The flash guide number formula explained
How GN equals aperture times distance, why raising ISO by two stops doubles reach, and the real-world limits of the number.
The core relationship
A guide number is a single figure that packs a flash unit's power into the aperture and distance it can support. The rule is compact: guide number equals aperture times flash-to-subject distance. Rearranged, aperture equals guide number divided by distance, and distance equals guide number divided by aperture. That is why one number lets you work out either setting. A GN of 56 in metres means the pairs f/8 at 7 m, f/11 at about 5 m and f/5.6 at 10 m all give the same exposure, because each pair multiplies back to 56.
Why distance costs so much light
The formula looks linear, but light does not spread linearly. Because illumination falls off with the square of distance, doubling the flash-to-subject distance quarters the light on the subject, which is a two-stop loss. The guide number already accounts for this, which is why moving from 7 m to 14 m at a fixed aperture is not something a small increase in power can fix. Understanding the inverse-square drop off explains why flash photographers fight so hard to keep the light close to the subject.
Scaling the guide number for ISO
A guide number is only meaningful next to the ISO it was rated at, usually ISO 100. Raise the shooting ISO and the sensor needs less light, so the same flash effectively reaches farther. The scaling follows the square root of the ISO ratio: the effective guide number is the rated number times the square root of shooting ISO divided by reference ISO. Two stops of ISO, for example 100 to 400, is a ratio of 4, whose square root is 2, so a GN of 56 becomes an effective 112. Enter your real ISO in the tool and it applies this multiplier before solving.
Where the number stops being exact
The guide number is a clean model of a messy situation. It assumes direct flash aimed at the subject in open surroundings, at a specific head zoom and full power. Bounce the flash off a ceiling and you lose light to the extra path and the wall's absorption. Drop the power setting and the effective guide number falls with it. Shoot in a bright room with reflective walls and you may need less. Use the calculated setting as a reliable first frame, then check the histogram and adjust rather than trusting the number blindly.