Moon Phase Calculator
Calculate the current moon phase and upcoming full and new moon dates. Enter values for instant results with step-by-step formulas.
Calculator
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Phase Details
Formula
Moon age is the number of days since the most recent new moon, computed from a known reference new moon (Jan 6, 2000). The synodic month averages 29.53059 days. Illumination follows a cosine curve from 0% (new) to 100% (full) and back.
Last reviewed: December 2025
Worked Examples
Example 1: Moon Phase on a Specific Date
Example 2: Planning a Stargazing Night
Background & Theory
The Moon Phase Calculator applies the following established principles and formulas. Astronomy and space science rely on a set of precisely defined physical relationships that allow distances, sizes, motions, and energies of celestial objects to be calculated from observational data. Kepler's three laws of planetary motion, derived empirically in the early seventeenth century, describe elliptical orbits, equal areas swept in equal times, and the harmonic law T² = a³, where T is the orbital period in Earth years and a is the semi-major axis in astronomical units (AU). This relationship holds for any object orbiting the Sun and can be generalized using Newton's law of gravitation. Distances in astronomy are expressed in multiple units: one light-year equals approximately 9.461 × 10¹⁵ meters, one parsec equals 3.086 × 10¹⁶ meters or about 3.26 light-years, defined as the distance at which one AU subtends one arcsecond of parallax. Angular size is calculated as θ = 206,265 × (d / D) arcseconds, where d is the physical diameter and D is the distance. The stellar magnitude system uses Pogson's formula: m1 − m2 = −2.5 × log10(F1 / F2), where F represents flux. Each magnitude step corresponds to a flux ratio of approximately 2.512, meaning a first-magnitude star is 100 times brighter than a sixth-magnitude star. Hubble's Law relates recessional velocity to distance: v = H₀d, where the Hubble constant H₀ is approximately 70 km/s/Mpc. Escape velocity from any body is given by v = √(2GM/r), yielding 11.2 km/s for Earth. Orbital period for a circular orbit follows T = 2π√(r³/GM). Luminosity and distance are linked by the inverse square law: F = L / (4πd²). Stars are classified by spectral type using the mnemonic OBAFGKM, corresponding to surface temperatures from approximately 30,000 K (O-type) to under 3,500 K (M-type). Each type reflects characteristic absorption spectra tied to ionization states of elements in the stellar photosphere.
History
The history behind the Moon Phase Calculator traces back through the following developments. The history of astronomy is one of progressive scale — each era expanding humanity's conception of the universe's size and structure. The Copernican revolution of 1543, when Nicolaus Copernicus published De revolutionibus orbium coelestium, displaced Earth from the center of the cosmos and placed the Sun at the center of the planetary system. Decades later, Galileo Galilei turned a Dutch-invented telescope toward the sky in 1609, discovering the moons of Jupiter, the phases of Venus, and the cratered surface of the Moon — observations that provided compelling evidence for the heliocentric model and led to his conflict with the Catholic Church. Johannes Kepler, working from Tycho Brahe's meticulous naked-eye observations, derived his three laws of planetary motion between 1609 and 1619. Isaac Newton unified celestial and terrestrial mechanics with his law of universal gravitation in 1687, explaining the cause behind Kepler's empirical laws and enabling precise prediction of planetary positions. The eighteenth and nineteenth centuries brought systematic sky surveys, stellar parallax measurements, and the discovery that the Milky Way is itself a galaxy among many. Edwin Hubble's 1929 observations using the 100-inch Hooker Telescope at Mount Wilson demonstrated that galaxies are receding from us at velocities proportional to their distance — the first direct evidence for an expanding universe and the empirical basis for Big Bang cosmology. NASA was founded in 1958 following the Sputnik shock, and the Apollo 11 mission landed humans on the Moon on July 20, 1969. The Hubble Space Telescope, launched in 1990, revolutionized observational astronomy by operating above Earth's atmosphere and producing imagery from ultraviolet to near-infrared wavelengths. The first confirmed exoplanet around a Sun-like star was detected in 1995 by Michel Mayor and Didier Queloz using the radial velocity method. The James Webb Space Telescope, launched in December 2021 and fully operational by 2022, extended infrared observations to probe the earliest galaxies formed after the Big Bang.
Frequently Asked Questions
Sources & References
Formula
Illumination = (1 - cos(2π × Moon Age / 29.53)) / 2 × 100%
Moon age is the number of days since the most recent new moon, computed from a known reference new moon (Jan 6, 2000). The synodic month averages 29.53059 days. Illumination follows a cosine curve from 0% (new) to 100% (full) and back.
Worked Examples
Example 1: Moon Phase on a Specific Date
Problem: What is the moon phase on March 20, 2026?
Solution: Days since reference new moon (Jan 6, 2000) = 9,570 days\n9,570 mod 29.53 ≈ days into current cycle\nIllumination = (1 - cos(2π × age/29.53)) / 2 × 100%
Result: Calculate using the tool above for the exact phase, illumination, and upcoming full/new moon dates.
Example 2: Planning a Stargazing Night
Problem: Find dates with minimal moonlight for deep-sky observation.
Solution: Best stargazing occurs within ±5 days of new moon when illumination is below 25%. Use the calculator to find the next new moon date and plan your observation window accordingly.
Result: Target dates around the new moon for darkest skies.
Frequently Asked Questions
How are moon phases calculated?
Moon phases are determined by the Moon's position relative to the Sun as seen from Earth. The synodic month (new moon to new moon) averages 29.53 days. By counting days since a known reference new moon and dividing by the synodic period, we determine where the Moon is in its cycle. The illumination percentage follows a cosine curve: 0% at new moon, 50% at quarters, and 100% at full moon.
What are the 8 phases of the Moon?
The 8 principal phases are: (1) New Moon — 0% illuminated, between Earth and Sun. (2) Waxing Crescent — 1-49% illuminated, growing. (3) First Quarter — 50% illuminated, right half lit. (4) Waxing Gibbous — 51-99% illuminated, growing toward full. (5) Full Moon — 100% illuminated, opposite the Sun. (6) Waning Gibbous — 99-51% illuminated, shrinking. (7) Last Quarter — 50% illuminated, left half lit. (8) Waning Crescent — 49-1% illuminated, shrinking toward new.
Why does the Moon appear to change shape?
The Moon always has half its surface illuminated by the Sun — what changes is how much of that illuminated half we can see from Earth. As the Moon orbits Earth (taking 29.53 days), the angle between the Sun, Moon, and Earth changes, altering our view of the sunlit portion. The Moon does not produce its own light; it reflects sunlight.
Why might my result differ from another tool or reference?
Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.
What inputs do I need to use Moon Phase Calculator accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting — for example, a weight measurement in kilograms, a distance in metres, or a dollar amount — and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy