Inverse Square Dose Rate Calculator

Use inverse square scaling to estimate dose changes. Enter reference values then pick your distance. Export CSV or PDF for fast compliance documentation needs.

Inverse square scaling assumes a point-like source and direct line-of-sight.
Use 0 < k ≤ 1.
Used for target or measurement, depending on mode.
Formula used

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.

  • (r₁/r₂)² scales dose by geometry.
  • k models shielding or attenuation as a multiplier.
  • The dose unit stays the same before and after scaling.
How to use this calculator
  1. Select a calculation mode.
  2. Enter your reference dose rate and reference distance.
  3. Provide the target distance or target dose rate as required.
  4. Optionally set k to represent shielding.
  5. Press Calculate to view results above the form.
  6. Use CSV or PDF buttons to save the results.
Example data table
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.

Practical notes
Very close distances, large sources, scattering, and shielding geometry can deviate from ideal scaling. Treat results as estimates and follow your site safety procedures.
Inverse square dose rate guide

1) What this calculator solves

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.

2) Core relationship and the “four times” rule

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.

3) Units you can use

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.

4) Transmission factor for shielding

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.

5) Typical workflow for field checks

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.

6) Why point-source assumptions matter

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.

7) Quality checks and uncertainty

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%.

8) Where this calculator is used

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.

FAQs

1) Does the inverse square law always apply?

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.

2) What should I enter for the transmission factor k?

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.

3) Can I convert between Sv/h and Gy/h here?

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.

4) Why does a small distance error change results a lot?

Because distance is squared. A 5% distance error creates roughly a 10% dose-rate error. Measure distances carefully, especially when working near the source.

5) Which distance should I use: source-to-detector or source-to-person?

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.

6) What if the source is behind a wall or collimator?

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.

7) How do I use back-calculation mode?

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.

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