), where D_i is the absorbed dose from radiation type i. For example, if an organ receives 0.5 Gy of gamma (w_R=1) and 0.01 Gy of alpha (w_R=20), the total H = (1×0.5) + (20×0.01) = 0.5 + 0.2 = 0.7 Sv. This additivity is the basis for mixed-field dosimetry in nuclear facilities and radiotherapy.

Equivalent dose (H) is the dose to a specific organ or tissue, considering only the radiation quality (w_R). Effective dose (E) is a whole-body risk-weighted quantity that sums the equivalent doses to all exposed organs, each multiplied by a tissue weighting factor (w_T) that reflects the organ's radiosensitivity. Effective dose allows comparison of different irradiation geometries and is used for regulatory limits. Equivalent dose is used for organ-specific assessments, e.g., for the lens of the eye (which has a separate dose limit) or the thyroid. Both are measured in sieverts.

Yes, neutron w_R varies from about 2.5 for thermal neutrons (0.025 eV) up to about 20 for intermediate energies around 1 MeV, then drops to around 6 for high energies (>20 MeV). ICRP 103 provides a continuous function and a step-function approximation. If the spectrum is unknown, a conservative approach is to use w_R = 10 (the average value for occupational exposure) or perform spectrometry to determine the actual dose. In practice, neutron dosimeters are designed with energy-response corrections to directly provide the equivalent dose.

Electrons and muons are lightly ionizing radiation; they deposit energy diffusely along their tracks, similar to X-rays and gamma rays, producing similar biological effects per gray. Their relative biological effectiveness (RBE) is close to 1, so w_R = 1. Heavier charged particles (protons, alpha, heavy ions) have higher linear energy transfer (LET), which increases the RBE. The w_R values are based on decades of radiobiological experiments comparing cell survival, transformation, and chromosome aberrations for different radiation qualities.

The lens of the eye is a deterministic effect organ—it develops cataracts at a threshold dose. The International Commission on Radiological Protection (ICRP) sets a separate limit for the equivalent dose to the lens (20 mSv/year averaged over 5 years, with no year exceeding 50 mSv). This limit is in terms of equivalent dose to the lens, not effective dose, because the organ-specific risk is assessed separately from stochastic cancer risk. Therefore, for eye lens monitoring, the equivalent dose is the relevant quantity, often measured with a special dosimeter placed near the eye.

The current w_R values (ICRP 103, 2007) replaced the older quality factors (QF) from ICRP 60 (1990), which used a simpler step-function. The update incorporated new radiobiological data, especially for neutrons and protons, and improved understanding of RBE for various endpoints. For example, the neutron w_R now varies continuously with energy instead of a fixed value. The alpha w_R remained 20, consistent with earlier recommendations. These factors are periodically reviewed as new evidence emerges, but they are considered stable for practical radiation protection.

Most dosimeters (like TLDs, OSL, film badges) measure absorbed dose (or a signal proportional to it) and are calibrated to display the equivalent dose for a specific radiation field (e.g., gamma) assuming w_R = 1. For mixed fields, dosimeters may be designed with multiple elements (e.g., albedo dosimeters for neutrons) that allow discrimination of radiation types, and the equivalent dose is calculated internally using known w_R. Active electronic dosimeters can provide real-time H*(10) (ambient dose equivalent) using built-in algorithms and energy-compensated detectors. However, for accurate equivalent dose to an organ, you need to know both the absorbed dose and the radiation quality, which often requires spectrometry or paired detectors.

w_R replaced Q in ICRP 60 and later. Q was defined for radiation protection at 1 cm depth (the ambient dose equivalent) and used for operational quantities. w_R is defined for the equivalent dose to organs and is used in protection quantities. Both are dimensionless and have similar values for most radiations (e.g., Q=1 for gamma, Q=20 for alpha), but the definitions differ: Q is for calculating the dose equivalent at a point in a phantom, while w_R is applied to the organ absorbed dose to get equivalent dose. In practice, for gamma and beta, they are numerically the same, but for neutrons, the energy dependence differs. They are not used interchangeably; w_R is the current standard for protection quantities.

Equivalent dose does not include a dose-rate correction; it assumes a linear relationship between absorbed dose and biological effect for stochastic effects. However, for deterministic effects (e.g., skin burns), the rate of delivery does affect the threshold, but that's addressed through separate dose limits for acute vs. chronic. w_R is based on the relative biological effectiveness at low doses and low dose rates (in accordance with the LNT model). For high dose rates (e.g., in radiotherapy), the RBE may differ, but w_R is a fixed value for protection purposes. Thus, the equivalent dose formula H = w_R D is independent of dose rate, though actual risk may vary, which is why radiation protection uses additional factors like the DDREF (dose and dose-rate effectiveness factor) for risk estimation.

Calculate each component: Neutron equivalent dose = 10 mGy × 10 = 100 mSv. Gamma equivalent dose = 50 mGy × 1 = 50 mSv. Total equivalent dose to the organ = 100 + 50 = 150 mSv, or 0.15 Sv. This sum is the organ equivalent dose, which can be used for assessing deterministic effects or, when combined with tissue weighting factors, for calculating effective dose. Note that the total absorbed dose is 60 mGy, but the equivalent dose is 150 mSv, illustrating the impact of the high w_R for neutrons.

CTDI_vol is an absorbed dose index in a phantom and is used to estimate the absorbed dose to the scanned volume. Effective dose is calculated using organ-equivalent doses (which use w_R = 1 for X-rays, so equivalent dose equals absorbed dose for organs) multiplied by tissue weighting factors. Since X-rays have w_R = 1, the organ equivalent dose is numerically equal to the organ absorbed dose. However, the effective dose is a whole-body risk metric, more useful for comparing risks across different exams and patients. Organ equivalent doses are not typically reported for individual patients because they would require detailed organ segmentation and are not necessary for routine assessment.

In proton therapy, the RBE (relative biological effectiveness) for the therapeutic beam is often about 1.1 relative to photons. This is applied to the physical dose to get an RBE-weighted dose, which is analogous to equivalent dose but uses a variable RBE that depends on LET, depth, and tissue. The radiation weighting factor w_R for protons in ICRP is 2 (for radiation protection), but that is a conservative protection value, not the therapeutic RBE. In radiotherapy, a lower RBE of 1.1 is used clinically. Thus, equivalent dose in protection (with w_R=2) is not directly used in therapy; instead, a clinically derived RBE is used to prescribe the biologically effective dose.