Use inverse square scaling to estimate dose changes. Enter reference values then pick your distance. Export CSV or PDF for fast compliance documentation needs.
For a point-like source in open space, dose rate follows an inverse square law with distance: D₂ = D₁ × (r₁/r₂)² × k. Here, D is dose rate, r is distance, and k is an optional transmission factor.
| Scenario | D₁ | r₁ | r₂ | k | Computed D₂ |
|---|---|---|---|---|---|
| Move detector farther | 120 µSv/h | 0.5 m | 2 m | 1 | 7.5 µSv/h |
| Add shielding at same distance | 25 mSv/h | 1 m | 3 m | 0.4 | 1.11 mSv/h |
| Back-calculate reference | — | 1 m | 4 m | 1 | Measured 0.8 mSv/h → D₁ = 12.8 mSv/h |
Examples are illustrative and assume a point-like source.
This tool estimates how a radiation dose rate changes when you move closer to, or farther from, a point-like source. It supports forward prediction (known reference dose rate), back-calculation (infer the reference from a measured value), and an optional transmission factor for shielding or attenuation.
The inverse square law states that dose rate is proportional to 1/r². Doubling distance reduces dose rate to one quarter; tripling distance reduces it to one ninth. Example: if D₁ = 2.0 mSv/h at r₁ = 1 m, then at r₂ = 2 m the estimate is 0.50 mSv/h, and at r₂ = 3 m it is 0.22 mSv/h.
Dose rate units commonly include µSv/h, mSv/h, Sv/h, and in some contexts Gy/h. Distance can be entered in meters, centimeters, millimeters, feet, or inches. Internally, the calculation uses consistent distance units so the squared ratio stays dimensionless.
Shielding is represented by a multiplier k (0 to 1 for attenuation). For instance, k = 0.40 means 60% reduction at the same geometry, while k = 0.05 represents strong attenuation. You can also use k > 1 to model buildup or calibration factors when appropriate.
Start by recording a stable reference point: dose rate, distance, detector orientation, and time. Then measure at a new distance and compare the observed value to the predicted value. Large deviations can indicate source size effects, scattering from walls, shielding geometry changes, or instrument energy response differences.
Inverse square scaling is most reliable when the source dimensions are small compared to distance. At close range, extended sources can behave closer to inverse-first-power or show plateaus. Rule of thumb: if you are within a few source diameters, treat results as approximate and validate with measurements.
Use consistent geometry: keep the detector at the same height and facing the source. Note that a ±5% distance error becomes roughly ±10% in dose rate because distance is squared. For example, 1.00 m vs 1.05 m changes the predicted dose rate by about 9.3%.
Common applications include radiation protection planning, controlled area boundary estimates, industrial radiography setup checks, and quick plausibility tests for survey meter readings. Always follow local safety rules, signage requirements, and regulatory limits for your site.
It applies best to point-like sources in open space. Close distances, large sources, shielding geometry, and strong scattering can cause significant departures from ideal inverse-square behavior.
Use k as a multiplier for attenuation: 1 means no shielding, 0.5 halves the dose rate, and 0.1 reduces it by 90%. If you have measured transmission data, use that value directly.
This calculator scales dose rate with distance but does not convert between different dose quantities. Convert units first using the correct radiation weighting and calibration context, then apply inverse-square scaling.
Because distance is squared. A 5% distance error creates roughly a 10% dose-rate error. Measure distances carefully, especially when working near the source.
Use the distance from the effective source location to the point of interest. For surveys, that is typically source-to-detector center. For planning, use source-to-occupancy position.
Inverse-square still describes geometric spreading, but shielding and beam shape dominate. Use a transmission factor only when geometry is comparable; otherwise rely on measured dose rates for the setup.
Enter your measured dose rate at the new distance, plus both distances and any transmission factor. The calculator returns the equivalent reference dose rate at the reference distance for the same geometry.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.