Star Magnitude Calculator
Calculate the brightness ratio between stars using Pogson's magnitude scale.
Enter two apparent magnitudes to find how many times brighter one star is.
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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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