The calculator uses an inverse-square model with an optional shielding factor and buildup factor:
- No shielding: F = 1
- Half-value layers: F = 0.5ⁿ
- Tenth-value layers: F = 0.1ⁿ
- Linear attenuation: F = e^(−μx)
This tool estimates dose rate; real fields depend on geometry, energy spectra, scattering, shielding build-up, and calibration conventions.
- Enter the source activity and select its unit.
- Enter the published gamma constant for the radionuclide.
- Enter the measurement distance from the source center.
- Select a shielding model and provide parameters if needed.
- Optionally enter exposure time for total dose.
- Optionally enter a desired dose rate to solve distance.
- Press Calculate Dose Rate to view results above.
- Use the CSV or PDF buttons to export results.
| Radionuclide | Activity | Γ (example unit) | Distance | Shielding | Estimated dose rate |
|---|---|---|---|---|---|
| Example A | 3.7 GBq | 0.35 mSv·m²/(h·GBq) | 2 m | None | 0.323 mSv/h |
| Example B | 0.5 GBq | 0.20 mSv·m²/(h·GBq) | 1 m | 2 HVL | 0.050 mSv/h |
| Example C | 1.0 Ci | 13 R·m²/(h·Ci) | 3 ft | μ=0.12 1/cm, x=2 cm | See calculator output |
Replace values with your source data for accurate planning.
1) Purpose of a gamma constant estimate
A gamma constant (Γ) provides a quick link between a radionuclide’s activity and the dose rate at a chosen distance. It is widely used for work planning, boundary setting, and sanity checks against survey meter readings. The result is an engineering estimate, not a compliance measurement.
2) Core relationship and proportionality
The calculator applies Ḋ = Γ × A / r², then multiplies by shielding attenuation and a buildup factor. Dose rate is proportional to activity, so a 10% activity increase raises Ḋ by 10%. Distance has a stronger effect because it is squared.
3) Distance effect with numeric example
If a source produces 200 μSv/h at 1 m with the same Γ and A, then at 2 m the inverse-square term reduces the rate to 200/4 = 50 μSv/h. At 3 m it becomes 200/9 ≈ 22.2 μSv/h. This is why distance is often the fastest control measure.
4) Working with activity units
Activity is accepted in Bq to TBq and in curies. Remember that 1 Ci equals 37 GBq, so 10 mCi equals 0.37 GBq. The calculator converts everything to GBq internally to keep the dose-rate math consistent and to reduce unit mistakes in field notes.
5) Shielding using HVL and TVL data
HVL and TVL are convenient when published for your energy and material. One HVL halves the unshielded rate. For example, 3 HVL gives 0.5³ = 0.125, an 87.5% reduction. Two TVL gives 0.1² = 0.01, a 99% reduction.
6) Shielding using linear attenuation μx
When you know μ and thickness x, the model uses e^(−μx). If μ = 0.12 1/cm and x = 5 cm, then μx = 0.6 and e^(−0.6) ≈ 0.549. This is the primary-beam reduction; real measurements may be higher due to scatter.
7) Buildup factor and why it changes results
Buildup factor B accounts for scattered photons that still reach the point of interest. In light shielding B may be near 1.0. In thicker barriers, B can exceed 1 and partially offset exponential attenuation. Use reference buildup data when you have it.
8) Turning dose rate into decisions
Use the optional time field to estimate total dose for a task, then compare to your planning criteria. You can also enter a desired dose rate to solve the required distance while keeping the same shielding assumptions. Always validate with survey measurements whenever practical.
1) What does the gamma constant represent?
It links activity to dose rate at a specified distance for a radionuclide. It packages emission probability and photon energy into one planning coefficient.
2) Why does the calculator use an inverse-square term?
For a compact source in open space, radiation spreads over a spherical area that grows with r². That geometric spread makes dose rate drop rapidly with distance.
3) How do HVL and TVL options work?
HVL reduces the unshielded rate by half per layer, using 0.5ⁿ. TVL reduces it by ten per layer, using 0.1ⁿ. Enter fractional layers if needed.
4) When should I use μx shielding instead?
Use μx when you have a linear attenuation coefficient for the material and photon energy range. The model applies e^(−μx), which is useful for thickness-based calculations.
5) What is the buildup factor?
It accounts for scattered photons that add to dose behind shielding. B may be near 1 for thin barriers, but can be greater than 1 when scatter becomes significant.
6) Does the output replace instrument measurements?
No. It is for planning and comparison. Real readings depend on geometry, room scatter, shielding gaps, and detector response. Use field surveys to confirm decisions.
7) Why can exposure-based constants differ from dose-based ones?
Exposure (roentgen) refers to ionization in air, while dose uses absorbed energy or equivalent dose conventions. Conversions depend on photon energy and assumptions, so treat them as approximations.