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Point-Source Intensity & Distance Scaling

Scale nonnegative intensity between two positive distances using an ideal inverse-square spreading model.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

An intensity of 100 at 2 m becomes 25 at 4 m, in the same intensity units. Doubling distance reduces intensity to one quarter.

I₂ = I₁ × (r₁ / r₂)²

Worked example

Enter these known values and leave the other values blank.

Intensity at the first distance
100 × 10⁰
First distance from the source
2 m
Second distance from the source
4 m
Intensity at the second distance
25 × 10⁰

Assumptions and limitations

  • Distances are positive and measured from the same source. Intensities are nonnegative and must use the same physical unit; the dropdown only changes the power-of-ten multiplier.
  • The model assumes point-source geometric spreading in an unobstructed medium without absorption or reflection. It is unsuitable for a collimated beam or a general near-field geometry.
  • With nonzero intensities the positive distance inverse is used. Zero intensity can be scaled forward, but two zero intensities cannot determine a distance ratio.

Common questions

Do I enter the distance between the two measurement points?

No. Enter each point’s distance from the common source. The calculation uses the ratio of those source distances.

Do the intensity selectors convert watts to lumens?

No. They only apply powers of ten. Choose and keep a single intensity unit appropriate to the quantity being compared.

References

Bookify requires nonnegative intensities at positive source distances. The light-year uses exactly 299792458 m/s times a 31557600-second Julian year, replacing the rounded reference factor. The parsec uses the IAU definition 648000/π astronomical units, with one astronomical unit exactly 149597870700 meters, instead of a rounded decimal factor.

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