Method and bounds

One geometric model, kept explicit.

Falloffnote compares relative illuminance at a subject using an ideal point source. It assumes the same emitted output, angular direction and receiver orientation, with no additional light or intervening losses. The NIST photometric calibration reference relates point-source illuminance to source luminous intensity and squared distance. It also describes real-source deviations. There is no universal distance threshold in this tool that certifies a lamp as a point source.

The exact fraction

Let a be the old source-to-subject distance and b the new distance, both in the same unit. New illuminance divided by old illuminance is (a ÷ b)². The unit cancels. For exact entered decimal numbers, the calculator reduces a and b as integers before squaring. The displayed fraction is exact arithmetic within this model, not evidence of exact physical measurements.

The reciprocal, (b ÷ a)², is the ideal source-output multiplier that would restore the old modeled illuminance at the new distance. It is a separate hypothetical compensation, not a claim about a flash dial, electrical watts or a camera setting. The spherical-area explanation gives the geometric basis for the inverse-square dependence.

Signs and approximate stops

A full stop represents a factor of two in light, as explained in Nikon’s exposure guide. Illuminance change is log₂ of the relative illuminance fraction. Compensating source-output stops have the opposite sign. Farther away means negative illuminance change and positive compensation; closer means the reverse.

Stop values and decimal ratios are approximate. They use ten significant digits, with scientific notation for very small changes. A stable logarithm calculation retains one-unit differences between very close decimal distances. That numerical care does not establish comparable precision for a real light source.

What is outside the model

Inputs are positive plain decimals with at most twelve fractional places, from 0.000000000001 to 1000000000 in the selected common unit. Those are computational limits, not physical applicability limits. Nearby extended lights, changed receiver angles, bounce, reflections, shadows, ambient light, absorption and multiple sources are not modeled.

No absolute lux, source calibration, safety limit or actual camera/flash recommendation is produced. The drawing is schematic and not to scale. Inspect practical lighting with suitable real measurements and context; use this page to understand the declared ratio, not to certify a setup.