Magnitude to Flux Ratio Calculator

How it is calculated

The magnitude scale is logarithmic and runs backwards: a smaller number is a brighter object. Five magnitudes are exactly a factor of 100 in flux, so one magnitude is a factor of 100^1/5 ≈ 2.512. The tool applies ratio = 100.4 × Δm, the same as 10Δm ÷ 2.5. Enter Δm as the magnitude of the object you compare against minus the magnitude of your object, so Δm = m_B − m_A gives the flux of A divided by the flux of B. A positive Δm gives a ratio above 1 and the text "Object is N× brighter"; a negative Δm gives a ratio below 1 and "fainter" with the reciprocal; 0 gives 1:1. The percent line is the ratio × 100. Δm can be any number, including fractions. The ratio is shown to four decimals, so a very large negative Δm (below about -11) displays as 0.0000×. Magnitudes must be in the same band for a physically meaningful flux ratio.

Common mistakes

• Subtracting in the wrong direction. Because a smaller magnitude means a brighter object, the sign of Δm decides whether the tool says brighter or fainter, so check which star you treat as the reference.
• Treating magnitudes as linear. A 5-magnitude difference is a factor of 100, not 5; one magnitude is about 2.51.
• Comparing magnitudes from different bands, such as visual against blue. The ratio is a true flux ratio only within one band.
• Entering the two magnitudes instead of their difference. The input is a single Δm, so subtract first.
• Confusing apparent and absolute magnitude. A flux ratio of apparent magnitudes says how bright the objects look from here, not how luminous they really are.