Moon Illumination Calculator
Calculate the exact percentage of the Moon's surface illuminated on any date.
How It Works
Enter any date. The tool converts it to a Julian Day Number, computes the phase fraction using the synodic month formula, then applies the illumination formula to return the precise percentage of the Moon's disc that appears lit from Earth on that date. The visual progress bar shows where the illumination falls between new moon (0%) and full moon (100%).
Formula
Illumination by Phase Stage
- New Moon: 0% — disc completely dark from Earth's perspective
- Waxing Crescent (day 1–7): 1–49% and growing
- First Quarter (~day 7): exactly 50% — right half lit
- Waxing Gibbous (day 7–14): 51–99% and growing toward full
- Full Moon (~day 14.77): 100% — entire visible disc illuminated
- Waning Gibbous (day 15–22): 99–51% and decreasing
- Last Quarter (~day 22): exactly 50% — left half lit
- Waning Crescent (day 22–29): 49–1% and shrinking toward new
Why Illumination Is Not Linear
The cosine formula means illumination does not change at a constant rate. Near new moon and full moon, illumination changes slowly — you may notice little difference between two consecutive days. Near the quarter phases (around 50%), illumination changes most rapidly. This non-linear rate is a direct consequence of the geometry of a sphere lit from a distant source: small changes in viewing angle produce large changes in visible area near the equator of the terminator line but small changes at the poles.
Illumination for Photography and Observation
Lunar photographers often prefer 60–80% illumination — enough light to reveal surface detail (especially along the terminator line where shadows highlight craters and mountains) without the "washed out" appearance of a full moon where the Sun is overhead and shadows are minimal. For deep-sky astronomy (nebulae, galaxies), low illumination nights (less than 20%) are ideal because moonlight raises the sky background and reduces contrast. Plan your observation sessions using this calculator to find nights with the right illumination for your goals.
Frequently Asked Questions
How is moon illumination calculated?
The formula is: Illumination = (1 − cos(phase × 2π)) / 2 × 100. This derives from the geometry of a sphere lit by a distant source. At phase = 0 (new moon), cos(0) = 1, giving 0% illumination. At phase = 0.5 (full moon), cos(π) = −1, giving 100%.
What is 50% illumination?
50% illumination corresponds to the quarter moon phases (First Quarter and Last Quarter), when exactly half the lunar disc appears lit. The boundary between light and dark on the lunar surface is called the terminator line.
Is illumination the same as phase?
No — they are related but different. Phase is a number from 0 to 1 representing position in the lunar cycle. Illumination is the percentage of the visible disc that appears lit, derived from phase using the cosine formula. Two different phase values can produce the same illumination percentage (e.g., Waxing Crescent at 25% and Waning Crescent at 25% have the same illumination but different phases).
Can illumination ever be exactly 100%?
In theory yes, at the precise moment of the full moon. In practice, the Earth's shadow (penumbra) can slightly reduce illumination during a near-miss lunar eclipse, and the geometry is rarely a perfect 100% due to the Moon's orbital inclination relative to Earth's orbital plane.