Engineering
Apparent vs Absolute Magnitude, Distance Modulus & Pogson Flux Ratio
Calculate stellar absolute magnitude and distance in parsecs using consistent photometric bands, with an explicit extinction correction.
Compare magnitudes in the same band and system
Absolute stellar magnitude is defined at 10 parsecs. For the same band and magnitude zero point, the extinction-corrected difference is m−A−M = 5 log10(d)−5, where A is extinction in magnitudes. B5 defaults to zero for the original idealized example.
The measured apparent magnitude B2 includes extinction; subtract B5 before comparing it with intrinsic absolute magnitude B4. B3 is an independently supplied distance used to estimate M; the inverse calculation instead uses B4 and does not read B3. Changing one input does not make these independent estimates automatically consistent.
A five-magnitude difference corresponds to a factor of 100 in flux. Specify the numerator: the example ratio is F at 10 pc divided by the extinction-corrected flux at the observer. It is not a luminosity ratio between different stars.
These equations do not supply a standard-candle calibration or account for cosmological redshift and band corrections. Negative magnitudes are valid; physical distances must be positive. Display rounding is separate from measurement uncertainty.
| Photometric Metric | Formula | Star m = 8.5 at d = 100 pc | At Reference d = 10 pc |
|---|---|---|---|
| Distance Modulus (m - M) | 5 * LOG10(B3) - 5 | 5 * 2 - 5 = +5.00 mag | 0.00 mag (M = m!) |
| Absolute Magnitude M | B2 - B5 - (5*LOG10(B3)-5) | 8.5 - 5.0 = +3.50 mag | +8.50 mag |
| Flux Dimming Factor (10pc vs d) | 10^(0.4*(m-A-M)) | 10 ^ 2.0 = 100x dimmer | 1x (Reference) |
Absolute magnitude with extinction correction
Subtract extinction and the geometric distance modulus from the observed apparent magnitude. The result is displayed to two decimals.
=IF(COUNT(B2:B3,B5)<>3,"Invalid inputs",IF(OR(B3<=0,B5<0),"Invalid inputs",ROUND(B2-B5-(5*LOG10(B3)-5),2)))Distance from a supplied absolute magnitude
The inverse returns parsecs without rounding small positive distances down to zero. It uses the known M in B4, not the forward estimate.
=IF(COUNT(B2,B4:B5)<>3,"Invalid inputs",IF(B5<0,"Invalid inputs",10^((B2-B5-B4+5)/5)))Geometric distance modulus
This term depends only on the positive distance B3 in parsecs.
=IF(COUNT(B2:B3,B5)<>3,"Invalid inputs",IF(OR(B3<=0,B5<0),"Invalid inputs",5*LOG10(B3)-5))Flux ratio with its direction stated
F10/Fcorrected is greater than one beyond 10 pc and less than one nearer than 10 pc, when the magnitudes and distance are consistent.
=IF(COUNT(B2,B4:B5)<>3,"Invalid inputs",IF(B5<0,"Invalid inputs",ROUND(10^(0.4*(B2-B5-B4)),4)))Try the example
Use the original values or change them to test your understanding.