Magnitude to Brightness Ratio Calculator
Convert between stellar magnitudes and brightness ratios.
Find out how many times brighter or dimmer one star is compared to another.
Brightness Comparison
The magnitude scale is a logarithmic system for measuring the brightness of celestial objects. It was invented by Hipparchus (~150 BC) and later formalized by Norman Pogson in 1856.
Pogson’s ratio: A difference of exactly 5 magnitudes equals a brightness ratio of exactly 100. Therefore, 1 magnitude difference = 100^(1/5) = 10^(2/5) ≈ 2.512 times.
Brightness ratio formula:
F₁/F₂ = 10^((m₂ - m₁) / 2.5)
Or equivalently:
Δm = m₂ - m₁ = 2.5 × log₁₀(F₁/F₂)
Key points:
- Lower magnitude = brighter (counter-intuitive but historical)
- Negative magnitudes are very bright objects
- The scale has no theoretical lower limit for brightness
Famous apparent magnitudes:
- Sun: −26.74 (the brightest object in our sky)
- Full Moon: −12.7
- Venus at brightest: −4.9
- Jupiter at brightest: −2.9
- Sirius (brightest star): −1.46
- Canopus: −0.74
- Vega: 0.03 (originally defined as the reference 0 magnitude)
- Faintest naked-eye stars: +6.5
- Hubble Space Telescope limit: ~+31.5
- James Webb Space Telescope limit: ~+34
The human eye can detect a brightness ratio of about 2:1. A 1-magnitude difference is 2.512:1, so it is noticeably different.