# What is the telescope magnification?

Telescope magnification calculator: M = telescope focal length ÷ eyepiece focal length, with a Barlow, plus the exit pupil, true field of view, focal ratio and resolving limit.

- Page: https://www.acalculator.org/physics/telescope-magnification-calculator
- JSON spec: https://www.acalculator.org/physics/telescope-magnification-calculator.json
- Version: df990bcd9671

## Default answer

Example with the default inputs (Telescope focal length 1,000 mm, Eyepiece focal length 25 mm, Barlow or reducer factor 1, Aperture (D) 100 mm, Eyepiece apparent field (°) 52): The magnification is 40×.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| f | Telescope focal length | The focal length of the main lens or mirror (the objective). |
| fe | Eyepiece focal length | The focal length printed on the eyepiece. |
| b | Barlow or reducer factor | Multiplies the focal length: 1 for none, 2 for a 2× Barlow, 0.63 for an f/6.3 reducer. |
| D | Aperture (D) | Optional: the diameter of the main lens or mirror, for the exit pupil, focal ratio and resolving limit. |
| afov | Eyepiece apparent field (°) | Optional: the apparent field of view of the eyepiece, in degrees (often 50° to 82°). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Magnification | M to 6 significant figures, written as a times sign: 40×. |
| magnification | Magnification (M) | Telescope focal length × Barlow factor ÷ eyepiece focal length. |
| effective | Focal length with the Barlow (mm) | The telescope focal length times the Barlow factor. |
| exitPupil | Exit pupil (mm) | D ÷ M: the width of the beam of light that leaves the eyepiece. |
| trueField | True field of view (°) | The apparent field ÷ M: how much sky you see. |
| trueFieldArcmin | True field of view (′) | The true field in minutes of arc (60 to a degree). |
| focalRatio | Focal ratio (f/) | The telescope focal length ÷ D, without the Barlow. |
| resolution | Resolving limit at 550 nm (″) | 1.22 × λ ÷ D in seconds of arc: the closest pair of stars it can split. |

## Method

M = telescope focal length × Barlow factor ÷ eyepiece focal length; exit pupil = D ÷ M; true field = apparent field ÷ M; focal ratio = focal length ÷ D; resolving limit = 1.22 × 550 nm ÷ D radians.

## Assumptions

- The final image is at infinity (a relaxed eye), and the image is upside down; the page gives the size of M.
- The true field is the apparent field ÷ M, the small-angle rule; the resolving limit is the diffraction (Rayleigh) limit, before the air and the optics blur it.

## Worked examples

1. f = 1, fe = 0.025, b = 1 gives magnification = 40, result = 40×. Source: OpenStax, University Physics Volume 3, §2.8 Microscopes and Telescopes (Equations 2.39 and 2.40, M = θ_image ÷ θ_object = −f_obj ÷ f_eye; a 1 m objective gives 40× with a 2.5 cm eyepiece and 80× with 1.25 cm), https://openstax.org/books/university-physics-volume-3/pages/2-8-microscopes-and-telescopes (retrieved 2026-10-19).
2. f = 1, fe = 0.0125, b = 1 gives magnification = 80. Source: OpenStax, University Physics Volume 3, §2.8 Microscopes and Telescopes (Equations 2.39 and 2.40, M = θ_image ÷ θ_object = −f_obj ÷ f_eye; a 1 m objective gives 40× with a 2.5 cm eyepiece and 80× with 1.25 cm), https://openstax.org/books/university-physics-volume-3/pages/2-8-microscopes-and-telescopes (retrieved 2026-10-19).
3. f = 1, fe = 0.025, b = 2, D = 0.1, afov = 52 gives magnification = 80, exitPupil = 1.25, trueField = 0.65, trueFieldArcmin = 39, focalRatio = 10, effective = 2,000. Source: OpenStax, University Physics Volume 3, §2.8 Microscopes and Telescopes (Equations 2.39 and 2.40, M = θ_image ÷ θ_object = −f_obj ÷ f_eye; a 1 m objective gives 40× with a 2.5 cm eyepiece and 80× with 1.25 cm), https://openstax.org/books/university-physics-volume-3/pages/2-8-microscopes-and-telescopes (retrieved 2026-10-19).
4. f = 57.6, fe = 0.025, b = 1, D = 2.4 gives resolution = 0.057668, magnification = 2,304. Source: OpenStax, University Physics Volume 3, §4.5 Circular Apertures and Resolution (Equation 4.5, θ = 1.22λ ÷ D; Example 4.6: the Hubble Space Telescope, D = 2.40 m at 550 nm, 2.80 × 10⁻⁷ rad), https://openstax.org/books/university-physics-volume-3/pages/4-5-circular-apertures-and-resolution (retrieved 2026-10-19): 2.80 × 10⁻⁷ rad = 0.0577″.

## FAQ

### How do you calculate telescope magnification?

Divide the focal length of the telescope by the focal length of the eyepiece: M = f_telescope ÷ f_eyepiece. A 1,000 mm telescope with a 25 mm eyepiece magnifies 1,000 ÷ 25 = 40 times (40×); a 12.5 mm eyepiece gives 80×.

### What does a Barlow lens do to magnification?

It multiplies the telescope’s focal length, and so the magnification, by its factor. A 2× Barlow turns the 25 mm eyepiece on a 1,000 mm telescope from 40× into 80×. A focal reducer of 0.63× lowers it instead.

### What is the exit pupil?

The width of the beam of light leaving the eyepiece: the aperture divided by the magnification. A 100 mm telescope at 80× has an exit pupil of 100 ÷ 80 = 1.25 mm. A larger exit pupil gives a brighter view, up to the width of your own pupil.

### How much sky will I see?

The true field of view is the eyepiece’s apparent field divided by the magnification. A 52° eyepiece at 80× shows 52 ÷ 80 = 0.65°, a little more than the full Moon (about 0.5°).

### Does more magnification show more detail?

Only up to the telescope’s resolving limit, θ = 1.22λ ÷ D, set by the aperture D. In green light (550 nm) a 100 mm telescope splits stars about 1.38″ apart and a 2.4 m mirror like Hubble’s about 0.058″. Past that, more power only enlarges the blur.

### What is the focal ratio of a telescope?

The focal length divided by the aperture, written f/10 for a 1,000 mm telescope of 100 mm. With the same eyepiece, a higher focal ratio gives more magnification and a smaller exit pupil.

## Sources

- OpenStax, University Physics Volume 3, §2.8 Microscopes and Telescopes: Equation 2.39 (angular magnification M = θ_image ÷ θ_object) and Equation 2.40 (M = −f_obj ÷ f_eye); a 1 m objective with a 2.5 cm eyepiece gives 40×, and with 1.25 cm gives 80×, retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-3/pages/2-8-microscopes-and-telescopes
- OpenStax, University Physics Volume 3, §2.4 Thin Lenses: Equation 2.19 (1 ÷ d_o + 1 ÷ d_i = 1 ÷ f) and Equation 2.22 (m = −d_i ÷ d_o), used for the exit pupil, retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-3/pages/2-4-thin-lenses
- OpenStax, University Physics Volume 3, §4.5 Circular Apertures and Resolution: Equation 4.5 (Rayleigh criterion θ = 1.22λ ÷ D); Example 4.6 (the Hubble Space Telescope, D = 2.40 m, λ = 550 nm: θ = 2.80 × 10⁻⁷ rad), retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-3/pages/4-5-circular-apertures-and-resolution
- NIST Special Publication 811 (2008), Appendix B.8: 1 in = 0.0254 m, retrieved 2026-10-19. https://www.nist.gov/pml/special-publication-811