How the moon phase calculator works
The moon's phases repeat every synodic month, about 29.53 days, the time between two new moons. Counting days from a known new moon and dividing by that period gives the moon's age, which determines the phase.
Illumination = (1 − cos(2π × age ÷ 29.53)) ÷ 2
Age 0 is new moon, about 7.4 days is first quarter, 14.8 days is full moon and 22.1 days is last quarter. Because the moon's orbit is elliptical, real phase times can differ from this average model by up to about 14 hours, so dates near a boundary may be off by a day. For exact times, consult the US Naval Observatory's moon phase data.
Worked example
On April 23, 2024, the moon's age works out to about 14.9 days and it is 100% lit: a Full Moon. The actual full moon that month occurred at 23:49 UTC on April 23, matching the estimate. Seven days later the moon is a waning gibbous heading toward last quarter.
Frequently asked questions
How long is a lunar cycle?
About 29.53 days from one new moon to the next.
How many full moons are there in a year?
Usually 12, and sometimes 13; the extra one is often called a blue moon.
What is a waxing moon?
A moon whose lit portion is growing, between new moon and full moon.
Is the same moon phase seen everywhere?
Yes, the phase is the same worldwide, though the moon appears rotated in the Southern Hemisphere.
Updated October 2026. Results are estimates for education, not financial or medical advice. All math runs in your browser; nothing you type is sent anywhere.