Moon Phase Illumination
Calculator

Inputs

Illuminated fraction
0.5

Results

Illuminated fraction
0.5
Illuminated percentage (%)
50
Phase index (0=new, 1=full)
0.5

Astronomy results

Illuminated fraction0.5
Illuminated percentage (%)50
Phase index (0=new, 1=full)0.5

formula-map diagram

Illuminated fraction
0.5
Illuminated percentage (%)
50
Phase index (0=new, 1=full)
0.5

Astronomical relationship

Formula

k = (1 + cos θ) / 2

= 0.5

Note

This result is a simplified model: it applies the displayed textbook formula to the values you entered, assuming ideal spherical bodies, circular orbits, blackbody radiation and perfect optics, and ignoring atmospheric seeing, relativistic corrections beyond those stated, cosmological models and measurement uncertainty. Use published ephemerides and catalogue data for real observations.

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