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Telescope Eyepiece Magnification & Sky Field

Estimate telescope magnification, true angular field and small-field circular area from focal lengths and eyepiece apparent field.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 1,000 mm telescope with a 20 mm eyepiece gives 50× magnification. A 50° apparent field then gives approximately 1° true field, with a small-field circular area of π/4 square degrees.

Magnification = telescope focal length / eyepiece focal length; true field ≈ apparent field / magnification; small-field area ≈ π × (true field / 2)²

Worked example

Enter these known values and leave the other values blank.

Eyepiece focal-length preset
20 mm
Telescope focal-length preset
1000 mm
Eyepiece apparent field
50 deg
Angular magnification magnitude
50 ×
Approximate true field diameter
1 deg
Approximate small-field circular area
0.7854 deg²

Assumptions and limitations

  • Focal lengths, magnification and angular fields are positive. Presets use millimeter focal lengths; choose Custom to enter a different positive focal length.
  • Apparent field divided by magnification is an estimate. Field stops, optical distortion, vignetting, focal reducers and Barlow lenses can change the effective field or focal length.
  • Area uses the planar small-angle circle formula. For a large field it is not the exact spherical-cap solid angle, 2π(1 − cos(true field/2)). The small-field approximation should be used only when appropriate.
  • Magnification is an unsigned magnitude. This model does not determine image orientation, exit pupil, resolving power or the highest useful magnification.

Common questions

What happens with a shorter eyepiece?

At the same telescope focal length, a shorter eyepiece raises magnification. For the same apparent field, the estimated true sky field becomes smaller.

Are the focal-length presets required?

No. Choose Custom in either preset selector and enter the corresponding focal length. Use the effective telescope focal length if an accessory changes it.

References

Bookify converts the telescope focal-length presets from millimeters to internal meters, correcting a captured factor-of-1000 preset error. Square-angle units use exact angular definitions in radians instead of rounded steradian factors.

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