NichesTools

Telescope Magnification Calculator

Magnification is the ratio of the telescope’s focal length to the eyepiece’s focal length. The actual field of view (FOV) equals the eyepiece’s apparent FOV divided by that magnification, expressed in degrees and then converted to arcminutes. Plate scale expresses how many arcseconds on the sky correspond to one millimeter on the telescope’s focal plane; it is simply 206.265 divided by the objective focal length.

The focal length of the telescope’s primary optic. Use the manufacturer’s specification; typical refractors range from 500 mm to 2000 mm, while large reflectors can exceed 5000 mm.
The focal length of the eyepiece you plan to use. Shorter eyepieces give higher magnification—common values are 10 mm, 15 mm or 20 mm.
The intrinsic wide‑field degree of view the eyepiece can display. Most modern achromats provide 40–70 °, while wide‑angle eyepieces can reach up to 90 °. This value is taken from the product catalogue.

What it is

The Telescope Magnification Calculator delivers three essential optical parameters for amateur astrophotographers and observers: the raw magnification factor, the usable field of view after accounting for that magnification, and the plate scale. Calculating magnification as the ratio of the telescope’s objective focal length to the eyepiece focal length is foundational for all optical systems; it tells how large objects will appear on a screen or in your eyes. Field‑of‑view prediction helps photographers gauge whether an image setup will capture a target and its surroundings, guiding decisions about camera framing and exposure length. Plate scale links angular sky coverage to physical size on the focal plane, enabling pixel‑by‑pixel conversion of images into real celestial scales – a must for precision imaging campaigns.

How to use it

Enter your telescope’s objective focal length in millimeters (mm). Next, type the eyepiece focal length also in mm; shorter numbers mean higher magnification. Finally, provide the eyepiece’s apparent field‑of‑view in degrees—read this from the product specifications. The calculator instantly returns three outputs: the magnification multiplier, the actual field of view expressed in arcminutes for easy comparison with sky images, and the plate scale indicating how many arcseconds correspond to each millimeter on your camera sensor or imaging focal plane.

Worked example

First, calculate the magnification by dividing the objective focal length (5000 mm) by the eyepiece focal length (15 mm): 5000 ÷ 15 = 333.33×.

Next, determine the field of view. Divide the eyepiece’s apparent FOV (70°) by the magnification: 70 / 333.33 ≈ 0.210°. Convert this to arcminutes by multiplying by 60: 0.210 × 60 = 12.60 arcmin.

Finally, compute the plate scale using the constant 206.265 divided by the objective focal length: 206.265 / 5000 = 0.0413 arcsec/mm, which we report as 0.041 when rounded to three decimals."},

Inputs

  • Objective Focal Length (mm): 5000
  • Eyepiece Focal Length (mm): 15
  • Eyepiece Apparent Field‑of‑View (°): 70

Result

  • Magnification (×): 333.333
  • Actual Field‑of‑View: 12.6
  • Plate Scale: 0.041

Frequently asked questions

Why is field of view smaller than the apparent FOV?

The apparent field‑of‑view printed on an eyepiece is how wide a sky region you see through the eyepiece alone, without a telescope. When combined with a telescope that magnifies images, each degree of true sky occupies more of your eyes or sensor, reducing the overall observable area proportionally to the magnification.

What if I have an OTA with a focal reducer?

A focal reducer multiplies the effective focal length of your objective. Multiply the reduction factor by the telescope’s nominal focal length before feeding it into this calculator; that gives you the correct optics for magnification, field‑of‑view and plate scale.

Can I convert the plate scale to arcseconds per pixel?

Yes – multiply the plate scale (arcsec/mm) by your sensor’s pixel size in millimeters. This yields how many arcseconds on the sky each pixel records, useful for astrometry or resolution planning.