Radiation Dose Rate Calculator
Calculate dose rate from radioactive sources and shielding effectiveness.
The Three Protection Levers
Radiation protection rests on three variables, and the inverse square law makes one of them dramatically more effective than the others.
| Lever | Effect | Relative power |
|---|---|---|
| Distance | Dose falls as 1/r² | Doubling distance cuts dose to 25% |
| Time | Dose is proportional to exposure time | Halving time halves dose |
| Shielding | Exponential attenuation with thickness | Depends on material and energy |
Distance is the cheapest and most powerful. Stepping from 0.5 m to 2 m — four times further — reduces dose to one sixteenth. No practical amount of lead achieves that as easily, which is why hospital protocols emphasise stepping back before reaching for shielding.
Dose Units and Context
| Quantity | Unit | Measures |
|---|---|---|
| Activity | Becquerel (Bq) | Decays per second in the source |
| Absorbed dose | Gray (Gy) | Energy deposited per kilogram |
| Equivalent dose | Sievert (Sv) | Absorbed dose weighted for radiation type |
| Exposure | Approximate dose |
|---|---|
| Natural background | 2–3 mSv per year |
| Chest X-ray | 0.02 mSv |
| CT scan | 5–15 mSv |
| Occupational annual limit | 20 mSv |
| Acute radiation syndrome threshold | ~1,000 mSv |
The weighting matters: alpha particles carry a factor of 20 because they deposit energy densely along a short track. One gray of alpha exposure is 20 sieverts of equivalent dose — which is why alpha emitters are relatively harmless externally but extremely hazardous if inhaled or ingested.
Worked Examples
Common Mistakes
Becquerels count decays; sieverts measure biological dose. A high-activity source of low-energy radiation can deliver less dose than a weaker high-energy one.
Because dose falls with the square of distance, stepping back is far more effective than most people assume. Four times the distance gives one sixteenth the dose.
Alpha radiation carries a weighting factor of 20. The same absorbed energy produces twenty times the equivalent dose.
Alpha emitters are stopped by skin and pose little external risk, but are among the most dangerous internal contaminants.
Frequently Asked Questions
Formula Explorer connections
Interpretation: This relationship connects isotopic composition, decay, radiation, mass defect or nuclear energy to a measurable quantity. Assumption: Use the correct nuclide, decay constant, branching behavior and time units. Radiation estimates also depend on geometry, shielding and detector response.