Calculation methods

Magnification ↗

Magnification = effective focal length ÷ eyepiece focal length. Exit pupil = aperture ÷ magnification.

Example: A 1,000 mm, 200 mm aperture telescope with a 25 mm eyepiece gives 40×, 5 mm exit pupil and f/5.

Optical factor multiplies focal length, not aperture. Results describe geometry and do not predict seeing, image quality or usable magnification.

Eyepiece fields ↗

Approximate true field = apparent field ÷ magnification. The field-stop method can differ.

Example: At 1,000 mm focal length, a 25 mm / 60° eyepiece gives approximately 1.5°, while a 10 mm / 60° eyepiece gives 0.6°.

The star pattern is illustrative, not a sky atlas. Apparent-field division is an approximation, especially for wide-angle eyepieces.

Camera field ↗

Field on each axis = 2 atan(sensor size ÷ (2 × effective focal length)), converted to degrees.

Example: A 23.5 × 15.6 mm sensor at 500 mm focal length spans approximately 2.692° × 1.787°.

Target size is user-entered in arcminutes; the circle represents an angular size, not a current celestial image. Distortion and obstructions are excluded.

Pixel scale ↗

Scale ≈ 206.264806 × pixel size in µm × binning ÷ effective focal length in mm.

Example: 3.76 µm pixels at 500 mm give about 1.551 arcsec/pixel. A 3 arcsec FWHM spans about 1.934 pixels.

This uses the small-angle approximation. Binning is modeled geometrically, without assuming any particular camera readout or sensitivity benefit.

Units and numerical limits

Conversions use 1 inch = 2.54 cm, 1 mile = 1.609344 km, and 1 avoirdupois ounce = 28.349523125 g. Empty, non-finite, out-of-range and unsupported values are rejected. Displayed values are rounded; calculations retain precision. Input-specific limits are reported alongside the field when exceeded.