How to use the lunar calculator
The lunar calculator computes the Moon's position, phase and visibility for any date between 1900 and 2100. Use the fields on the left to set date, time, location and physical parameters. Results update immediately on the right — current phase, equatorial and topocentric position, upcoming primary phases, Supermoons, eclipses and the altitude curve over the coming hours.
What this lunar calculator delivers
- Spotlight: phase, illumination, lunar age, distance (km + R⊕ + lunar diameters), magnitude, light time
- Additional cards: Brown lunation number, optical libration, bright-limb angle, earthshine, orbital position
- Events: next 4+ primary phases, upcoming Supermoons and Micromoons, upcoming lunar and solar eclipses with visibility from Brazil
- Altitude curve: SVG of the next N hours with horizon line and pulsing "now" marker
- Position: J2000 equatorial RA/Dec, topocentric (alt/az/hour angle/refraction), ecliptic longitude
- Sun and Time: solar position, JD UTC/TT scales, ΔT, local sidereal time, local events (Moon and Sun rise/transit/set)
- Geometry: elongation, phase angle, synodic fraction, geocentric and topocentric distances in km/R⊕, horizontal parallax, anomalistic orbit with Super/Micro classification
- Orientation: colongitude, libration lat/lon, subsolar lat/lon, tracking rates
- JSON payload: raw engine output for technical inspection
About accuracy
The OCSE-Lite engine implements: truncated ELP-2000/82B (60 longitude + 60 latitude + 46 distance terms for the Moon, ~3 arcsec on lunar position), truncated VSOP87D (58 terms for heliocentric Earth, ~13 arcsec on the Sun), low-order IAU nutation, annual aberration, topocentric parallax, Bennett 1982 refraction, Espenak-Meeus ΔT (4000 BC – 3000 AD), exact Easter Computus, and equinoxes/solstices accurate to the minute. Sufficient for amateur use, teaching, astrophotography and naked-eye observation. For critical spaceflight work, use NASA SPICE.
This lunar calculator is free, requires no sign-up, collects no data and runs entirely on the server — no paid external APIs, no heavy JavaScript, no dependencies. In-house code reproducible from the public formulas in Meeus 1998, Astronomical Algorithms, 2nd ed.
Guide to input fields and results
This lunar calculator lets you configure physical and observational parameters to reproduce the Moon's position and geometry on any date. Below, what each field means.
Inputs - Time and location
- Date and Time: base instant of the calculation (in the timezone given under "IANA Timezone"). Default: now, Brasília time.
- Latitude / Longitude: observer coordinates in decimal degrees. Negative in the Southern / Western Hemisphere. Default: Brasília −15.78°, −47.93°.
- Altitude (m): observer altitude above sea level. Affects parallax and refraction marginally.
- IANA Timezone: standard identifier (e.g.:
America/Sao_Paulo,UTC). Determines how the given local time is converted to UTC.
Inputs - Atmospheric refraction
- Apply refraction: "Yes" applies the Bennett formula to correct the apparent altitude of the Moon and Sun near the horizon; "No" returns pure geometric altitude. Pressure (1013 hPa), temperature (15 °C) and humidity (50%) use defaults appropriate for sea level.
Inputs - Personal and display
- Your birth date: optional. When provided, the "Your lunar journey" card shows how many lunations you have lived through and when the next New Moon falls.
- Calendar system: Gregorian is the current civil calendar; Julian shows the converted date alongside the main date (accumulated Gregorian offset). Useful for pre-1582 historical dating and religious sources.
Inputs - Search horizons
- Eclipses (years) and Apsides (months): how far ahead the engine should search for lunar/solar eclipses and perigees/apogees.
- Super/Micro Moons (months): time window to detect a Full Moon coincident with perigee (Super) or apogee (Micro).
- Upcoming phases (count): how many primary phases (New, First Quarter, Full, Last Quarter) to list.
- Altitude curve (h and min): hours ahead plotted in the SVG and sampling step in minutes.
Outputs - Spotlight (highlight card)
- Illumination (%): percentage of the visible disc that is lit.
k = (1 + cos i)/2, where i is the phase angle. 0% at New Moon, 100% at Full Moon. - Lunar age (d): days elapsed since the last New Moon. Synodic cycle = 29.53 days.
- Distance: topocentric (from the observer) in km, Earth radii (R⊕) and multiples of the lunar diameter (⌀L = 3,474.8 km).
- Apparent diameter: angular size of the Moon in arcmin. Larger at Supermoon, smaller at Micromoon.
- Apparent magnitude: estimated visual brightness. Full Moon ≈ −12.7. Computed via Allen 1976.
- Light time: seconds a photon takes to travel Moon → Earth. ~1.28 s on average.
Outputs - Additional cards
- Brown lunation: current synodic cycle number counted from the 1923-01-17 New Moon (lunation #1).
- Optical libration: angular shift in longitude and latitude that makes ~59% of the Moon visible over the course of a month.
- Bright-limb angle: direction of the illuminated limb on the celestial sphere, measured from celestial north in degrees.
- Earthshine: intensity of Earth-reflected light on the Moon's dark side ("Da Vinci glow"). Visible only near New Moon.
- Orbital position: percentage along the perigee→apogee cycle (0% perigee, 100% apogee).
Outputs - Equatorial and topocentric position
- RA (Right Ascension): equatorial coordinate analogous to celestial longitude, in hours:minutes:seconds (HMS) or degrees.
- Dec (Declination): equatorial coordinate analogous to celestial latitude, in degrees DD:MM:SS.
- Ecliptic longitude λ: coordinate along the ecliptic, the base of lunar computations.
- Ecliptic latitude β: the Moon's displacement from the ecliptic.
- Geometric/apparent altitude: elevation above the horizon, without/with atmospheric refraction.
- Azimuth: horizontal direction measured from North (0°), East (90°), South (180°), West (270°).
- Hour angle: angle between the local meridian and the object. Positive west of the meridian.
Outputs - Apparent corrections and photometry
- Nutation Δψ / Δε: short-period oscillations of Earth's axis. Δψ in longitude, Δε in obliquity.
- Annual aberration: apparent shift caused by Earth's orbital motion. Maximum ~20.5".
- True obliquity: actual tilt of Earth's axis including nutation.
- Elongation ψ: Sun−Moon angular separation. 0° at conjunction (New), 180° at opposition (Full).
- Phase angle i: Sun−Moon−Earth angle. 0° at Full, 180° at New.
- Synodic fraction: position in the cycle, 0 = New, 0.5 = Full, 1 = New again.
Outputs - Local events and scales
- Moon rise/transit/set: local times of horizon crossings and culmination.
- Sun rise/set: the same events for the Sun (reference).
- JD UTC / JD TT: Julian Day on UTC (Coordinated Universal Time) and TT (Terrestrial Time, used for coordinates).
- Local Sidereal Time: local sidereal time in degrees or HMS. Defines which right ascension is currently on the meridian.
- ΔT (s): effective TT−UT1 difference applied to the calculation.
Outputs - Orbital geometry and tides
- Geocentric distance: Earth−Moon measured from Earth's center. Standard 384,400 km.
- Topocentric distance: Moon seen from the observer (parallax-corrected). May differ by up to ~6,378 km.
- Distance in Earth radii: in multiples of R⊕ = 6,378.137 km.
- Horizontal parallax: angle subtended by Earth's radius as seen from the Moon. Maximum ~1°.
- Anomalistic orbit: classifies the Moon between perigee (closest) and apogee (farthest).
- Colongitude: selenographic longitude of the terminator. Indicates which region is currently being illuminated.
- Subsolar lon/lat: point on the lunar surface where the Sun is currently at the zenith.
- Tracking rates: RA/Dec rates of change per second. Useful for telescope tracking.
- Tides (coefficient 0–100): approximation of tidal regime (syzygy/quadrature) based on synodic geometry.
Export and reproduce
The 3 buttons at the top of the result let you download the computed instant as CSV (50+ key-value-unit rows), JSON (raw engine output) or copy directly to the clipboard. Handy for spreadsheets, scripts or citation in academic work. The filename already includes date and location.
Frequently asked questions
How does the lunar calculator work?
You enter date, time and location. The lunar calculator uses the OCSE-Lite engine with truncated ELP-2000/82B series (60+ terms for the Moon, Chapront-Touzé 1988) and VSOP87D (50+ terms for the Sun, Bretagnon 1988), with typical ~3″ accuracy in lunar position. It computes phase, equatorial and topocentric position, libration, upcoming eclipses and Supermoons.
How accurate is the lunar calculator?
In default mode (engine_mode=auto), lunar position ~5″ RSS (truncated ELP-2000/82B). In de440 mode with SOFA polyfill active, ~0.005″ (~5 mas) using the DE440 kernel (Park et al. 2021, NASA/JPL) with IAU 2000A nutation and IAU 2006 P03 precession. Distance <1 km (de440), <50 km (lite). Phase times ±30s (lite) or ±5s (de440). Eclipses: magnitude ~0.5% canonical with Besselian elements + DE440 + light-time correction. Equinoxes and Easter exact to the minute. For academic use / paper citation, see the scientific version + methodology. For mission-critical spacecraft work, use NASA SPICE.
What does each output field mean?
Illumination: % of the visible face lit. Moon age: days since New Moon. RA/Dec: J2000 equatorial position. Az/Alt: altitude above your local horizon. Libration: effectively visible lunar face. Magnitude: apparent brightness. Next eclipse: date, magnitude, visibility from your location.
Can I query any date?
Yes, any date between 4000 BC and 3000 AD with Espenak-Meeus ΔT (accuracy degrades at the extremes). Ideal window 1900-2100.
Does the lunar calculator work for other countries?
Yes. Under "Observer location" you can change latitude, longitude and altitude to any point on the globe, or pick a city in the selector. Times default to your detected timezone; change it if needed.
How do I export the results?
Use the buttons at the top of the result: "Copy link" puts the full URL (with every parameter) on the clipboard; "Print" opens the print dialog; "Download JSON" saves the full computation (engine + derived + upcoming events) as pretty-printed JSON. CSV for spreadsheets and direct engine-payload copy are also available.
What are a Supermoon and a Micromoon?
A Supermoon is a Full Moon coinciding with perigee (~360,000 km from Earth) - it appears ~14% larger and ~30% brighter than a Micromoon, which is the Full Moon at apogee (~405,000 km). The calculator lists upcoming ones over the next 24 months.
What is lunar libration?
Optical libration is the apparent "wobble" of the Moon that lets us see up to 59% of its surface over each lunation (without libration we would see only 50%). The calculator shows libration in longitude (±7.9°) and latitude (±6.7°) from Meeus theory.
Can I use this for astrophotography?
Yes. The "Best time to photograph the Moon today" section computes lunar golden hour (Moon near the horizon), landscape-with-Moon window, best close-up window (near transit - less atmospheric extinction) and when to avoid (Moon almost on the horizon). It pairs with the altitude curve + twilight bands for full planning.
What does Live mode do?
The "Live (now)" toggle in the date/time field makes the browser clock tick in real time and, on compute, uses the exact moment you clicked. Useful to confirm Moon phase and altitude right now, or to lock the computation at the exact minute of a transit or photo. "Select" mode (default) keeps the date and time you typed.
How do I read the "good for observing?" verdict and the 24h window?
The calculator combines lunar altitude, twilight phase, estimated limiting magnitude (Bortle + aperture entered) and illumination to tell whether tonight is good, fair or poor for observing the Moon from your spot. The 24h window shows how many hours of actual visibility you have (Moon above the horizon and Sun below -6°/-12°/-18°), filtering out the poor times.
Why is the distance shown in km, R⊕, ⌀L and AU?
Each scale serves a different reader: km is the familiar distance; R⊕ (Earth radii, 6,378.137 km) helps compare with low orbits; ⌀L (lunar diameters, 3,474.8 km) gives a sense of "how many Moons would fit along the way"; AU (astronomical unit, 149.6 million km) puts the Moon on Solar-System scale. The comparative apparent size (arc-minutes) appears alongside.
How does the Bortle limiting-magnitude estimate work?
The reported limiting magnitude uses a simplified model based on Schaefer 1990 (PASP 102:212) combining: sky background brightness derived from Bortle, Moon contribution when above horizon (Krisciunas-Schaefer 1991 approx), twilight contribution by Sun altitude, atmospheric extinction by airmass at target altitude (with pressure correction) and aperture gain (5·log10(D/7)). Full Schaefer also accounts for observer age, eyepiece magnification, dark-adaptation state and instrument MTF — not modelled here. For scientific precision use the scientific calculator with the full Schaefer 1990 implementation.
Is the data free to reuse?
Yes. Calculations derive from Meeus 1998 (public algorithms) - you may cite freely in school work, blogs and posts. For formal academic citation, prefer the scientific version + methodology page with peer-reviewed references.
You have just used the lunar calculator and now have phase, illumination, age, distance in four scales, libration, topocentric position and the visibility verdict for the date and location you picked, with a 24-hour window, estimated limiting magnitude and the popular name of this month's Full Moon. The computation comes from the ELP-2000/82B + VSOP87D engine with parallax correction, refraction (Bennett or Saemundsson, depending on the supplied pressure and temperature) and can be exported as CSV or JSON for spreadsheets, scripts or observing notebooks. For a complete scientific workflow with DE440, GUM/JCGM 100:2008 uncertainty budget, stellar occultations and OEM/CCSDS export, see the scientific version.