What this calculator does
This tool converts a radiation exposure value between the Roentgen family of units (R, mR, uR) and the SI Coulomb-per-kilogram family (C/kg, mC/kg, uC/kg). Exposure measures the amount of ionization that X-rays or gamma rays produce in air, expressed as the electric charge liberated per unit mass of air. It is a universal physics conversion that applies identically everywhere.
Exposure is distinct from absorbed dose (gray, Gy, or rad) and from dose equivalent (sievert, Sv, or rem). Do not use this calculator to convert those quantities.
How to use it
Enter the exposure value, pick the unit it is expressed in, and the calculator instantly shows the same exposure in all six units, grouped by the Coulomb and Roentgen systems.
The formula explained
The conversion rests on one exact definition: \(1\ \text{R} = 2.58 \times 10^{-4}\ \text{C/kg}\). The input is first normalized to the SI base unit by multiplying by its factor (base = value x factor), then divided by each output unit's factor. Useful relationships: \(1\ \text{C/kg} = 10^{3}\ \text{mC/kg} = 10^{6}\ \text{uC/kg}\), and \(1\ \text{R} = 10^{3}\ \text{mR} = 10^{6}\ \text{uR}\).
$$C_{base}\ \text{(C/kg)} = \text{Exposure} \times f_{unit}$$$$\text{R} = \frac{C_{base}\ \text{(C/kg)}}{2.58\times10^{-4}}$$
Worked example
For 1 R: $$\text{base} = 1 \times 2.58\text{e-}4 = 2.58\text{e-}4\ \text{C/kg}.$$ That equals 0.258 mC/kg, 258 uC/kg, 1 R, 1,000 mR and 1,000,000 uR.
FAQ
Is the Roentgen still used? It is a legacy unit; the SI unit is C/kg, but R and mR remain common on older instruments.
Why 2.58e-4? It is the exact historical SI definition of the Roentgen and is hard-coded for accuracy.
Can I enter zero or negative values? Yes. The conversion is linear, so zero in gives zero out and there is never a divide-by-zero.
