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Limiting Magnitude Calculator

Find a telescope's limiting magnitude.

Result

14.21

How it is calculated

The tool applies a rule-of-thumb formula: m = 2.7 + 5 × log10(D), where D is the aperture (the diameter of the main lens or mirror) in millimetres and m is the faintest star magnitude visible, rounded to two decimals. Higher m means fainter stars. Because of the 5 × log factor, doubling the aperture adds about 1.5 magnitudes. The aperture must be greater than zero. The result is an estimate for a dark sky, good eyesight and a well-adapted eye; it assumes nothing about magnification, light pollution, moonlight or the telescope's optical quality, all of which lower what you actually see.

Worked example

A 200 mm (8 inch) telescope. log10(200) ≈ 2.301. Multiply by 5: 11.505. Add 2.7: 14.205. The limiting magnitude is 14.21. For comparison, a 7 mm eye pupil gives 6.93 with the same formula, close to the naked-eye limit under a dark sky.

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Common mistakes

  • Entering the aperture in inches or centimetres. The formula expects millimetres, so an 8 inch scope must be typed as 200, not 8.
  • Using the focal length instead of the aperture. Focal length sets magnification, not how faint a star you can reach.
  • Expecting to reach the full value from a city. Light pollution and moonlight can cost several magnitudes of the estimate.
  • Confusing limiting magnitude with magnification. A higher eyepiece power does not make stars fainter-visible by the same rule; the estimate depends on aperture only.

About this calculator

This calculator estimates a telescope's limiting magnitude — the faintest star it can detect — using the approximation 2.7 + 5·log₁₀(D), where D is the aperture diameter in millimeters, reflecting the fact that a larger light-collecting surface gathers more photons from a dim, distant source. Because the magnitude scale is logarithmic and inverted (lower numbers mean brighter objects), each roughly 2.5x increase in aperture area adds about one magnitude of reach.

Amateur astronomers deciding which deep-sky objects (faint galaxies, nebulae, globular clusters) a given telescope can actually show, and shoppers comparing telescopes before buying use this to set realistic expectations. Enter the aperture diameter to get the estimated limiting magnitude.

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