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Telescope Magnification Calculator

Computes the magnification of a telescope and eyepiece combination (with optional Barlow), the exit pupil, true field of view, focal ratio, useful magnification range, Dawes and Rayleigh resolution limits and an estimated limiting magnitude.

When to use

You are choosing an eyepiece or Barlow for a telescope and want to know the resulting power, field of view and whether the magnification is useful for the aperture.

Do not use when: You need the angle of view of a camera lens (use field-of-view) or exposure settings for astrophotography.

Formula

magnification = telescope_focal_length_mm × barlow_factor / eyepiece_focal_length_mm; exit_pupil_mm = aperture_mm / magnification; true_field = eyepiece_afov_degrees / magnification; dawes = 116 / aperture_mm; rayleigh = 138 / aperture_mm; limiting_magnitude = 7.5 + 5·log10(aperture_mm / 10)

Geometric optics for visual use; the true field is approximate for wide-field eyepieces (field-stop method is exact). Resolution limits assume perfect optics and steady seeing, which typically caps resolution at 1–2 arcsec.

Inputs

ParameterTypeUnitRequiredDescription
telescope_focal_length_mmnumbermmyesFocal length of the telescope objective or mirror. Range: ≥ 50, ≤ 20000
eyepiece_focal_length_mmnumbermmyesFocal length of the eyepiece. Range: ≥ 1, ≤ 100
aperture_mmnumbermmyesClear aperture (objective or primary mirror diameter). Range: ≥ 10, ≤ 5000
barlow_factornumberdefault 1Magnification of a Barlow lens (2, 3) or focal reducer (0.63); 1 for none. Range: ≥ 0.2, ≤ 10
eyepiece_afov_degreesnumber°default 50Apparent field of view of the eyepiece design (Plössl 50°, wide-field 68–82°, ultra-wide 100°). Range: ≥ 20, ≤ 120

Outputs

OutputTypeUnitDescription
magnificationnumber×telescope focal length × barlow_factor / eyepiece focal length.
effective_focal_length_mmnumbermmTelescope focal length × Barlow factor.
exit_pupil_mmnumbermmaperture / magnification; above ~7 mm the eye cannot use all the light, below ~0.5 mm the image is dim.
true_field_of_view_degreesnumber°Eyepiece apparent field / magnification (the full Moon is about 0.5°).
focal_rationumberNative f-number = telescope focal length / aperture.
max_useful_magnificationnumber×Rule of thumb 2 × aperture in mm (50× per inch); beyond it the image only gets larger and dimmer.
min_useful_magnificationnumber×aperture / 7 mm, the power at which the exit pupil equals a dark-adapted eye pupil.
dawes_limit_arcsecnumberarcsec116 / aperture_mm: closest double star the telescope can split (empirical).
rayleigh_limit_arcsecnumberarcsec138 / aperture_mm: diffraction-limited resolution for 550 nm light.
limiting_magnitudenumbermag7.5 + 5·log10(aperture in cm): faintest star visible under dark skies (rule of thumb).

Example

200 mm f/6 Newtonian (1200 mm) with a 10 mm eyepiece: {"telescope_focal_length_mm":1200,"eyepiece_focal_length_mm":10,"aperture_mm":200} → {"magnification":120,"exit_pupil_mm":1.67,"true_field_of_view_degrees":0.417,"focal_ratio":6,"max_useful_magnification":400,"dawes_limit_arcsec":0.58,"limiting_magnitude":14}

Same telescope with a 2× Barlow: {"telescope_focal_length_mm":1200,"eyepiece_focal_length_mm":10,"aperture_mm":200,"barlow_factor":2} → {"magnification":240,"exit_pupil_mm":0.83,"true_field_of_view_degrees":0.208,"effective_focal_length_mm":2400}

GET https://tttkmbb.com/api/v1/calculate/telescope-magnification?telescope_focal_length_mm=1200&eyepiece_focal_length_mm=10&aperture_mm=200

Machine access

Sources

FAQ

Why is more magnification not always better?

Magnification also enlarges the diffraction blur and dims the image; above about 2× the aperture in mm (or an exit pupil below 0.5 mm) no further detail appears. Atmospheric seeing usually limits usable power to 200–300×.

What does the true field of view tell me?

The angular width of sky visible in the eyepiece. 0.417° is smaller than the full Moon (0.5°), so at 120× the Moon does not fit in the view.

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