Astronomy
Illuminated fraction
Converts the phase fraction into the fraction of the disc that is lit. The cosine makes the change slow near full and new moon and fast through the quarters.
The Formula
illumination = (1 - cos(2 pi f)) / 2
Converts the phase fraction into the fraction of the disc that is lit. The cosine makes the change slow near full and new moon and fast through the quarters.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| f | Phase fraction | dimensionless | Position in the cycle, from 0 to 1. |
| illumination | Illuminated fraction | dimensionless | 0 at new moon, 1 at full moon, about 0.5 at the quarters. |
What Each Symbol Means
fdimensionless
Phase fraction
Position in the cycle, from 0 to 1.
illuminationdimensionless
Illuminated fraction
0 at new moon, 1 at full moon, about 0.5 at the quarters.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the moon phase page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Moon Phase, filed under Science. Every number the guide produces comes from substituting into this one line.