Understand the relationship
The reasoning behind the result
Lower magnitude means more flux
mA−mB=−2.5 log₁₀(FA/FB)
Magnitude is a logarithmic coordinate for brightness. The negative sign reverses the ordering: a negative A-minus-B difference means A delivers more flux. Five magnitudes lower corresponds to a hundred times the flux, independent of the starting magnitude.
The ratio is of measured flux in a compatible passband and convention. It is not automatically a ratio of total luminosity, source size or distance.
A reference anchors the difference
mA=mB+Δm
A difference determines a ratio but does not determine either absolute flux. Supplying B's magnitude locates A on the same magnitude scale. Negative magnitudes are valid and do not mean negative flux.
The reciprocal FB/FA reverses the comparison. A source with half the reference flux is about 0.752575 magnitudes fainter; saying it is half a magnitude fainter would describe a different ratio.
Fractional change keeps its sign
Percentage flux change relative to B=100(R−1)
The flux increase uses B as its denominator. A ratio of two means a 100% increase; a ratio of one-half means a 50% decrease. These changes are asymmetric when the reference is reversed.
The graph uses log10 of A/B on the horizontal axis, so equal spacing represents equal multiplicative changes. Its straight line is a logarithmic relationship, not a linear-flux brightness law.
Logarithmic magnitudes require positive flux
A zero or negative measured flux can occur after background subtraction, but it has no finite ordinary logarithmic magnitude. This converter requires a strictly positive ratio. It does not substitute a detection limit or use an asinh magnitude convention.
Extremely large differences can still be represented logarithmically while their ratios exceed numerical range. Those derived ratios are labelled explicitly; the signed difference and log ratio remain available.
Follow the numbers
Half the flux of a magnitude-10 reference
- Enter FA/FB=0.5 and mB=10.
- Δm=−2.5 log10(0.5)=0.752574989 mag, so mA=10.752574989 mag.
- The reciprocal ratio is 2 and the flux change relative to B is 100(0.5−1)=−50%.
A is fainter even though its numerical magnitude is larger.
Quick guide
How to use this calculator
- State the shared band and magnitude convention.
- Choose a pair, a signed A-minus-B difference or a positive A/B flux ratio.
- If B’s magnitude is known, enable the reference anchor to infer A. Otherwise retain the ratio and difference alone.
- Read the direction statement and reciprocal ratio before using the comparison.
Calculation method
Calculation and interpretation
Follow the reversed magnitude scale without losing which source is brighter.
Δm=mA−mB=−2.5 log₁₀(FA/FB); R=FA/FB=10^(−0.4Δm); mA=mB+Δm.
Worked example
Half the flux of a magnitude-10 reference
A is fainter even though its numerical magnitude is larger.
Δm=mA−mB=−2.5 log₁₀(FA/FB); R=FA/FB=10^(−0.4Δm); mA=mB+Δm.
Supported inputs
Precision and limits
Matched photometry
Different bands, zero points, extinction corrections or magnitude conventions must be reconciled before interpreting the ratio.
No absolute power inference
A relative flux ratio does not determine luminosity or source distance, and no uncertainty is inferred from the entered digits.
Continue calculating
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