Telescope Magnification Calculator
Calculate the magnification, resolution, and light-gathering power of any telescope from its objective focal length, eyepiece, and aperture. Ideal for astronomers choosing eyepieces for a target.
About this calculator
A telescope's magnification is the ratio of the apparent size of an object as seen through the scope versus with the naked eye. The primary formula is: M = f_objective / f_eyepiece, where f_objective is the focal length of the objective lens or primary mirror and f_eyepiece is the focal length of the eyepiece. For example, a 1000 mm focal-length telescope with a 10 mm eyepiece gives 100× magnification. Angular resolution (the ability to separate fine detail) is governed by the Rayleigh criterion: θ = 1.22 · λ / D (in radians), where λ is the wavelength of light and D is the aperture diameter. Light-gathering power scales with aperture area: Power ∝ D². Larger apertures gather more light and resolve finer detail, which is why aperture is often considered more important than magnification for deep-sky observing.
How to use
Suppose you have a Newtonian reflector with a 1200 mm objective focal length and a 25 mm eyepiece, with a 150 mm aperture observing at 550 nm. Step 1 — Magnification: M = 1200 / 25 = 48×. Step 2 — Resolution (Rayleigh criterion): θ = 1.22 × (550 × 10⁻⁶ mm) / 150 mm = 1.22 × 3.667 × 10⁻⁶ = 4.47 × 10⁻⁶ radians ≈ 0.92 arcseconds. Step 3 — Switch to a 10 mm eyepiece: M = 1200 / 10 = 120×. Higher magnification reveals finer planetary detail but requires steadier seeing conditions and more light.
Frequently asked questions
What is the maximum useful magnification for a telescope?
A widely used rule of thumb puts the maximum useful magnification at roughly 50× per inch of aperture (about 2× per millimeter of aperture). Beyond this limit, the image becomes a blurry, dim blob because the telescope is magnifying beyond what its aperture can resolve — a condition called 'empty magnification.' Atmospheric turbulence (seeing) often restricts practical maximums further, especially at lower altitudes. For a 150 mm (6-inch) aperture telescope, the theoretical maximum is about 300×, but excellent seeing nights that support even 200× are relatively rare from most suburban locations.
How does aperture affect light-gathering power and deep-sky viewing?
Light-gathering power increases with the square of the aperture diameter, meaning doubling the aperture collects four times as much light. A 200 mm telescope gathers about 816 times more light than a fully dark-adapted human eye (pupil ≈ 7 mm), making objects appear dramatically brighter and revealing detail invisible to the naked eye. This makes aperture the single most important specification for deep-sky objects such as nebulae and galaxies, which are extended and faint. Magnification alone cannot reveal a faint galaxy that the aperture cannot gather enough light to display; only a larger mirror or lens can do that.
What eyepiece focal length gives the best magnification for planetary viewing?
For planetary viewing, you generally want higher magnification — typically 150× to 300× on a night of good seeing — which means shorter eyepiece focal lengths such as 5 mm to 10 mm. However, exit pupil (the diameter of the light beam entering your eye) also matters: exit pupil = aperture / magnification, and values below about 0.5 mm make the image dim and uncomfortable. A balanced approach is to start with a medium eyepiece (15–20 mm) to locate and center the planet, then switch to a shorter focal length (6–10 mm) to increase detail. Barlow lenses that double or triple the effective focal length of an eyepiece offer a cost-effective way to extend your magnification range.