F-Number Calculator
The f-number (focal ratio) of a lens is N = f/D, where f is the focal length and D is the entrance pupil diameter. It directly determines how much light reaches the sensor. Because exposure is proportional to aperture area (pi D^2/4), doubling the f-number (halving D) reduces exposure by a factor of 4, or two stops. The f-number also affects depth of field: lower f-numbers give shallower depth of field. This calculator computes the f-number from focal length and aperture, finds the aperture diameter from the f-number, and calculates the exposure stop difference between any two f-numbers.
F-number formulas
N = f / D
Stops = 2 log2(N2 / N1)
Relative exposure = (N1 / N2)2
Where f = focal length, D = entrance pupil diameter. One stop = factor of 2 in exposure. The standard full-stop series is f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22.
Understanding the f-number scale
- Each full stop multiplies the f-number by sqrt(2) (approximately 1.414), which halves the aperture area and halves the light.
- Third-stop increments are common on cameras: e.g. f/2.8, f/3.2, f/3.5, f/4.0.
- At f/1.0 (diameter equals focal length), the lens is theoretically at its light-gathering maximum for a single refracting surface.
- Astronomical telescopes are rated by focal ratio: f/4 is considered fast, f/10 slow.
F-number: frequently asked questions
What is the f-number of a lens?
The f-number (also called focal ratio or f-stop) N = f/D, where f is the focal length and D is the entrance pupil diameter (the effective aperture). It describes the light-gathering power: lower f-numbers mean larger apertures and more light. For example, f/2 admits four times more light than f/4 because doubling the f-number halves the diameter and quarters the area.
What is an exposure stop?
A stop is a factor of 2 change in exposure. Going from f/2.8 to f/4 reduces light by one stop (half the light). The full stop f-number 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. Each step multiplies the f-number by sqrt(2) approximately 1.414.
What is the difference between f-number and T-stop?
The f-number is a geometric ratio of focal length to aperture diameter. The T-stop (transmission stop) is an effective f-number corrected for lens transmission losses (reflections, absorption). A lens labeled T/2.0 transmits as much light as a hypothetically perfect f/2.0 lens. Cinema lenses are usually marked with T-stops for accurate exposure matching.
How do I calculate stops between two f-numbers?
Stops = log2((N2/N1)^2) = 2 log2(N2/N1). For example, from f/2.8 to f/8: stops = 2 log2(8/2.8) = 2 log2(2.857) = approximately 2 x 1.514 = 3.03 stops (approximately 3 stops).
What is the relationship between f-number and numerical aperture?
For a lens focused at infinity in air, NA = 1/(2N). So f/2 gives NA = 0.25 and f/1.4 gives NA approximately 0.36. This relationship is the paraxial approximation and becomes less accurate at very large apertures (low f-numbers).
Official sources
- OpenStax University Physics Volume 3, Chapter 2: Geometric Optics. openstax.org.
- ANSI/ISO 517, Photography: Aperture designations and related quantities. Referenced via nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.