Unit converter

Why conversions go wrong

Most conversion mistakes in radiation protection are not arithmetic. They happen when two numbers that look interchangeable describe different physical quantities. A becquerel counts nuclear transformations per second. A gray counts joules deposited per kilogram. A sievert is a gray multiplied by a weighting factor chosen for biological effect. A roentgen counts charge liberated per kilogram of dry air. Converting inside any one of those is a fixed factor. Converting between them is physics, and it needs information the number itself does not carry.

This converter therefore refuses to cross between quantities. Pick what you have, and every unit of that quantity appears at once. The one bridge it does offer — exposure to air kerma — is labelled as a physical step rather than a conversion, because it multiplies by W/e, the mean energy expended per ion pair formed in dry air, 33.97 joules per coulomb.

The factors, and which are exact

The curie is defined as exactly 3.7 × 10¹⁰ becquerel. The rad is exactly 0.01 gray and the rem exactly 0.01 sievert. The roentgen is exactly 2.58 × 10⁻⁴ coulomb per kilogram. None of these is rounded, so a conversion between them loses nothing. The disintegration per minute is exactly one sixtieth of a becquerel, which is why 6000 dpm per 100 cm² is exactly 1 Bq/cm² — a coincidence worth memorising, because those two units appear on the same survey report more often than any other pair.

Surface contamination

Surface units carry a hidden area. dpm/100 cm² is quoted per probe window, Bq/cm² per single square centimetre, and Bq/m² per square metre. A factor of 100 between the first two and 10⁴ between the last two is the single most common error on a decommissioning record. If a number looks two orders of magnitude out of place, this is usually why.

Per mass and per volume

Activity concentration is quoted two ways. Soil, waste and food are reported per unit mass — Bq/g, Bq/kg, pCi/g. Water, air and source vials are reported per unit volume — Bq/L, Bq/mL, pCi/L. Those are not two spellings of one quantity. They have different denominators, and moving between them requires the density of the material, which the number itself does not carry. This converter therefore keeps them in separate groups and offers the crossing as a separate step with a density you enter.

Water hides the distinction, because at 1.00 g/mL a litre weighs a kilogram and the two readings coincide: 1 Bq/L is 1 Bq/kg. That coincidence is exactly what makes the mistake hard to see, since it holds for water and fails for everything else, and it is a factor of a thousand out if the gram is used in place of the kilogram. A drinking-water limit quoted as 5 pCi/L is 0.185 Bq/L, which is 0.185 Bq/kg and 0.000185 Bq/g.

Gray and sievert

For photons and electrons the radiation weighting factor is 1, so a dose in gray and a dose equivalent in sievert are numerically equal. That equality tempts people to treat the units as synonyms. They are not. For alpha particles the factor is 20, for neutrons it varies with energy from about 2 to 20, and applying the wrong one changes a compliance decision by more than an order of magnitude. A converter cannot know which particle you mean, so it does not guess.

What this tool does not do

It does not convert absorbed dose to effective dose, which additionally needs tissue weighting factors and an exposure geometry. It does not convert air kerma to an operational dose equivalent such as the ambient dose equivalent H*(10), which needs a conversion coefficient that depends on photon energy. Both of those are answered by published coefficient sets, not by a fixed factor. Elsewhere on this site, where gamma figures are set against µSv/h targets, 1 µGy of air kerma is counted as 1 µSv; Methods states that convention and how far it sits from H*(10).

Worked examples

Checking a wipe result against a transport limit

A wipe from the outside of a package reads 2400 dpm/100 cm² after correction for counter efficiency and wipe area. The transport regulations of the IAEA (SSR-6) limit non-fixed contamination on a package surface to 4 Bq/cm² for beta and gamma emitters and low-toxicity alpha emitters, and to 0.4 Bq/cm² for all other alpha emitters. Does the package pass?

For a beta or gamma emitter the wipe is one tenth of the limit and the package passes. For an alpha emitter outside the low-toxicity group the same reading sits exactly on the limit, and a reading on the limit is not a pass. The unit conversion is the easy part; knowing which emitter is on the wipe decides the answer. Check also that both figures describe the same thing: the limit applies to removable contamination averaged over 300 cm² of any part of the surface, so one small spot can pass on average and still deserve a second wipe.

Reading an old survey meter in milliroentgen

An older ionisation chamber meter, still calibrated in exposure rate, reads 2.5 mR/h near a shielded container. A current procedure states its action level in µGy/h of air kerma.

The first step is exact; the second uses the energy needed to make one ion pair in dry air. The result is air kerma, not a dose equivalent. If the action level is written in µSv/h, the conversion needs a coefficient for the photon energy, which this tool deliberately does not supply. The conversion is also only as good as the meter: an instrument calibrated with Cs-137 can over-read or under-read at low photon energies, whatever unit its scale is printed in.

FAQ

How many becquerels are in a curie?

One curie is 3.7 × 10¹⁰ Bq, or 37 GBq, by definition. Each prefix step down keeps the factor 37: one millicurie is 37 MBq and one microcurie is 37 kBq, so a 10 mCi source holds 370 MBq.

How do I convert dpm/100 cm² to Bq/cm²?

Divide by 6000. One becquerel is 60 disintegrations per minute, and the reading is spread over 100 square centimetres, so 60 × 100 = 6000. To go the other way, multiply by 6000.

How do I convert roentgen to gray?

Multiply the exposure in C/kg (one roentgen is 2.58 × 10⁻⁴ C/kg) by the mean energy needed to make an ion pair in dry air, 33.97 J/C in ICRU Report 90. One roentgen therefore corresponds to 8.76 mGy of air kerma. Dose to tissue needs a further factor that depends on photon energy.

How do I convert mrem to µSv?

One millirem is 10 µSv, because one rem is exactly 0.01 Sv. So 100 mrem is 1 mSv, the annual effective dose limit for members of the public recommended in ICRP Publication 103.

Is Bq/L the same as Bq/kg for water?

Numerically yes, because a litre of water has a mass of one kilogram to within a fraction of a percent at room temperature. For any other liquid, divide the volume concentration by the density in kg/L to get Bq/kg. Soils and solids are reported per mass, so a volume figure there needs the bulk density.

Is a gray the same as a sievert?

Both units equal one joule per kilogram, but they measure different quantities. The gray is used for absorbed dose and kerma; the sievert is used for equivalent and effective dose, which apply the radiation and tissue weighting factors of ICRP Publication 103. For photons the radiation weighting factor is one, yet converting air kerma to a sievert quantity still needs an energy-dependent coefficient.