How Our Astrology Calculators Work

Written by Orbitarot · Sources: our own engine, positions checked against NASA JPL Horizons (method); place data GeoNames (CC BY 4.0); interpretations our own · Updated October 17, 2026

Planet positions

For any moment, the engine computes the geocentric ecliptic longitude of each body (its position along the zodiac as seen from Earth) and its daily speed, which tells us whether it is retrograde.

• Sun and planets, Mercury to Neptune: a truncated form of the VSOP87 planetary theory and the methods in Jean Meeus's Astronomical Algorithms.
• Moon: the lunar theory in Meeus, chapter 47, a truncated ELP-2000/82 series.
• Pluto: Meeus, chapter 37; we checked its positions against NASA JPL from 1900 to 2100, the years the calculators accept.
• Chiron: it has no simple analytic theory, so we use a daily table generated from NASA JPL's Horizons system for 1900 to 2100, interpolated to your birth time. Outside those years Chiron is not shown.
• Lunar nodes: both the mean node and the true (osculating) node.
• Black Moon Lilith: the mean lunar apogee, from its standard polynomial.

How we checked the engine against NASA JPL

We compared the engine with NASA JPL's Horizons ephemeris at 500 random instants between 1900 and 2100. The largest differences in ecliptic longitude were:

• Sun and planets, Mercury to Neptune: 0.0011 degrees
• Moon: 0.0050 degrees
• Pluto: 0.0010 degrees
• Chiron: 0.0004 degrees

Half of the checks came within 0.00005 degrees for the Sun and 0.00067 degrees for the Moon (the medians). The true lunar node, compared at 500 instants with the node computed from Horizons state vectors, came within 0.021 degrees.

For scale, the Moon moves about half a degree an hour, so a one-minute error in a birth time moves it by about 0.009 degrees, and moves the Ascendant by about a quarter of a degree. A body can still land on the wrong side of a sign boundary if it sits within these margins of it; when a placement is that close, the calculators say so. For the Saturn return calculator, which uses its own dedicated Saturn engine, see the figures on that page.

Zodiac: tropical and sidereal

The Western tools use the tropical zodiac: 0 degrees Aries is the point of the March equinox, and each sign is exactly 30 degrees. It is tied to the seasons, not to the constellations.

The Vedic tools (kundli, nakshatra, dasha, navamsa, Manglik and Sade Sati) use the sidereal zodiac with the Lahiri (Chitrapaksha) ayanamsa, the standard of the Indian national calendar. The sidereal position is the tropical one minus the ayanamsa, which is about 24 degrees in 2026 and grows by about 1 degree every 72 years. The BaZi calculator takes its solar terms from the Sun's tropical longitude, as the Chinese calendar does.

Houses and angles

The Ascendant is the ecliptic degree on the eastern horizon and the Midheaven the degree on the local meridian, both computed from local sidereal time, latitude and the obliquity of the ecliptic. Three house systems are available:

• Placidus (default): divides the time each degree takes to rise to the meridian into thirds. It is the most common system in modern Western software.
• Whole Sign: the rising sign is the whole first house, the next sign the second, and so on. The oldest system, and the one Vedic charts use.
• Equal: twelve 30-degree houses starting from the Ascendant degree.

Above about 66 degrees north or south, some degrees of the zodiac never rise or never set at certain times, and Placidus cusps cannot be calculated. For births there we switch to Whole Sign houses automatically and say so on the chart. Inside the polar circles the standard Ascendant formula sometimes returns the degree setting in the west, so there we use the opposite degree, the one rising in the east, and the chart says so.

Aspects and orbs

Two bodies are in aspect when the angle between them is within a set distance (the orb) of one of these angles:

When the Sun or Moon is one of the two bodies, the orb is 2 degrees wider. Orbs are a convention and astrologers use different values, so every aspect is listed with its exact orb, closest first, and you can judge for yourself. Synastry and transit lists use the same table by default.

Birth time, time zones and places

Time zones. You enter the clock time of your birth as it was written down. The calculator converts it to Universal Time with the time zone history built into your browser (the IANA time zone database, through the browser's Intl API), using the time zone of the birthplace you choose, so daylight saving and historical changes of zone are applied for that date. The database is very reliable from 1970 on; for some countries before 1970, and anywhere before standard time was adopted, its rules are reconstructions, so the calculators show the UTC offset they used and let you enter a different one. Browsers also miss part of the pre-1970 history of 99 zones, mostly ones the database has since merged with a neighbour (Iceland, Norway, Sweden, the Netherlands and others), so for those births we take it from the full IANA database (tzdata 2026e with its backzone file).

Places. The city search uses GeoNames data: 171,306 places with a population of at least 1,000, each with latitude, longitude and time zone. You can also type a latitude and longitude yourself. Place data © GeoNames, licensed under Creative Commons Attribution 4.0.

Unknown birth time. If you leave the time empty, we use 12:00 noon local time. The Sun and planets are then almost always in the right sign. The Moon moves about 13 degrees a day, so we also compute it at the start and end of your birth day and tell you if it changed sign. The Ascendant, Midheaven and houses depend on the exact time, so we leave them out rather than guess.

Calendars and relationship charts

The calendar and relationship tools add a few conventions of their own:

• Sunrise and sunset (planetary hours): the moment the top of the Sun's disc touches the horizon, with the Sun's centre 0.833 degrees below it (standard refraction plus the Sun's radius), the convention of the US Naval Observatory.
• Void of course Moon (calendar): from the Moon's last major aspect (conjunction, sextile, square, trine or opposition) in a sign until it enters the next sign, counting aspects to the Sun through Pluto by default, or to the Sun through Saturn with the traditional option.
• Stations and shadows (retrograde calendar): a station is the moment a planet's speed along the zodiac changes sign. The shadow starts when the planet first reaches the degree where it will later turn direct, and ends when it passes again the degree where it turned retrograde.
• Composite chart (composite): each point is the midpoint of the two positions, taken on the shorter arc; houses come from the midpoint of the two Midheavens at the average of the two birth latitudes.
• Davison chart (Davison): a real chart for the moment halfway between the two births in Universal Time, at a place halfway between them, either the simple average of latitudes and longitudes (taken the short way across the date line) or the great-circle midpoint.
• Returns (solar, lunar, Jupiter, Saturn, Chiron): an exact search for the moment the body comes back to its natal longitude.
• Dasha (dasha calculator): periods counted in years of 365.25 days by default, with 365.256 days (sidereal year) and 360 days as options.
• BaZi (BaZi calculator): the hour pillar uses true solar time by default, your clock time corrected for your longitude and for the equation of time, and the day can change at 23:00 or at midnight, as the two schools do.

Privacy

Every calculation runs in your browser. Your birth date, time and place are never sent to our server and we keep no record of them. The city search downloads small files of place names from our server, split by their first letters, so our server sees which file was requested, as it would for any page, but nothing about your birth. Share links put the chart details after the # in the address, a part that browsers do not send to servers.

What the interpretations are

The readings attached to each placement, house and aspect are our own words, written once and reused across the tools. They present astrology as a symbolic tradition: what astrologers associate with a placement, with its gifts and its challenges. They never predict health, pregnancy, death, legal matters or money. How we write and check all our texts is on the editorial standards page; the full list of tools is on the astrology hub.

Korean saju

The saju calculator uses the BaZi pillars above with Korean conventions. The hour pillar is taken, by default, from the mean time of 127.5 degrees east (Korean Standard Time minus 30 minutes, with summer time removed because the birth moment is in UT); birthplace longitude, true solar time and clock time are options. By default the new day starts with the rat hour; the 야자시 rule (day pillar kept until midnight, next day's hour stem) and a midnight rule with the same day's hour stem are options. Luck pillars (대운): forward for a yang year stem and a male chart or a yin year stem and a female chart, otherwise backward; calendar days to the next or previous major solar term divided by 3, a remainder of 1 dropped and of 2 rounded up, for the 대운수 (it matched a Korean 만세력 site on all 22 test values), and the exact count for the start date. Hidden stems follow the Korean three-part table. The Korean lunar calendar is computed from new moons and principal solar terms in Korean time (UTC+9; UTC+8 before 1912) and reproduces all 1,867 months of KASI's tables 1900 to 2050, with 56 leap months; KASI's day pillars on 1,867 dates match as well.

Kundli matching (Guna Milan)

The kundli matching calculator scores the eight Ashtakoot kootas from each person's sidereal Moon (Lahiri ayanamsa), computed exactly as on the nakshatra calculator. Tables follow the convention of the large Indian matching sites; Varna, Vashya and Gana are read with Person 1 as the boy and Person 2 as the girl. On 25 test couples entered in Prokerala's Guna Milan calculator, all eight koota scores were identical for 25; the published Prokerala and AstroSage sample reports are reproduced, apart from AstroSage's 2 points for the buffalo and serpent yonis (1 in the published tables). Nadi and Bhakoot exceptions are reported and never added to the score. Without a birth time, the day is split at every point where the Moon changes sign, nakshatra or Vashya group, and every possible score is listed.

Human Design chart

The Human Design chart takes the Personality positions at birth and the Design positions at the moment the Sun was 88 degrees of longitude earlier (solved by iteration, 86 to 92 days before birth), each for Sun, Earth, both lunar nodes (true node by default), Moon and Mercury to Pluto. Gate 41 starts at 302 degrees; each gate is 5.625 degrees and each line 0.9375 degrees. We compared 15 charts from two public calculators (390 activations): no differences. Shares in a sample of 20,000 random birth moments, 1970 to 2024: Generator 36%, Manifesting Generator 32%, Projector 21%, Manifestor 10%, Reflector 0.9%.

Astrocartography lines

The astrocartography map converts each body's apparent ecliptic longitude and latitude into right ascension and declination with the true obliquity of the date. MC line: the longitude where the apparent sidereal time equals the body's right ascension (hour angle 0); IC line: 180 degrees away. AC and DC lines: for each latitude, the hour angle H with cos H = -tan(latitude) x tan(declination), negative (rising, in the east) for the AC line and positive (setting, in the west) for the DC line; beyond latitude 90 degrees minus the declination the body neither rises nor sets that day, so the curve stops. Rising and setting are geometric and geocentric: no refraction and no lunar parallax. By default the lines keep the body's ecliptic latitude (in mundo); an option uses the zodiac degree alone. Distances to a line are great-circle distances on a sphere of 6,371 km. The relocation chart is the same birth moment cast for the new coordinates, with the same house formulas as every other chart.

Checks (6 October 2026): at points on our lines for 4 random moments from 1900 to 2100, NASA JPL Horizons put the Sun, the planets and Chiron within 0.002 degree of the meridian on MC and IC lines and within 0.007 degree of the horizon on AC and DC lines; the Moon sat about 1 degree below the horizon there, which is its parallax, left out by convention. Our right ascensions and declinations agreed with Horizons within 0.004 degree. With the zodiac option, the house engine's own Midheaven and Ascendant equal the planet's degree on every MC and AC line we sampled. The world outline is Natural Earth 1:110m land, a public domain dataset (naturalearthdata.com).

Questions

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