Telescope Focal Ratio Calculator
The focal ratio (f-ratio or f-number) of a telescope determines how fast it gathers light and how wide its field of view is. It is calculated by dividing the focal length by the aperture diameter. Together with your choice of eyepiece, the f-ratio determines magnification and exit pupil size, both critical for comfortable and effective observing. This calculator takes telescope focal length, aperture, and eyepiece focal length as inputs and returns the f-ratio, magnification, and exit pupil so you can optimize your setup for planets, deep-sky objects, or astrophotography.
Telescope optics formulas
f-ratio = focal length / aperture
Magnification = focal length(scope) / focal length(eyepiece)
Exit pupil (mm) = aperture (mm) / magnification
All lengths must be in the same unit (millimeters is standard). The exit pupil can also be computed as the eyepiece focal length divided by the f-ratio, which gives the same result.
Choosing the right f-ratio
Fast scopes (f/4 to f/6) suit wide-field astrophotography and visual deep-sky work. Slow scopes (f/8 to f/15) suit planetary observing and tolerate more optical imperfections in eyepieces. For visual observing, aim for an exit pupil between 2 mm and 7 mm. Exit pupils below 1 mm are dim and hard to use; above 7 mm, the sky background becomes bright relative to objects.
Telescope focal ratio: frequently asked questions
What is the focal ratio (f-number) of a telescope?
The focal ratio, written as f/N, is the telescope's focal length divided by its aperture (objective diameter). For example, a telescope with 1,000 mm focal length and 100 mm aperture has an f-ratio of f/10. Lower f-ratios mean faster, wider-field optics.
How does focal ratio affect astrophotography?
A lower f-ratio (e.g., f/5) collects light more quickly than a higher one (e.g., f/10), halving the required exposure time for each full f-stop change. Fast scopes are preferred for extended objects like nebulae; slower scopes give more magnification per unit aperture.
How is magnification calculated?
Magnification = focal length of telescope / focal length of eyepiece. A 1,000 mm scope with a 10 mm eyepiece delivers 100x magnification.
What is exit pupil and why does it matter?
Exit pupil = aperture / magnification = eyepiece focal length / f-ratio. The human dark-adapted pupil is about 7 mm; exit pupils larger than this waste light. Smaller exit pupils (1-3 mm) suit high-magnification planetary viewing.
What is a good f-ratio for a beginner telescope?
f/8 to f/10 reflectors and refractors are common for beginners. They tolerate cheaper eyepieces better than fast optics and perform well for planets and the Moon. For wide-field photography or star parties, f/4 to f/6 is preferred.
Official sources
- NASA Telescope Basics: imagine.gsfc.nasa.gov.
- NIST: Optical terminology reference: nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.