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Magnitude Brightness Ratio Calculator

Convert a magnitude difference into a brightness ratio.

How it is calculated

The tool applies Pogson's relation. First the magnitude difference Δm = m2 − m1, shown in magnitudes. Then the brightness ratio ratio = 100(Δm ÷ 5), which equals about 2.512Δm. The ratio tells how many times brighter object 1 is than object 2. Smaller (or more negative) magnitudes mean brighter objects, so when m1 is lower than m2 the ratio is above 1. Swapping the two values gives the reciprocal, with a negative Δm. Magnitudes can be any real numbers, including negative ones. The tool compares apparent brightness values you supply; it does not correct for distance, extinction or filters.

Worked example

Object 1 has magnitude 1.0 and object 2 has magnitude 4.5. The difference is 4.5 − 1.0 = 3.50 mag. Divide by 5: 3.5 ÷ 5 = 0.7. Then 1000.7 ≈ 25.12×. Object 1 is about 25 times brighter than object 2. Reversing the inputs gives -3.50 mag and a ratio of about 0.04×, meaning the second object is only a twenty-fifth as bright.

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Common mistakes

  • Thinking a higher magnitude is brighter. The scale runs backwards: magnitude 1 is brighter than magnitude 4.
  • Treating the magnitude scale as linear. A difference of 5 magnitudes is a factor of 100, not 5.
  • Entering m1 and m2 in the wrong order and reading the ratio the wrong way round. A result below 1 means object 1 is the fainter one.
  • Comparing an apparent magnitude with an absolute magnitude. The tool compares the values as given, and the result is only meaningful if both are of the same kind.
  • Using the rounded 2.5 as the base for a quick check. The exact base is 1001/5 ≈ 2.512, which makes a visible difference over several magnitudes.

About this calculator

Astronomical magnitude is a logarithmic brightness scale where lower (or more negative) numbers mean brighter objects, and each step of 5 magnitudes corresponds to exactly a 100× difference in brightness. Pogson's law formalizes this: the brightness ratio between two objects is I₁/I₂ = 100^((m₂−m₁)/5) = 2.512^(m₂−m₁), where 2.512 (the fifth root of 100) is often called the "Pogson ratio" — the brightness multiple for each single magnitude step.

Astronomers, both professional and amateur, use this conversion to translate catalog magnitude differences into an intuitive "how many times brighter" figure — for example, the Sun (magnitude −26.7) is about 400,000 times brighter than the full Moon (magnitude −12.7) as seen from Earth. It's a standard step when comparing stars, exoplanet transit depths, or telescope limiting magnitudes.

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Comments (1)

  • Editorial team

    Two anchor points make the log scale easy to sanity-check: a gap of 5 magnitudes is exactly 100 times, and a gap of 2.5 magnitudes is exactly 10 times. If your result for a 2.5 gap is not 10.00, a value was mistyped. The tool accepts any real numbers, so negative magnitudes for very bright objects work fine. Which two objects are you comparing?

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