Formula & Calculator
f-number (Focal Ratio) of a Lens
Calculates a lens's f-number, the ratio of focal length to aperture diameter, which determines light-gathering power and depth of field.
Interpretation
N = f/D. Ratio of focal length to aperture diameter. Determines light‑gathering power and depth of field. Used in photography and optical design.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| N | f-number | |
| f | Focal length | mm |
| D | Aperture (entrance pupil) diameter | mm |
What it means
The f‑number (f/#) is the ratio of the focal length of a lens to the diameter of its aperture. A smaller f/# means a faster lens, collecting more light and allowing shorter exposures, but with shallower depth of field. It is a fundamental parameter in photography and optical design. It affects image brightness, diffraction limit, and depth of field. Understanding f‑number is essential for photographers and optical designers to control exposure and image quality.
Worked example
f‑number (Focal Ratio) – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| f (mm) | 50 |
| D (mm) | 25 |
| Parameter | Value |
|---|---|
| f | 1000 |
| D | 200 |
Common mistakes
- f‑number (focal ratio): N = f / D – where f is focal length and D is aperture diameter.
- Units: f and D must be in the same units – N is dimensionless.
- Smaller N: Means a faster lens (more light) – e.g., f/2.8 is faster than f/5.6.
- Photography: The f‑number affects depth of field and exposure – lower N gives shallower depth of field.
- Effective aperture: For macro photography, the effective f‑number changes with magnification – use corrected values.
Applications
The f‑number (focal ratio) of a lens, N = f/D, is the ratio of the focal length to the aperture diameter. This determines the brightness of an image; lower N means a faster lens (more light). Photographers, cinematographers, and optical designers use it to control exposure, depth of field, and image quality. By adjusting the aperture (f‑stop), they balance light gathering and diffraction effects. In microscopy, the numerical aperture is often preferred. This concept is also used in telescope design to determine image brightness and resolution. Understanding the f‑number is essential for selecting and using optical systems effectively.
- Camera exposure and depth‑of‑field control
- Lens performance evaluation and comparison
- Design of optical systems for specific light gathering
- Astronomy – comparing telescopes by speed
- Education on photographic optics
Frequently Asked Questions
It calculates the f‑number (N) as the ratio of focal length to aperture diameter: N = f / D. This determines light‑gathering power and depth of field.
N = f‑number (dimensionless).
f = focal length of the lens.
D = aperture diameter (entrance pupil).
A lower f‑number means a larger aperture relative to focal length, allowing more light to reach the sensor (faster lens) and shallower depth of field.
It is defined as the ratio of focal length to the effective aperture; it is a geometric measure of the lens's light‑collecting ability.
NA is defined as n sinθ and is related to f‑number by NA ≈ 1/(2N) for small angles. NA is used in microscopy; f‑number is common in photography.
A lens has f = 50 mm and aperture diameter D = 25 mm. N = 50/25 = 2, so it is an f/2 lens.
- Confusing f‑number with focal length.
- Forgetting that f‑number is a ratio, so a smaller number means a larger aperture.
- Using the physical aperture diameter instead of the entrance pupil.
Smaller f‑numbers (larger apertures) give shallower depth of field; larger f‑numbers give deeper depth of field.
Each full stop change in f‑number (e.g., from f/2 to f/2.8) halves the light reaching the sensor, requiring compensation in shutter speed or ISO.
It is a standard specification; for example, a 50mm f/1.4 lens indicates a fast lens with a large maximum aperture.