Understand the relationship
The reasoning behind the result
Attenuation is additive in magnitudes
mobs=mref+A; Fobs/Fref=10^(−0.4A)
A positive attenuation makes an object fainter and raises its numerical magnitude. Removing that attenuation subtracts A. In flux space the same operation multiplies by a transmission fraction, so subtracting a fixed percentage of the magnitude is incorrect.
The total-attenuation mode assumes the supplied A applies to the exact band and measurement. Enter zero if no extra loss is being applied. This does not assert that a real line of sight is dust-free.
An airmass correction can be differential
ΔA=k(Xobs−Xref)
The linear model uses an externally measured k in magnitudes per airmass. Correcting to Xref=0 uses the model's above-atmosphere reference. Correcting between two positive airmasses removes only their difference.
If the observed airmass is lower than the reference, ΔA is negative and the observed/reference flux ratio exceeds one. This is a change between observing conditions, not negative physical dust extinction. The tool does not infer airmass from altitude or fit k from observations.
Color excess needs an explicit band law
Aband=Rband E(B−V)
Color excess E(B−V) is the difference between observed and intrinsic B−V under a stated photometric convention. A band coefficient converts that excess into attenuation in one particular band. The coefficient depends on the adopted law and band response.
The input is deliberately a named band coefficient rather than a universal prescribed value. Neither source color, coordinates nor distance selects a dust law automatically. A negative measured color excess is not treated as physical negative attenuation by this mode.
The correction does not replace calibration
Instrumental zero points, color transformations, extinction and cosmological K corrections address different effects. Only the entered correction shown here is applied. If an input magnitude has already received it, applying it again would overcorrect the result.
The graph varies the signed correction while holding the reference magnitude fixed. Its arithmetic direction is exact, but the actual coefficient, law and applicability remain external measurement assumptions. No uncertainty or suitability threshold is inferred.
Follow the numbers
A differential atmospheric correction
- Let mref=10 at Xref=1, with observed Xobs=2 and k=0.2 mag per airmass.
- The signed correction is 0.2×(2−1)=0.2 mag, giving mobs=10.2.
- The flux ratio is 10^(−0.4×0.2)=0.831763771. Returning to the reference subtracts 0.2 mag.
The reference is the stated airmass, not automatically a dust-free or above-atmosphere magnitude.
Quick guide
How to use this calculator
- Identify the band and the actual correction convention.
- Choose the quantity to solve and enter the other magnitude.
- Supply a total attenuation, two airmasses with an external coefficient, or a color excess with an external band coefficient.
- Read the signed correction and reference-relative flux ratio. A differential airmass reference is not necessarily an unextinguished source.
Calculation method
Calculation and interpretation
Show exactly which correction moves a magnitude between its stated reference and observed conditions.
mobs=mref+ΔA; ΔA=A, k(Xobs−Xref), or Rband E(B−V); Fobs/Fref=10^(−0.4ΔA).
Worked example
A differential atmospheric correction
The reference is the stated airmass, not automatically a dust-free or above-atmosphere magnitude.
mobs=mref+ΔA; ΔA=A, k(Xobs−Xref), or Rband E(B−V); Fobs/Fref=10^(−0.4ΔA).
Supported inputs
Precision and limits
Entered model only
No atmospheric conditions, dust map, universal extinction coefficient, spectral integration or validity range for an extinction law is inferred.
Reference and corrections must match
Airmass, passband, zero point and prior correction state must be compatible. The result is not a calibrated photometric measurement by itself.
Continue calculating
Related calculators
