modern electronic flash devices have manually adjustable power settings. Moreover, virtually all modern on-camera flash devices that have manually adjustable power settings also provide either a built-in mechanical circular calculator (such as shown in the photo at the top of this article) or a digital display that automatically shows the effect power levels have on fstop and distance (guide number). Nevertheless, for those who want to master the math, guide numbers diminish from their full-power ratings as the square root of their fractional setting per the following formula: …where is the numerator in the fraction of the power setting is the denominator in the fraction of the power setting The following is a step-by-step example of using the above formula: Suppose your full-power guide number is 48 (it is irrelevant if it is scaled for meters or feet for this purpose) and the flash device is set to power. Divide 1 by 16 to obtain 0.0625. Take the square root of that (the button on a calculator), which equals 0.25, and multiply that by the guide number of 48 to obtain a reduced-power guide number of 12.0. The mathematical relationship between guide numbers and power levels can also be understood using the below alternative formula, which is suitable whenever the numerator in the fractional power setting is 1 (which is usually the case with flash devices): …where is the denominator in the fraction of the power setting Example: Suppose your full-power guide number is 51 and your flash device is set to power. Take the square root of 32 (the button on a calculator), which equals approximately 5.657. Divide 51 by 5.657 to obtain a reduced-power guide number of 9.0. Effect of flash angle (zoom setting) Many flash devices have auto- or manual-adjust zoom features that permit the illumination angle to be widened (lessening the guide number) to fully illuminate the image area of wide-angle lenses, or narrowed (increasing the guide number) for telephoto lenses. Such coverage angles may be given in degrees but are often expressed as being equivalent to lens focal lengths for full-frame, 35 mm cameras. Manufacturers' advertising practices vary as to the angle of coverage underlying their guide number ratings, in large part because some flash devices can be zoomed whereas others are fixed. Virtually all modern on-camera flash devices with zoomable flash heads also have either a built-in mechanical circular calculator (such as shown in