BINOCULAR TOOLS RELATIVE BRIGHTNESS
Compare two brightness indexes, not two promises.
Enter the magnification and objective size for two binocular configurations. Compare the traditional squared-exit-pupil indexes side by side, with the limits of that calculation kept visible.
Two configurations, one formula
Relative brightness index = (objective diameter ÷ magnification)².
Enter both configurations, then select Compare.
These figures do not include coating efficiency, measured transmission, eye pupil size, optical design, or viewing conditions.
THE CALCULATION
What the relative brightness index measures
This traditional index squares the diameter of the exit pupil. Calculate each exit pupil by dividing effective objective diameter in millimeters by magnification. Then square each unrounded result. A larger number identifies a larger nominal exit-pupil geometry, not a proven brighter image.
exit pupil (mm) = objective diameter (mm) ÷ magnification
relative brightness index = exit pupil²
index ratio A/B = index A ÷ index BThe full input precision is used until the values are displayed. The indexes are dimensionless comparison values, not lux or transmission percentages.An 8×42 specification gives 42 ÷ 8 = 5.25 mm and an index of 27.5625. A 10×42 specification gives 4.20 mm and an index of 17.64. The nominal index ratio is 1.5625, shown in the result panel as 1.56 : 1. That is not a claim that one real image is 1.56 times brighter.
Manufacturer examples may use different published precision. Nikon’s relative-brightness overview lists 28.1 for 8×42, whereas directly squaring 42 ÷ 8 gives 27.5625. The calculator consistently uses the full supplied arithmetic; do not infer a particular manufacturer rounding rule from that discrepancy alone.
READ THE COMPARISON CORRECTLY
What the index cannot establish
No measured light transmission
Coatings, prisms, lens elements, internal losses, and build quality affect the light reaching your eye. None appears in the equation.
No universal eye-pupil fit
The viewer’s own pupil changes with light and differs between people. A larger exit beam may not be fully used in every condition.
No buying verdict or optical score
The ratio is not measured perceived brightness, contrast, resolution, field of view, edge sharpness, or overall image quality.
References and Sources
- Nikon, Relative brightness: Defines the squared-exit-pupil formula, provides a published numerical example, and explains real-light transmission limitations.
- Celestron, Twilight Factor and Relative Brightness: Separates the traditional index from other low-light measures and optical quality.