Understand the relationship
The reasoning behind the result
Magnitudes cannot be added directly
mtot=−2.5 log₁₀(Σi 10^(−0.4mi))
Independent source light adds as flux. The logarithmic coordinate must first be converted to a common relative flux scale; only the sum is converted back into a magnitude. Averaging magnitudes would describe a geometric mean of fluxes, not the unresolved total.
The same reference zero point cancels when every component belongs to the same band and system. Different bandpasses cannot be combined into an ordinary same-band magnitude merely by listing their magnitudes together.
Flux shares reveal the dominant contributor
wi=Fi/Σj Fj
A component's percentage is its fraction of the total light, not its fraction of the summed magnitude numbers. With components at 5, 7.5 and 10 mag, the relative fluxes are 1, 0.1 and 0.01. The brightest contributes about 90.09% of their combined light.
The implementation scales the sum around its brightest component before taking a logarithm. This avoids overflowing an arbitrary zero-point flux and preserves useful results when the absolute magnitudes are large or negative.
Removing a source requires a positive remainder
mrem=mtot−2.5 log₁₀(1−Fknown/Ftot)
In separation mode the unresolved total is a separate measurement. Known components are added in flux space and removed once. A remaining component is possible only when their sum is less than the total; equal or greater known flux does not produce a finite positive remaining magnitude.
A very small difference between nearly equal measured fluxes is ill-conditioned. This tool blocks a remaining fraction of 10⁻⁸ or less because the subtraction cannot be reliably resolved at the supported magnitude precision. That numerical boundary is not a detection threshold; measurement errors can dominate much sooner.
Repeated observations are not extra sources
The addition mode describes simultaneous light from components such as unresolved stars. Repeated exposures of the same source require exposure normalization, uncertainty weighting and a measurement model. Summing their apparent magnitudes as if they were distinct stars would make the source artificially brighter.
The component ledger is bookkeeping for entered fluxes. It does not deblend an image, estimate missing components or establish that a faint residual is statistically detected. Extremely tiny shares may fall below display range while their magnitudes remain in the table.
Follow the numbers
Two magnitude-10 sources
- Choose either source's flux as one relative unit. The two component fluxes are 1 and 1.
- The sum is 2, so its brightening relative to either source is 2.5 log10(2)=0.752574989 mag.
- The total magnitude is 10−0.752574989=9.247425011 mag, with each component contributing 50%.
The combined source has twice the flux and a lower magnitude.
Quick guide
How to use this calculator
- Choose addition or removal from an independently measured total.
- List the individual components in a shared passband and magnitude system.
- Inspect relative flux contributions before reading the combined or remaining magnitude.
- Use separation only when the total flux exceeds the known-component flux by a numerically resolvable amount.
Calculation method
Calculation and interpretation
Add and subtract light in flux space while keeping magnitudes as the reporting scale.
Ftot/F0=Σ10^(−0.4mi); mtot=−2.5 log₁₀(Σ10^(−0.4mi)); Frem=Ftot−ΣFknown.
Worked example
Two magnitude-10 sources
The combined source has twice the flux and a lower magnitude.
Ftot/F0=Σ10^(−0.4mi); mtot=−2.5 log₁₀(Σ10^(−0.4mi)); Frem=Ftot−ΣFknown.
Supported inputs
Precision and limits
Common band and reference
All components and any measured total must use the same passband, calibration and correction state. No color transformation is inferred.
No deblending or uncertainty fit
The result does not establish physical association, measurement independence or detectability. Separating nearly equal fluxes is particularly sensitive to measurement errors.
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