Star Magnitude Calculator

Apparent magnitude measures how bright a star appears from Earth — not how intrinsically luminous it actually is. The scale is logarithmic and inverted: lower numbers mean brighter objects.

Pogson’s formula (magnitude difference to brightness ratio): m₁ - m₂ = -2.5 × log₁₀(F₁ / F₂)

Or rearranged to find flux ratio from magnitude difference: F₁ / F₂ = 10^((m₂ - m₁) / 2.5)

Where:

• m₁, m₂ = apparent magnitudes of two stars
• F₁, F₂ = measured flux (brightness) at the observer

Key reference points:

• The Sun: magnitude −26.7 (by far the brightest)
• Full Moon: magnitude −12.7
• Venus at brightest: magnitude −4.9
• Sirius (brightest star): magnitude −1.46
• Vega: magnitude 0.0 (used as the photometric zero-point)
• Naked-eye limit (dark sky): magnitude +6.5
• Hubble Space Telescope limit: magnitude +31.5

Worked example: Sirius (m = −1.46) vs. Betelgeuse (m = +0.42). Magnitude difference = 0.42 − (−1.46) = 1.88 Brightness ratio = 10^(1.88 / 2.5) = 10^0.752 ≈ 5.6× Sirius appears 5.6 times brighter than Betelgeuse from Earth.

Absolute magnitude (M) removes the distance factor: M = m - 5 × log₁₀(d / 10) where d is distance in parsecs.

The Sun’s absolute magnitude is +4.83, a rather average star when placed at the standard 10-parsec reference distance.

A worked example. Sirius sits 2.64 parsecs away and shines at apparent magnitude −1.46, the brightest star in our sky. Its absolute magnitude is M = −1.46 − 5 × log₁₀(2.64/10) = −1.46 − 5 × (−0.5784) = +1.43. So Sirius is genuinely brighter than the Sun, by about 3.4 magnitudes or a factor of 23, but nowhere near as dominant as it looks from here. It tops our sky mostly because it is close. Move the Sun out to Sirius’s distance and it would sit at magnitude +2.0, an unremarkable star you would struggle to pick out of the constellation around it.

Why the scale runs backwards. Brighter objects have smaller, and eventually negative, magnitudes, which trips up everyone at first. Blame Hipparchus, who around 130 BC (Before Christ) sorted the visible stars into six classes with “first magnitude” for the brightest. The system was already two thousand years old and universally used by the time anyone worked out that the eye responds logarithmically to light, so nineteenth-century astronomers standardised the scale to fit the existing numbers rather than renumber every star in the sky.