Radiation Converter
Convert radiation dose units between gray, sievert, rad, rem, roentgen, and their sub-multiples.
Radiation Converter
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Formula: Converted = Input x (From Unit Base Factor) / (To Unit Base Factor)
Worked example โ 2 Gy = 200 rad = 2,000 mGy = 2,000,000 uGy
Formula
Converted = Input x (From Unit Base Factor) / (To Unit Base Factor)
Radiation units are converted through their SI base unit. For absorbed dose: 1 Gy = 100 rad. For equivalent dose: 1 Sv = 100 rem. For exposure: 1 R = 2.58e-4 C/kg. Multiply the input by its conversion factor to the base unit, then divide by the target unit factor.
Worked Examples
Example 1: Converting Gray to Rad
Problem:A radiation therapy session delivers 2 Gray. Convert to rad and milligray.
Solution:Rad = Gray / 0.01 = 2 / 0.01 = 200 rad Milligray = Gray x 1000 = 2 x 1000 = 2,000 mGy Microgray = Gray x 1,000,000 = 2,000,000 uGy
Result:2 Gy = 200 rad = 2,000 mGy = 2,000,000 uGy
Example 2: Millisievert to Millirem
Problem:A worker receives 5 millisieverts of exposure. Convert to millirem and microsieverts.
Solution:Sievert = 5 x 0.001 = 0.005 Sv Rem = 0.005 / 0.01 = 0.5 rem Millirem = 0.5 x 1000 = 500 mrem Microsievert = 5 x 1000 = 5,000 uSv
Result:5 mSv = 500 mrem = 0.5 rem = 5,000 uSv
Frequently Asked Questions
What is the difference between gray and sievert?
Gray (Gy) measures absorbed radiation dose, which is the amount of energy deposited per kilogram of matter regardless of radiation type. Sievert (Sv) measures equivalent dose, which accounts for the biological effectiveness of different types of radiation. For X-rays and gamma rays, 1 Gy equals 1 Sv. However, alpha particles are 20 times more damaging biologically, so 1 Gy of alpha radiation equals 20 Sv. The sievert is used for radiation protection because it reflects actual biological harm.
What is the difference between rad and rem?
Rad (radiation absorbed dose) and rem (roentgen equivalent man) are older CGS units that have been largely replaced by gray and sievert in scientific use. One rad equals 0.01 gray, and one rem equals 0.01 sievert. The relationship between rad and rem parallels that of gray and sievert: rad measures raw absorbed dose while rem accounts for biological effectiveness. Many industries, particularly in the United States, still use rem and millirem for regulatory compliance and everyday radiation monitoring.
What is a roentgen and how does it relate to other units?
The roentgen (R) is a unit of radiation exposure that measures the ionization produced in air by X-rays or gamma rays. One roentgen equals 2.58 x 10^-4 coulombs per kilogram of air. While the roentgen only applies to photon radiation in air, it was historically the most common radiation measurement unit. For soft tissue, one roentgen of exposure produces approximately one rad of absorbed dose. The roentgen is still used in some medical and industrial applications despite being replaced by SI units.
What are safe radiation dose limits?
For the general public, the recommended annual dose limit is 1 millisievert (100 millirem) above natural background radiation, which averages about 2.4 mSv per year globally. Radiation workers are limited to 20 mSv per year averaged over five years, with no single year exceeding 50 mSv. For context, a chest X-ray delivers about 0.02 mSv, a CT scan delivers 2-10 mSv, and a transcontinental flight adds about 0.04 mSv. Acute doses above 1 Sv cause radiation sickness, and doses above 5 Sv are often fatal.
What is a radiation weighting factor and how does it link absorbed dose to equivalent dose?
Equivalent dose in sieverts is absorbed dose in grays multiplied by a radiation weighting factor that reflects how damaging a given radiation type is per unit of energy deposited. Photons, X-rays, electrons and beta particles carry a factor of one, so grays and sieverts match numerically. Alpha particles and heavy ions carry a much larger factor because their dense ionisation tracks cause more clustered biological damage per gray.
What is the difference between effective dose and equivalent dose?
Equivalent dose applies to a single tissue or organ and accounts only for the type of radiation. Effective dose goes further, weighting each organ dose by that organ radiosensitivity and summing across the body, so a partial-body exposure can be expressed as a whole-body equivalent. Both are reported in sieverts, which is why a dose figure should always state which of the two quantities it represents.
What is the difference between dose and dose rate?
Dose is the total energy absorbed, measured in grays or sieverts, while dose rate is dose per unit time, such as microsieverts per hour. A survey meter reads a rate, and a personal dosimeter accumulates a dose. Multiplying a steady rate by the exposure time gives the accumulated dose, so a small rate over a long occupancy can equal a large rate over a brief one.
Why is the roentgen defined in coulombs per kilogram?
The roentgen predates the modern dose quantities and measures exposure, meaning the ionisation that X-rays or gamma rays produce in air rather than the energy deposited in tissue. Its SI equivalent is simply charge liberated per mass of air, with one roentgen equal to 2.58 x 10 to the minus 4 coulombs per kilogram. Because it is defined in air, exposure must be converted before it says anything about tissue dose.
How do I convert between the SI units and the older rad and rem?
The conversions are decimal and fixed. One gray equals 100 rad, so a rad is one hundredth of a gray, and one sievert equals 100 rem, so a rem is one hundredth of a sievert. Millirad and millirem are therefore ten microgray and ten microsievert respectively. SI units are standard in scientific and international practice, while rad and rem persist in some older United States instrumentation and records.
What is kerma and how does it differ from absorbed dose?
Kerma is the kinetic energy released per unit mass to charged particles by indirectly ionising radiation such as photons or neutrons, and like absorbed dose it is expressed in grays. Absorbed dose counts the energy actually deposited locally. The two are close under charged-particle equilibrium but diverge near boundaries or at high photon energies, where liberated electrons travel some distance before depositing their energy.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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