Calculator Inputs
Plotly Graph
The curve below uses the solved reference condition and plots how intensity changes as distance increases.
Example Data Table
Example scenario: a point source measures 120 µSv/h at 1 meter. Intensities at larger distances follow the inverse square relationship.
| Distance (m) | Distance Ratio | Expected Intensity (µSv/h) | Reduction vs 1 m |
|---|---|---|---|
| 1 | 1.00 | 120.00 | 0.00% |
| 2 | 2.00 | 30.00 | 75.00% |
| 3 | 3.00 | 13.33 | 88.89% |
| 4 | 4.00 | 7.50 | 93.75% |
| 5 | 5.00 | 4.80 | 96.00% |
Formula Used
For a point-like source, radiation intensity decreases with the square of the distance:
Here, I represents radiation intensity or dose rate, and r represents distance from the source.
This relationship is most accurate for point sources in open space without shielding, scattering, collimation, or strong absorption by surrounding materials.
How to Use This Calculator
- Select a calculation mode based on the quantity you want to solve.
- Enter the known intensity values and distances in consistent units.
- Choose a distance unit for each distance field.
- Set an optional threshold to evaluate a safer comparison intensity.
- Add uncertainty and graph settings if you want wider analysis.
- Press the calculate button to show results above the form.
- Review the graph, derived ratios, and threshold status.
- Export the results using the CSV or PDF buttons.
Frequently Asked Questions
1. What is the inverse square law in radiation?
It states that intensity from a point-like source drops in proportion to one divided by distance squared. If distance doubles, intensity becomes one quarter of the original value.
2. Why does doubling distance reduce intensity so strongly?
The emitted radiation spreads over a larger spherical area as distance increases. Because surface area grows with the square of radius, the same energy is distributed more thinly.
3. Which units can I use for intensity?
You may use dose-rate or relative count units such as µSv/h, mSv/h, counts per second, or counts per minute. Keep the same unit throughout one calculation.
4. Can this calculator find a safer working distance?
Yes. Use the safe distance mode, enter a known intensity and measurement distance, then supply a threshold. The calculator estimates the minimum distance needed to reach that target intensity.
5. Does shielding affect the answer?
Not directly. This model handles geometric spreading only. Real shielding materials, beam direction, scattering, and absorption can make field measurements lower or higher than the ideal inverse square estimate.
6. Is this valid for every radiation source?
It works best for sources that behave approximately like points and where the measurement distance is large compared with source size. Extended, collimated, or heavily shielded sources need more detailed modeling.
7. Why can real detector readings differ from the estimate?
Detector geometry, background radiation, shielding, air attenuation, source size, and alignment all matter. The inverse square law is a strong baseline, but practical measurements include these extra influences.
8. When should I avoid relying only on this calculator?
Avoid sole reliance during safety-critical planning, compliance work, or medical and industrial radiation assessments. Use calibrated instruments, official procedures, and qualified radiation safety guidance for real decisions.