Last updated: 2026-06-16

F-number and the focal ratio

The f-number, also called the focal ratio or f-stop, is the ratio of a lens focal length to its effective aperture diameter:

$N = \frac{f}{D}$

where $f$ is the focal length and $D$ is the diameter of the entrance pupil. A 50 mm lens set to a 25 mm aperture has an f-number of 2, written f/2. The notation is a fraction: f/2 represents a wider opening than f/4.

The f-number is dimensionless — both quantities share the same length unit, so the ratio is a pure number that characterises how much light a lens admits relative to its focal length.

How aperture controls light

The aperture is a circular opening, so its area is proportional to the square of the diameter:

$A \propto D^2 = \left(\frac{f}{N}\right)^2$

The light gathered by the lens scales with this area, and therefore with $1/N^2$. Halving the f-number quadruples the light; doubling it cuts the light to one quarter. This square relationship is the reason the standard stop sequence uses factors of $\sqrt{2} \approx 1.414$.

The standard stop sequence

Each step in the sequence f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22 multiplies the f-number by $\sqrt{2}$, which halves the aperture area and therefore halves the light:

Going down one stop halves the light and therefore requires twice the exposure time to achieve the same image brightness.

Worked example

A 50 mm lens is opened to a diameter of 25 mm. The f-number is

The lens is said to be set to f/2. If the aperture is stopped down to 12.5 mm the f-number becomes $N = f/D = 50\,\text{mm}/12.5\,\text{mm} = 4$, and the light admitted falls to one quarter of its former value — two stops less.

Effect on depth of field

A wider aperture (lower f-number) produces a shallower depth of field — the zone of acceptable sharpness around the focus point. At f/1.8 only a narrow plane is in sharp focus, which separates a subject from a blurred background. At f/11 or f/16 the depth of field extends far enough to keep objects at many distances simultaneously sharp.

Portrait photographers favour wide apertures to blur distracting backgrounds. Landscape and architectural photographers tend to use narrow apertures to maximise the depth of field across the scene.

Applications

The f-number applies wherever light must be collected and focused:

• Photography and videography — all interchangeable lenses carry an f-number rating; the widest (lowest) f-number is printed on the barrel as the maximum aperture.
• Telescopes — the focal ratio of a telescope determines how fast it photographs faint objects; an f/4 telescope concentrates light into a smaller, brighter image than an f/8 instrument of the same aperture.
• Microscopy and machine vision — objective lenses are specified by numerical aperture (NA), a related measure that also accounts for the refractive index of the medium.

Limits

The f-number describes only the geometric ratio of focal length to aperture diameter. It does not account for light lost to reflection, absorption, or scattering inside the lens. Cinema lenses are often rated in T-stops (transmission stops), which are calibrated by measuring actual light transmission rather than computing a ratio. A lens rated at f/2 might transmit only as much light as a theoretically perfect lens at T/2.2, for example.

The formula also assumes the lens behaves as a thin lens with a well-defined entrance pupil at the front. Complex zoom lenses and retrofocus wide-angle designs can have effective apertures that differ from the physical iris diameter.