Star Magnitude Calculator

Apparent magnitude (m) measures how bright a star appears in the sky from Earth. The scale is logarithmic and inverted: lower (more negative) numbers mean brighter objects. The Sun has m = -26.74, the full Moon m = -12.74, Venus at brightest m = -4.9, Sirius m = -1.46, and the faintest stars visible to the naked eye m = 6. A difference of 5 magnitudes corresponds to a factor of exactly 100 in brightness (Pogson's ratio: 5th root of 100 = 2.512).

Absolute magnitude (M) is the apparent magnitude a star would have at a standard distance of 10 parsecs (32.6 light-years). It measures the true luminosity of a star, independent of distance. The Sun's absolute magnitude is M = 4.83. Supergiants can have M = -8; the faintest brown dwarfs have M = 20+. Absolute magnitude is derived from apparent magnitude via: M = m - 5*log10(d/10), where d is distance in parsecs.

The distance modulus (mu) = m - M = 5*log10(d) - 5, where d is in parsecs. It is the difference between apparent and absolute magnitude. If mu = 0, the star is at 10 pc. Positive mu means the star is farther than 10 pc (appears dimmer than absolute). mu = 5: 100 pc. mu = 10: 1,000 pc. mu = 15: 10,000 pc. mu = 25: 1 Mpc (megaparsec).

The Pogson equation: m2 - m1 = -2.5 * log10(F2/F1), where F is flux (energy per unit area per second). Equivalently, F2/F1 = 10^((m1-m2)/2.5). A magnitude difference of 1 corresponds to a flux ratio of 10^(1/2.5) = 2.512. A difference of 5 magnitudes = factor of 100. A difference of 10 magnitudes = factor of 10,000.

Limiting magnitude scales with aperture: m_lim approximately 2.1 + 5*log10(D_mm) for visual observation. A 100 mm telescope: m_lim approximately 12.1. A 200 mm telescope: m_lim approximately 13.6. Hubble Space Telescope: m_lim approximately 31 in long exposures. The naked eye dark-sky limit is approximately magnitude 6-7. Sky brightness (light pollution) reduces limiting magnitude significantly.