Focal Ratio Calculator: F-Number, Aperture Diameter and Brightness
The focal ratio, or f-number, is the ratio of a lens's focal length to its aperture diameter. It governs how much light a lens transmits to the film or sensor: a lower f-number means a wider opening and more light, while a higher f-number means a narrower opening and less light. The formula is simply f-number = focal length (mm) divided by aperture diameter (mm). A 200 mm lens with a 50 mm diameter opening is an f/4 lens. The aperture area scales with the square of the diameter, so moving from f/2.8 to f/4 does not reduce light by a fraction of 4/2.8 but by the square of that ratio, cutting light roughly in half (one stop). This calculator has two sections. Section A computes the f-number and aperture area from the focal length and aperture diameter. Section B compares any two f-stops and shows the number of stops difference and the relative brightness ratio between them. A reference table of standard full stops and 1/3-stop values is included below. Use this tool for camera lenses, telescopes, and any optical system where the focal ratio matters.
f-number: f/2.00, aperture area: 1,963.50 mm²
Section A: Calculate f-number
Section B: Compare two f-stops
Focal ratio formula
f-number (N) = focal length (f) / aperture diameter (D)
Aperture area = π * (D / 2)^2
Stops difference = log2((N2^2) / (N1^2)) = 2 * log2(N2 / N1)
Relative brightness = (N2 / N1)^2 (ratio of light at N2 vs N1)
Light reduction (%) = (1 - 1 / brightness_ratio) * 100
Worked example
Focal length 100 mm, aperture diameter 50 mm:
- f-number = 100 / 50 = f/2
- Aperture area = π * (50 / 2)^2 = π * 625 = 1,963.50 mm²
Comparing f/2.8 to f/8:
- Stops = 2 * log2(8 / 2.8) = 2 * log2(2.857) = 2 * 1.514 = 3.03 stops
- Brightness ratio = (8 / 2.8)^2 = 8.16, so f/2.8 admits 8.16 times more light
Standard f-stop sequence
Each full stop multiplies the f-number by the square root of 2 (approximately 1.414), which halves the aperture area and halves the light admitted.
| Full stop | 1/3 stop below | 1/3 stop above | Relative light (full stop = 1.00) |
|---|---|---|---|
| f/1.0 | f/1.0 | f/1.1 | 1.00 (reference) |
| f/1.4 | f/1.2 | f/1.6 | 0.50 (1 stop less) |
| f/2.0 | f/1.8 | f/2.2 | 0.25 (2 stops less) |
| f/2.8 | f/2.5 | f/3.2 | 0.13 (3 stops less) |
| f/4.0 | f/3.5 | f/4.5 | 0.06 (4 stops less) |
| f/5.6 | f/5.0 | f/6.3 | 0.03 (5 stops less) |
| f/8.0 | f/7.1 | f/9.0 | 0.02 (6 stops less) |
| f/11 | f/10 | f/13 | 0.008 (7 stops less) |
| f/16 | f/14 | f/18 | 0.004 (8 stops less) |
| f/22 | f/20 | f/25 | 0.002 (9 stops less) |
| f/32 | f/29 | f/36 | 0.001 (10 stops less) |
1/3-stop values are spaced by a factor of 2^(1/3) = 1.260. Cameras mark 1/3-stop increments as: f/1.0, f/1.1, f/1.2, f/1.4, f/1.6, f/1.8, f/2.0, f/2.2, f/2.5, f/2.8, f/3.2, f/3.5, f/4.0, f/4.5, f/5.0, f/5.6, f/6.3, f/7.1, f/8.0, f/9.0, f/10, f/11, f/13, f/14, f/16, f/18, f/20, f/22.
Focal ratio calculator: frequently asked questions
What is an f-number (focal ratio)?
The f-number, also called the focal ratio or f-stop, is the ratio of a lens's focal length to its aperture diameter. For example, a 100 mm lens with a 50 mm aperture opening has an f-number of f/2. A lower f-number means a wider aperture, which admits more light. The f-number is dimensionless and the same formula applies to camera lenses, telescopes, and any other optical system.
How does f-stop affect the amount of light reaching the sensor?
Light is proportional to the area of the aperture opening, which scales with the square of the diameter. Because f-number = focal length / diameter, doubling the f-number halves the diameter and reduces the aperture area to one quarter, admitting one quarter as much light. That reduction of 2 stops. Conversely, halving the f-number quadruples the light (a gain of 2 stops). Each full stop either doubles or halves the light.
What are full stops vs 1/3 stops?
A full stop doubles or halves the light. The traditional full-stop sequence is f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32. Each step is a factor of the square root of 2 (approximately 1.414). Modern cameras and lenses also offer 1/2-stop and 1/3-stop increments for finer exposure control. Each 1/3-stop step is the cube root of 2 (approximately 1.26) applied to the f-number ratio.
What is a fast lens?
A fast lens has a large maximum aperture (low f-number), typically f/2.8 or wider. Fast lenses admit more light, allowing faster shutter speeds in low light (hence the name), and they produce a shallower depth of field for subject isolation. Common fast primes include f/1.4 and f/1.8 lenses. Zoom lenses with constant f/2.8 maximum aperture are also considered fast.
Why are fast lenses more expensive?
A fast lens requires a physically larger front element to achieve a wide aperture at a given focal length. Larger glass elements are harder to manufacture to the same optical tolerances, require more complex internal designs to correct aberrations introduced by wide apertures (such as spherical aberration and coma), and need heavier, more robust barrels. These factors drive up material and manufacturing costs significantly compared to slower lenses with the same focal length.
Sources
- F-number definition and derivation: Wikipedia: F-number.
- Aperture and light transmission tutorial: Cambridge in Colour: Understanding Aperture.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.