What is the focal ratio and how is it calculated?

The focal ratio (or f-number) N is simply the focal length f divided by the aperture entrance-pupil diameter D: N = f / D. A 200 mm lens with a 50 mm aperture is f/4. It is dimensionless, so any consistent length unit works.

Why does a larger f-number mean a darker image?

Image illuminance is proportional to 1/N². Closing down from f/2.8 to f/5.6 doubles N, which cuts the aperture area (and therefore light) by a factor of four. That is exactly two stops of exposure. The shutter speed must be lengthened by 4× to compensate.

What are the standard f-stop values and why are they spaced the way they are?

The standard full-stop series is f/1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64. Each consecutive value is the previous one multiplied by the square root of 2 (roughly 1.414). Multiplying N by sqrt(2) doubles the area of the aperture disc, which halves the light — hence one stop.

What is hyperfocal distance?

The hyperfocal distance H is the closest focus point at which a lens renders objects at infinity acceptably sharp within a given circle of confusion c: H = f² / (N × c) + f. When you focus at H, depth of field extends from H/2 to infinity — the maximum depth of field achievable at that aperture. Landscape photographers frequently focus at the hyperfocal distance to keep both a foreground subject and the horizon sharp.

How does the depth-of-field calculator use the circle of confusion?

The circle of confusion (CoC) is the maximum blur-spot diameter that still appears sharp on a final print or display. It depends on sensor size and output size. Typical values are 0.030 mm for a 35 mm full-frame sensor, 0.019–0.020 mm for APS-C, and 0.015 mm for Micro Four Thirds. Using the correct CoC is important: the same f/8, 50 mm combination gives a noticeably shallower depth of field on a full-frame body than on a cropped sensor.

What is the Airy disc and why does it matter?

When light passes through a circular aperture it diffracts, producing a bright central disc (the Airy disc) surrounded by rings. The Airy disc diameter is 2.44 × wavelength × N. At visible wavelengths around 550 nm it is roughly 2.44 × 0.00055 × N mm. Stopping down increases N, which enlarges the Airy disc. At very small apertures (f/16 and beyond on many modern sensors) diffraction softening can exceed the gain from increased depth of field — the sweet spot is often f/8 to f/11.

Focal Ratio Calculator (f-number / f-stop)

The focal ratio (also called the f-number or f-stop) is one of the most fundamental numbers in photography, cinematography, and optics. It controls how much light the lens passes, how blurry the background is, and how sharp fine detail can be before diffraction limits resolution. This calculator solves the core relationship in three directions, adds a full depth-of-field model, and computes exposure equivalents when you change f-stops — all inside your browser, with no data ever leaving your device.

What is the focal ratio?

The focal ratio N is the ratio of a lens’s focal length f to its entrance pupil (effective aperture) diameter D:

N = f / D

A 50 mm lens opened to a 25 mm entrance pupil is f/2. The same lens stopped down to 6.25 mm is f/8. Because the area of the aperture scales as D², and image illuminance is proportional to area, the illuminance scales as 1/N²: double the f-number, quarter the light. That is why each standard “stop” in the series f/1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32 multiplies N by √2 — every step changes the light by exactly 2×.

How the calculator works

Focal Ratio tab — enter any two of (N, f, D) and the third is solved immediately. The result panel shows the nearest standard full-stop values, how many stops the result sits from f/1, and the Airy disc diameter for 550 nm green light using the Rayleigh diffraction formula ⌀ = 2.44 × λ × N. A schematic circle scales to show the relative aperture opening.

Depth of Field tab — uses the standard photographic DoF formulae. The hyperfocal distance is:

H = f² / (N × c) + f

where c is the circle of confusion for your sensor. Near and far limits are:

Dn = H × d / (H + d) Df = H × d / (H − d) (infinite when d ≥ H)

Pre-set CoC values are provided for full-frame 35 mm (0.030 mm), APS-C Canon (0.019 mm), APS-C Nikon/Sony (0.020 mm), Micro Four Thirds (0.015 mm), medium format GFX 50S (0.054 mm), and 1-inch sensors (0.011 mm). You can also enter a custom CoC for telescope eyepieces or large-format film.

Exposure tab — given two f-numbers N₁ and N₂ and a shutter speed t₁ at N₁, it finds the equivalent shutter speed at N₂:

t₂ = t₁ × (N₂ / N₁)²

and the relative illuminance (N₁ / N₂)², shown as a percentage.

Worked example

A 200 mm telephoto lens has a maximum aperture of 50 mm. What is the focal ratio?

N = f / D = 200 mm / 50 mm = f/4
Nearest standard stop: f/4 (exact match)
Airy disc at 550 nm: 2.44 × 0.00055 × 4 ≈ 5.4 μm — well below a modern 24 MP full-frame pixel pitch of roughly 6 μm, so diffraction is not yet the limiting factor

Now stop down to f/11 and focus at 3 m (3000 mm) on a full-frame body (CoC = 0.030 mm):

Hyperfocal distance H = 200² / (11 × 0.030) + 200 ≈ 121.4 m
Near limit Dn = 121 400 × 3000 / (121 400 + 3000) ≈ 2.93 m
Far limit Df = 121 400 × 3000 / (121 400 − 3000) ≈ 3.07 m
Total depth of field: about 0.14 m — typical for a long telephoto at medium distance

Switching from f/4 (t = 1/500 s) to f/11 for the above shot:

Stops difference = 2 × log₂(11/4) ≈ 2.93 stops
New shutter speed = (1/500) × (11/4)² ≈ 1/66 s (use 1/60 s in practice)

Scenario	f-number	D	Airy disc
50 mm, 25 mm aperture	f/2	25 mm	2.7 μm
200 mm, 50 mm aperture	f/4	50 mm	5.4 μm
400 mm, 50 mm aperture	f/8	50 mm	10.7 μm
100 mm, 3.1 mm aperture	f/32	3.1 mm	42.9 μm

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