Relative Brightness and Twilight Factors for Binoculars & Scopes

small boy using binocularsIf you have been looking for a new pair of binoculars or spotting scope, you have probably seen brightness and/or twilight factors reported with the various specifications and in reviews.

Both values are useful if you understand what the numbers mean and under what situations they can be used.

Relative Brightness

Relative brightness is a theoretical estimation of how bright the image should be when viewed through binoculars or spotting scopes. It is calculated by simply squaring the exit pupil value. The exit pupil is the size of the beam of light that comes out into your eye. Sometimes, this value is also reported with the binocular or spotting scope specifications, but it is also easily calculated by dividing the size of the objective lens by the magnification.

For example (see Table 1), an 8 x 50 (8 power magnification and 50 mm objective lens) binocular has an exit pupil value of 6.25 (50/8). Compare that to 10 X 50 pair of binoculars, where 50/10= 5.0 exit pupil. Then square each exit pupil value to get relative brightness values of 37.5 for the 8 X 50 and 25.0 for the 10 X 50 binoculars. The 10 X 50s have only 67% of the relative brightness of the 8 X 50 binoculars.

Table 1. Exit Pupil and Relative Brightness Calculations for Common Binocular Sizes

Mag. & Objective Equation 1 Exit Pupil Equation 2 Rel. Brightness Rel. to 8×50
       8 x 50   50/8 =    6.25 6.25 x 6.25 =         39.1      1.00
      10 x 50  50/10 =    5.0  5.0 x 5.0 =         25.0      0.67
      12 x 50  50/12 =    4.17 4.17 x 4.17 =         17.4      0.46
       8 x 42   42/8 =    5.25 5.25 x 5.25 =         27.6      0.74
      10 x 42  42/10 =    4.2  4.2 x 4.2 =         17.6      0.47
       8 x 32   32/8 =    4.0  4.0 x 4.0 =         16.0      0.43
      10 x 32  32/10 =    3.2  3.2 x 3.2 =         10.2      0.27

In table 1, you can see relative brightness values for several sizes of binoculars. I also included the ratio of each value to the 8 x 50 binoculars for comparison.

You will notice that as magnification increases and/or as objective lens size becomes smaller, the relative brightness values decrease as light is lost. In the table, the 8 x 50 binoculars will have the brightest image and the 10 x 32s will have the darkest image.

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Twilight Factor

Twilight factor is a theoretical estimation of how much detail can be seen in low light and is estimated by first multiplying the magnification by the objective lens size, and then taking the square root of that product. So twilight factor can increase with an increase of either magnification and objective lens size or both. The twilight factor can also remain the same if the magnification is doubled but the objective size is cut in half (and vice versa).

For example, the 8 X 50 binoculars would be 8 times 50 =400, then the square root of 500 = 20.0 value for twilight factor. The twilight factor for the 10 X 50 is simply 10 times 50 = 500 and the the square root of 500 = 22.4, so the 10 X 50s have a 12% detail advantage over the 8 X 50s in low light.

Table 2. Twilight Factor Calculations for Common Binocular Sizes

Mag. & Objective Equation Twilight Factor Rel. to 12×50
        8 x 50 sq. root (8 x 50) =        20.0       0.82
       10 x 50 sq. root (10 x 50) =        22.4       0.91
       12 x 50 sq. root (12 x 50) =        24.5       1.00
        8 x 42 sq. root (8 x 42) =        18.3       0.75
       10 x 42 sq. root (10 x 42) =        20.5       0.84
        8 x 32 sq. root (8 x 32) =        16.0       0.65
       10 x 32 sq. root (10 x 42) =        17.9       0.73

In table 2, the twilight factor has been calculated for several sizes of binoculars. I also included the ratio of each value to the 12 x 50 binoculars for comparison. You will notice that as magnification decreases and as the objective lens becomes smaller, the twilight factor decrease as detail is lost. In the table, the 12 x 50s will show the most detail in low light and the 8 x 32s will have the least detail.

How to Use Relative Brightness and Twilight factors

Remember that both the relative brightness and twilight factors are theoretical, so we have to be careful about using these values to make comparisons between different brands and styles of binoculars or spotting scopes. If we want to compare optics of similar quality and style, then theory and reality can be nearly equal and we can get a good idea of which models should have better light gathering ability or ability to see detail in low light conditions. So both of these values are very useful for comparing different magnifications and objective lenses of the same brand and model.

But if you try comparing cheap optics with good quality optics, then theory and reality part company. If you test this in the field, you will see that high quality binoculars gather more light than cheaper binoculars even when the brightness numbers tell you they should be about the same. You will also see more detail in low light with quality binoculars than less expensively built binoculars.

Roof Prism vs Poro Prism Binoculars

Roof prism binoculars are very popular today because of the smaller size and streamlined shape, but that design is inherently more expensive than the classic poro prism designs.

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Also be aware that low light conditions accentuates the imperfections of our vision. As it gets darker, our pupils begin to dilate which allows more scattered light to enter the eye. This causes images to be fuzzy. If our vision is a little “fuzzy” in bright light, then it will be more fuzzy in twilight conditions. That is why young eyes with poor quality binoculars can sometimes see better in low light than old eyes using very expensive binoculars.

Costs of Quality Optics

The reasons that higher quality optics gather more light and allow you to see more detail in low light conditions is the use of higher quality glass, coatings, mirrors and all parts are aligned more precisely. Quality parts and construction can transmit more light than poorer quality glass, coatings or poor alignment.

Light is lost as it is absorbed by imperfections in the glass and coatings and is also lost with poor quality mirrors and imperfect alignment within the binoculars. Quality glass, coatings, mirrors and precise alignment costs money.

 Highest Quality, Best of the Best Binoculars

The highest quality and binoculars are also usually the most expensive as they attempt to push the technological boundaries of glass, mirrors and coatings. For those that are curious about the absolute best quality binoculars:

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  1. Which is the CORRECT way to calculate Brightness Factor? I’ve always used the squaring of the result of dividing the object lens size by the magnification. e.g. using 10 x 42mm as a base I would divide 42 by 10 to get 4.2 and then square 4.2 (4.2 x 4.2 = 17.64).

    But I see some people simply multiply 10 x 42 (= 420) and take the square root of THAT but that does NOT give the same result! The square root of 420 is 20.49!


    • Yes, you are correct.
      Since they don’t get the same result, they are violating the “Pemdas” rule… Remember the mnemonic phrase “Please Excuse My Dear Aunt Sally“…
      Which stands for Parentheses first, Exponents second, Multiplication and Division (left to right) third and then Addition and Subtraction (left to right).

      If by Brightness factor, you mean Relative Brightness, it is simply the square of the exit pupil value.
      The Exit pupil value is the Objective lens size (mm) divide by the magnification.

      So, your example for 10 x 42 mm equals an exit pupil of 4.2 (See Table 1 in the post). Then 4.2 times 4.2 = Relative Brightness of 17.6.

      Why is the term “Relative” important? Think about what does a Relative Brightness of 17.6 really mean? What are the units?

      What is a mm divided by 10 power magnification mean? Then take that and square it?

      It is only relative to other binocular/scope lens sizes and magnifications, but it is useful because it gives a way to compare Relative Brightness between different binoculars or scopes.

      The 10 x 42 mm binoculars will be brighter than a 10 x 32 mm binocular, but less bright than a 10 x 50 mm binocular. That makes sense, but do you think you could tell the difference between the Relative Brightness of the 10 x 42 mm (17.6) and an 8 X 32 mm (16.0)? Probably not.

      But you will definitely see a difference between a 10 x 42 mm (17.6) a 10 x 50 mm (25.0) binoculars.

  2. I’m in deciding to get Levenhuk brand, model Karma Pro 8×42. Can you advise me about this bino and other brands of the same quality, Please.

    • Hi Emmy: I am not that familiar with Levenhuk binoculars. They are head-quartered in Tampa, Florida and the binos are made in China.

      I can see the low price is attractive, but I caution everyone from buying binoculars or spotting scopes based on price. I have done that too many times in the past.

      The Levenhuk Karma pro 8×42 model is priced in the high $90s or low $100s, but they have very few reviews and the reviews are just average.

      I use two models of binoculars for beginners to use as benchmarks.

      The Nikon Monarchs and Vortex Diamondback binoculars. They are priced in the low to mid $200 and they both have hundreds of good reviews. We have and still use both of these binoculars ourselves.

      If the price point is the sole reason for choosing the Levenhuk binoculars, consider the Celestron Nature DX Binoculars. They are similar prices and have hundreds of good reviews.
      Good luck.

  3. I will reconsider about that. But I have no more choice for brands or models in my country (Thailand) at this price range. So I will try my best for my lovely bird ^_^.
    Thank you so much for your advice.👍

  4. John ROY Copeland says

    Very professional and detailed ninformation. WELL DONE!!

    I am interested in binoculars best suited for astronomical use, star- and moon-gazing etc.

    PS. I am old — 81yrs!!!

  5. As you get older your eye cannot dilate as much. So how do you figure your actual Rel Brightness? Use your own eye ^2 ? This presuming that the glass Exit Pupil is >= your pupil.

  6. And what about when your pupil dia is larger than the Exit Pupil dia? In dark, your eye would lose some focus. So don’t you want both to be as close as possible? Which is worse, your pupil is 10% smaller, or 10% larger?

    • Backcountry Chronicles says

      yes, loose brightess and focus. Larger pupil would be worse, but don’t think pupil would be smaller in the dark.

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