Radiation units are necessary to express quantities of physical entities on a numerical scale for comparative purposes. Quantification of physical entities is normally done by estimating a measurable physical effect of the physical entity, e.g., heat is quantified on the basis of expansion it produces in materials. The fundamental condition for quantification is that the amount of the physical entity and its measured effect should maintain a strict linear relationship.

In radiological physics, medical imaging, radiation therapy, and radiation safety, radiation units are broadly classified into six major categories based on what physical phenomenon or biological effect they measure:

• Radiation Field / Beam Quantities: Measure the spatial and temporal distribution of photons (Fluence, Flux, Energy Fluence).
• Radioactivity / Source Activity Units: Measure the rate of nuclear disintegration from a radioactive source (Curie, Becquerel).
• Exposure Units: Measure the ionization produced by photons in air (Roentgen, Coulomb/kg).
• Energy Transfer Units (Kerma): Measure the initial kinetic energy transferred from uncharged photons to charged particles in a medium.
• Absorbed Dose Units: Measure the actual energy deposited per unit mass in any material or tissue (Gray, Rad).
• Equivalent and Effective Dose Units: Measure the biological risk and weighted health detriment across tissues and radiation types (Sievert, Rem).

In 1981, the International Commission on Radiation Units and Measurements (ICRU) issued standardized units based on the International System of Units (SI) to maintain global uniformity across all radiological and medical physics applications.

Radiation Field Quantities (Fluence & Flux vs Distance)

1. Fluence, Flux, and Energy Fluence (Radiation Field Quantities)

Before radiation interacts with a medium, its spatial and temporal characteristics as it travels through space must be accurately mapped using specialized beam geometry metrics.

• Photon Fluence (Φ): The number of photons passing through a unit cross-sectional area. Its standard unit is cm^-2. It quantifies the overall particle concentration crossing a given geometric boundary.
• Photon Flux (φ̇): The time-rate derivative of fluence. It measures the speed at which photons pass through a unit area per second, expressed in cm^-2s^-1. This parameter is crucial for evaluating active beam intensity rates.
• Energy Fluence (ψ): The total amount of radiant energy passing through a unit area, measured in joules per square meter (J/m²). It accounts for both particle population density and the energy spectrum of the radiation beam.

Advantages

• Crucial for designing structural radiation shielding, calculating primary beam profiles, and determining geometric divergence from point and extended sources.
• Provides exact spatial mapping of radiation fields before encountering matter.

Limitations

• Purely geometric and physical descriptors; they do not account for how energy interacts with or deposits inside matter.
• Completely ignore the biological properties and elemental composition of the interacting medium.

2. Activity Units (Radioactivity)

Activity refers to the number of unstable atomic nuclei that regain stability through radio-disintegration per unit time. This information is significant as the quantity of radiation released from a radioactive material is directly proportional to its activity. Activity gives a direct measurement of the quantity of radiation released per unit time (disintegration rate) from a given radioactive source.

Activity Units (Radioactive Decay Curve over Time)

The disintegration rate of a radioisotope is measured traditionally by the unit curie (Ci). One curie is defined as the number of disintegrations per second (dps) from 1 gram of radium (Ra-226), which is precisely found to be 3.7 × 10^¹⁰ dps . Smaller traditional submultiples such as millicurie (mCi) and microcurie Ci) are also used:

• 1 mCi = 3.7 × 10⁷dps
• 1 mu Ci = 3.7 × 10⁴ dps

Becquerel (Bq) is the modern SI unit of activity, and it is equal to 1 dps. In clinical practice, mega Becquerel (MBq) and giga Becquerel (GBq) are utilized:

• 1MBq = 10⁶ Bq
• 1 GBq = 10⁹ Bq

In day-to-day practice, the useful relation is 1mCi = 37 MBq. Hence:

1 Ci = 3.7 × 10¹⁰ Bq = 37 GBq

Advantages

• Perfectly tracks the strength, decay rate, and half-life of radioactive sources, sealed teletherapy isotopes, and unsealed radiopharmaceuticals used in nuclear medicine.
• Essential for radioactive waste management, transport safety regulations, and source inventory control.

Limitations

• Because activity deals exclusively with nuclear emissions, it does not have any direct practical application in diagnostic radiology or external beam therapy. These units do not tell us the dose delivered to a biological system.
• A high activity of a low-energy emitter presents a completely different biological risk profile compared to a low activity of a high-energy emitter.

3. Exposure Units (Roentgen)

Exposure indicates the amount of ionizing photons present in a field. The number of charged particles produced by ionization is directly proportional to the ionization events. Hence, ionizing photons are quantified on the basis of the total electrical charge produced by them in a given medium. Air is the universal reference medium to measure exposure because its effective atomic number (Z ≅ 7.6) closely matches that of soft tissue (Z ≅ 7.4). The average minimum energy necessary for photons to produce ionization in air is about 34 eV (33.97 J/C).

The term exposure (X) refers to the radiation quantity measured in terms of ionization in air within a small volume around a point. Exposure is a source-related term that obeys the inverse square law. The traditional unit of exposure is the roentgen (R).

Exposure Units (Air Ionization vs Tube Current / mAs)

One roentgen (established in 1928) is defined as the quantity of X or gamma radiation such that the associated corpuscular emission per 0.001293 grams of air (1 cc of dry air at Standard Temperature and Pressure: 273 K and 760 mm of Hg) produces in air ions carrying 1 esu of electricity of either sign. If an open-air chamber is used, ambient temperature and pressure variations alter the density of air molecules present in the chamber, requiring strict temperature and pressure corrections.

In modern SI units, these practical difficulties are avoided by replacing volume of air with mass of air, which remains unaffected by temperature and pressure variations. One exposure unit is defined as the amount of photons producing one coulomb of charge in one kilogram of air, expressed as coulomb per kilogram (C/kg) in air. The roentgen unit is related to the SI unit as:

1 R = 2.58 × 10^-4 C/kg of air

In practice, the following submultiples of the roentgen are used:

• 1 milliroentgen (mR) = 10^-3 R
• $1\text{ microroentgen (μ R) = 10^-3 mR = 10^-6 R

Radiation monitors are usually calibrated in roentgens and milliroentgens (mR) to measure the output of X-ray machines. The output of an X-ray unit is frequently expressed in mR/mAs (e.g., a 75 kV X-ray unit with 2 mm Al filtration may yield 5 mR/mAs} at 100 cm distance). Measuring exposure rate in air using air-filled ion chambers is straightforward because air’s effective atomic number equals soft tissue in the diagnostic X-ray energy range, making measured exposure proportional to soft tissue dose.

Advantages

• Easily measured experimentally using standard cavity or open-air ionization chambers.
• Follows the inverse square law, simplifying distance-based calculations for radiation safety.

Limitations

• It is not a unit of absorbed dose, which measures actual deposited energy.
• It can be utilized only up to a maximum photon energy of 3 MeV.
• It is strictly defined only for X and gamma radiations measured in air.

4. Kerma Units (Kinetic Energy Released in Medium)

Kerma stands for Kinetic Energy Released in the Medium, describing the initial interaction of a photon with an atom in a medium. When X-rays and gamma rays pass through matter, they transfer kinetic energy to secondary charged particles (electrons and protons). Kerma (K) measures the kinetic energy transferred to these charged particles.

Kerma Units (Energy Transfer Coefficient vs Photon Energy)

It is formally defined as the sum of the initial kinetic energies of all charged ionizing particles liberated by photons in a material of unit mass. The unit for kerma is joules per kilogram (J/kg). The modern SI unit is the gray (Gy) and the traditional unit is the rad. When the reference material is air, the quantity is called air kerma:

1 air kerma (Gy)} = 114 R

Mass Energy Transfer Coefficient

For X and gamma rays, kerma can be calculated from the mass energy transfer coefficient (μ_tr/ρ_o) of the material and the energy fluence (Ψ). The mass energy transfer coefficient is the product of the mass attenuation coefficient and the fraction of photon energy transferred as kinetic energy to charged particles. It is always less than the mass attenuation coefficient because scattered photons do not contribute to the kinetic energy of the charged particles. The ratio of the mass energy transfer coefficient to the mass attenuation coefficient is 0.68 for 20 keV photons in tissue, decreasing to 0.18 at 50 keV due to increased Compton scattering dominance.

If Ψ is the energy fluence and (μ_tr/ρ_o)_E is the mass energy transfer coefficient at energy E, then kerma (K) is given by:

K = Ψ(μ_tr/ρ_o)_E

Advantages

• Bridges uncharged photon radiation fields with charged particle energy transfer mechanics, serving as a primary metric in radiotherapy beam calibration.
• Directly tracks energy deposition initiation points within material structures.

Limitations

• Measures energy transferred, not energy absorbed, failing to account for energy escaping via bremsstrahlung radiation.
• Becomes complex at ultra-high photon energies where electronic equilibrium breaks down.

5. Absorbed Dose Units (Gray / Rad)

Exposure to radiation results in the transfer of energy from radiation to the interacting medium (kerma). However, this transferred energy may not be fully absorbed locally within the medium because a portion is radiated out in the form of bremsstrahlung X-rays. Consequently, absorbed dose equals the difference between kerma and bremsstrahlung loss.

Absorbed Dose Units (Depth Dose Build-up in Medium)

The term absorbed dose (D) refers to the amount of energy absorbed per unit mass of a substance. The traditional unit of absorbed dose is the rad (short for radiation absorbed dose), where:

1 rad = 100 ergs/gram

This unit is independent of the radiation type and interacting medium.

The SI unit of absorbed dose is the gray (Gy), where:

1 Gy = 1 J/kg

To convert between rad and gray:

1 Gy = \frac{10^7\text{ ergs}}{10^3\text{ g}} = 10,000\text{ erg/g} = 100\text{ rad}$$

Hence, 1 Gy = 100 rads. Practical submultiples of gray include:

• 1 milligray (mGy)} = 10^-3 Gy
• 1 microgray (\μ Gy)} = 10^-6 Gy

Since 1 Gy = 100 rad, 1 mGy = 100 mrad and 1 \mu Gy = 100 \μ rad.

Because the rad or gray is defined based on the energy delivered directly within a medium, it is ideally suited to describe biological effects and quantify radiation doses delivered to patients in clinical radiotherapy.

Mass Energy Absorption Coefficient

The initial kinetic energy transferred to charged particles is absorbed in tissue as absorbed dose, minus any energy escaping as bremsstrahlung X-rays. This true absorbed dose absorption efficiency is represented by the mass energy absorption coefficient (μ_en/ρ_o) of the medium. The mass energy absorption coefficient is always less than the mass energy transfer coefficient. However, in diagnostic X-ray energy ranges with low-Z materials, both coefficients are nearly identical because bremsstrahlung losses are extremely small.

Advantages

• Universal physical metric applicable across all materials, tissue types, and radiation modalities.
• Serves as the primary direct predictor for deterministic biological tissue damage (e.g., radiation burns, organ failure).

Limitations

• Equal physical absorbed doses (e.g., 1 Gy) delivered by different radiation types (alpha particles vs. X-rays) produce wildly different levels of biological damage.
• Direct in-vivo measurement inside human organs is clinically challenging and relies on complex cavity theories.

6. Equivalent Dose and Effective Dose Units

Exposure to radiation can involve whole-body or partial-body irradiation, resulting in uniform or non-uniform exposure patterns. Furthermore, the radiosensitivity of individual tissues in the human body varies significantly. Individual tissues contribute differently to the total health detriment of an exposed person, depending on damage severity and curability.

Equivalent and Effective Dose Units (Weighting Factor Comparison)

Equivalent Dose (H)

To account for biological variations per unit dose across radiation types, the ICRP introduced the radiation weighting factor (w_R) (ICRP Report 60, 1990). This factor modifies absorbed dose to reflect relative biological effectiveness:

where D is absorbed dose and w_R is the weighting factor. The weighting factor is 1 for X-rays, gamma rays, and electrons of all energies. High-LET radiations cause greater biological harm and carry higher radiation weighting factors.

The SI unit of equivalent dose is the sievert (Sv), where 1 Sv = 1 J/kg. The traditional special unit is the rem (radiation equivalent man), where 100 rem = 1 Sv. In practice, millisieverts (mSv) are widely used:

• 1 Sv = 1000 mSv
• 100 rem = 1000 mSv
• 100,000 mrem = 1000 mSv (1 rem = 1000 mrem)

Therefore, 100 mrem = 1mSv, and 100 mR = 1 mSv (assuming an f-factor of 1).

Table 5.1: Radiation Weighting Factors (w_R)

Effective Dose (E)

To account for variations in radiosensitivity across different tissues and the non-uniformity of partial-body radiation exposure, the ICRP established tissue weighting factors (w_T). The weighting factor of a particular tissue or organ represents the relative risk of stochastic health effects induced in that organ when irradiated alone, compared to total stochastic risk if the same dose were received uniformly by the whole body. The sum of the products of equivalent dose to each irradiated tissue (H_T) and its corresponding tissue weighting factor is called the effective dose (E):

where w_T is the weighting factor of tissue T and H_T is the mean equivalent dose received. This quantity (E) expresses an overall measure of health detriment associated with partial-body or whole-body exposure. The sum of all tissue weighting factors equals unity (Σ w_T = 1.0). The unit of effective dose is the sievert (Sv).

Table 5.2: Tissue Weighting Factors (w_T – ICRP 2005)

Advantages

• Seamlessly bridges physical dose measurements with human health risk assessment and regulatory radiation protection standards.
• Combines internal, external, partial-body, and whole-body exposures into a single intuitive risk index.

Limitations

• Weighting factors are generalized averages derived from reference populations and do not account for individual genetic variations, age, or gender anomalies.
• Strictly restricted to radiation protection, stochastic risk estimation, and regulatory compliance. They must never be used for acute clinical radiotherapy treatment planning.

Summary Master Table of Radiation Unit Types