Photography Exposure Math: Stops, Aperture, Shutter Speed, and ISO

Equivalent Exposures

If the correct exposure is f/8 at 1/125 s and ISO 100, then opening the aperture one stop to f/5.6 requires a shutter speed one stop faster, 1/250, to keep the same exposure. All of these are equivalent: f/8 at 1/125, f/5.6 at 1/250, f/4 at 1/500, f/11 at 1/60. They differ in look: wider apertures give a shallower depth of field; faster shutter speeds freeze motion. Raising ISO from 100 to 800 is 3 stops, letting you use 3 stops less light, for example from 1/125 to 1/1000 at the same aperture, at the cost of more noise.

The number of stops between f/2 and f/8 is 4 (2, 2.8, 4, 5.6, 8), and the light changes by 2⁴ = 16 times. In general, stops = 2 × log₂(N₂ ÷ N₁) for f-numbers.

F-Number and Aperture Diameter

The f-number is focal length divided by the diameter of the aperture: N = f ÷ D. A 50 mm lens at f/1.8 has an aperture diameter of 50 ÷ 1.8 = 27.8 mm. A 200 mm lens at f/2.8 has a diameter of 71.4 mm, which is why long, fast lenses are large and heavy.

Handheld Shutter Speed Rule

A common guideline is to use a shutter speed of at least 1 ÷ focal length to avoid blur from camera shake: 1/50 s for a 50 mm lens, 1/200 s for 200 mm. On a crop-sensor camera with a 1.5× crop factor, use the equivalent focal length: 50 mm becomes 75 mm, so 1/75 s. Image stabilization can extend this by 3 to 5 stops, so a stabilized 200 mm lens might be handheld at 1/25 s. High-resolution sensors may need faster speeds.

Practical Workflow

Choose the creative priority first: aperture for depth of field, shutter for motion, ISO as low as the light allows. Check the histogram to ensure the exposure is correct. Use exposure compensation in stops (±1 EV) to correct for bright snow or dark scenes. Shooting in RAW provides latitude of a stop or two for recovery.