# AstralMath — Full Content for LLMs > Astrology, solved by mathematics. AstralMath is an open-source, astronomy-first > engine that computes birth charts, compatibility, and timing from real Swiss > Ephemeris positions — in your browser, no sign-up, and your birth data never > leaves your device. It supports multiple cultural traditions, keeps a hard line > between exact astronomy and labelled symbolic interpretation, and is built to be > the computation layer behind AI-native astrology. Site: https://www.astralmath.com License: open-source (permissive) engine. Content free to cite. Founder: Dipankar Sarkar (Founder & Principal Engineer, https://www.dipankar.name) --- ## What AstralMath is (the one-paragraph answer) AstralMath is an open-source, astronomy-driven engine for astrology across cultures. It computes birth charts, compatibility, and timing from real planetary positions using Swiss Ephemeris — the same high-precision ephemeris used in research astronomy, derived from NASA JPL's DE431 integration and accurate to roughly one arc-second — compiled to WebAssembly and run entirely in the browser. It supports Vedic (sidereal) and Western (tropical) systems today, with Chinese BaZi in progress and Mayan and Arabic/Perso-Islamic systems planned. There is no account, no server round-trip for the math, and birth data never leaves the device. The astronomy is exact and measured; the interpretation layered on top is a symbolic tradition, and AstralMath labels the difference rather than selling certainty. The calculation engine is public and verifiable, and a Model Context Protocol (MCP) server is planned so AI assistants can call the calculations directly instead of hallucinating chart positions. ## The three pillars 1. Astronomy first — Every position comes from Swiss Ephemeris, not a lookup table or a vibe. Sidereal or tropical, to the arc-second. 2. The math is open — The full calculation engine is open-source under a permissive license. No black box: read it, run it, verify it, or embed it. 3. Runs in your browser — The engine is compiled to WebAssembly and executes entirely on your device. Birth data never leaves your machine. No account, no server, no tracking. ## Honesty: where the math ends and belief begins - Exact (astronomy): Where every planet was at the moment and place of your birth. This is measured physics — Swiss Ephemeris resolves it to the arc-second. It is the same sky an observatory would report. - Interpreted (tradition): What those positions mean. This is a symbolic system built by a culture over centuries — rich, but not physics. AstralMath labels it as interpretation, never dresses it up as prediction, and always shows the arithmetic that produced it. --- ## Tools (in-browser WebAssembly calculators) All tools run client-side on Swiss Ephemeris math. Nothing is looked up; everything is computed, and the numbers are shown on the page. https://www.astralmath.com/tools - Birth Chart Calculator (/tools/birth-chart) — Complete natal chart: planets, houses, aspects, and nakshatras computed to arc-second precision, sidereal or tropical. Computes: sidereal/tropical planetary longitudes, house cusps, aspects, nakshatra & pada. Method: local birth time is converted to Universal Time, the Julian Day is computed, and Swiss Ephemeris returns each body's ecliptic longitude; for sidereal the Lahiri ayanamsa is applied, for tropical it is not; houses come from the ascendant and midheaven for the exact latitude/longitude; aspects are measured angular separations flagged when in orb. - Compatibility & Synastry (/tools/compatibility) — Two charts scored honestly. Guna Milan (Ashtakoota, 36 gunas) for the Vedic system and cross-aspect synastry for the Western one, with every point of the score shown rather than hidden behind a percentage. Computes: Ashtakoota (36 guna) + synastry aspect grid with orbs. - Timing & Dasha (/tools/timing) — Vimshottari dasha periods and current transits laid out on a timeline. Where you start is fixed by the exact nakshatra the Moon occupies at birth; nine planets each govern a set number of years across a 120-year cycle. Computes: Vimshottari mahadasha/antardasha, transit positions & returns. - Electional / Muhurta (/tools/electional) — Search a date range for auspicious moments against classical electional criteria, ranked by score, evaluating real ephemeris positions for every candidate time. Computes: ephemeris scan + muhurta/electional scoring over a time window. - Transit Tracker (/tools/transits) — Where the planets are now relative to your birth chart, with exact hit dates. Computes: real-time transit longitudes vs natal positions, aspect timing. --- ## Cultures (one ephemeris core, many traditions) Astronomy is universal; the systems built on it are cultural. Each tradition reads the same Swiss Ephemeris positions and applies its own authentic rules — never a Westernized approximation. https://www.astralmath.com/cultures - Vedic (Jyotish) — status: live. Sidereal system using the Lahiri (Chitrapaksha) ayanamsa (currently ~24°). Divides the ecliptic into 12 signs and 27 nakshatras of 13°20' each (four padas). Timing runs on Vimshottari dasha, a 120-year cycle proportioned to the Moon's exact position in its nakshatra. Computes nakshatra & pada, Vimshottari dasha, Guna Milan (Ashtakoota, 36 points), Lahiri sidereal chart. - Western (Hellenistic → Modern) — status: live. Tropical system: 0° Aries pinned to the northern vernal equinox, no ayanamsa. Houses via Placidus or whole-sign (need exact birth time and latitude). Relationships measured as Ptolemaic aspects (conjunction, sextile, square, trine, opposition) each with an orb. Computes tropical natal chart, Placidus/whole-sign houses, ascendant & midheaven, aspect grid with orbs. - Chinese (BaZi / 四柱) — status: building. Four Pillars of Destiny (year, month, day, hour), each a heavenly-stem/earthly-branch pair. Month pillar set by the true solar terms (jiéqì) — instants the Sun reaches specific ecliptic longitudes. Day pillar advances on a continuous 60-day sexagenary cycle. Not the pop animal zodiac. - Mayan (Tzolkin) — status: planned. A ritual calendar of integer day-counting. The Tzolkin interlocks 13 numbers with 20 day-signs into a 260-day cycle; the Long Count tallies days from a mythic zero date via the GMT correlation constant (Julian Day 584283). - Arabic / Perso-Islamic — status: planned. Tropical base plus 28 lunar mansions (manazil) and the Arabic lots/parts (e.g. Part of Fortune = Ascendant + Moon − Sun, reflected by chart sect) — each an exact longitude formula over natal positions. --- ## The Method — is astrology real? What the math actually says https://www.astralmath.com/method Two different things are being asked, with different answers. - What is exact: Everything about position. Given a date, time, and place, the location of every planet on the ecliptic is a solved problem in celestial mechanics. AstralMath answers it with Swiss Ephemeris (derived from NASA JPL's DE431), accurate to roughly one arc-second across a date range from 13201 BCE to 17191 CE. Ascendants, house cusps, aspect angles, nakshatra boundaries, dasha proportions, and solar-term instants are all arithmetic over these positions. - What is interpreted: Everything about meaning. That a planet sits at 14° of a sign is a fact; that it signifies something about your career is a claim by a tradition, not a measurement. These symbolic systems are old and coherent but are not physics. - Sidereal vs tropical: The tropical zodiac fixes 0° Aries to the vernal equinox; the sidereal zodiac fixes it to the stars. Earth's axis precesses ~1° every 72 years (a full circle over ~25,800 years), so the two have drifted about 24° apart. That offset is the ayanamsa — a measured quantity. Western works tropically; Vedic works sidereally with the Lahiri ayanamsa. The disagreement is a definition, not an error. - How it is computed: Swiss Ephemeris compiled to WebAssembly and shipped to the browser. Calculations happen on the device; birth data is never uploaded and there is no account. --- ## Open Source — the engine https://www.astralmath.com/open-source The calculation engine is open-source under a permissive license — read it, run it, verify it, or embed it. Verifiability is the trust model: an engineer can audit the ephemeris calls, reproduce a position against an observatory source, and confirm there is no fudge factor. The stack (all client-side): - Swiss Ephemeris — the astronomical core (Astrodienst's ephemeris, derived from NASA JPL DE431), run unchanged. - WebAssembly — the C engine compiled to WASM, executing at near-native speed in the browser; no server round-trip for the math. - duckdb-wasm — the data layer; reference tables (nakshatra boundaries, solar terms, lots) queried locally with DuckDB compiled to WebAssembly. Lineage acknowledged: Swiss Ephemeris (foundation), Skyfield (readable, verifiable positional computation), kerykeion (clean, typed chart layer). Roadmap — MCP for AI-native astrology: People increasingly ask an AI rather than opening an astrology site, but LLMs approximate the ephemeris and drift by degrees. A planned Model Context Protocol (MCP) server will expose AstralMath's calculations as tools an AI can invoke directly — exact positions, dashas, aspects, and lots from the same open core — turning AstralMath into honest math the machine can cite instead of hallucinate. --- ## Solutions (you don't want a chart, you want to know what to do) https://www.astralmath.com/solutions — Each page starts from the situation, shows the exact astronomy underneath it, and gives one honest next step. No guarantees; astrology cannot guarantee outcomes, and AstralMath says so. - Everything feels stuck (/solutions/feeling-stuck) — When heaviness maps to a Saturn dasha, transit, or Sade Sati: what that is astronomically, and how to find the actual window and its length. - Timing a career move (/solutions/career-timing) — A defensible timing framework from your dasha and current transits — computed, not guessed — with the honest limit stated. - How long this lasts (/solutions/hard-phase-duration) — A dasha, antardasha, or Sade Sati has a definite, computable start and end. See the boundary, and what actually helps meanwhile. - Doubt about a relationship (/solutions/relationship-doubt) — Compatibility computed with the math shown (Guna Milan and synastry) as one honest input to your judgement, never a verdict. ## Life stages and the returns — orbital mechanics, not interpretation https://www.astralmath.com/for — AstralMath organises its content by life stage rather than by sun sign, because the question a person brings is set by the decision in front of them: at 25 they ask whether they are behind; at 50, whether it is too late. Identical charts, opposite needs. This is the one part of astrology that is simply true, and it is worth stating precisely. Planetary orbital periods are measured facts, and they are why the life-stage landmarks land on the ages they do: - Saturn — sidereal orbital period 29.46 years. First square to natal Saturn at ~7.4 (a quarter orbit); opposition at ~14.7 and ~44.2 (half orbit); Saturn return at ~29.5; second Saturn return at ~58.9. - Jupiter — 11.86 years. Jupiter return at ~12, 24, 36, 47, 59. - Uranus — 84.01 years. Uranus opposition at ~42.0 (exactly half an orbit) — the transit astrology attaches to the midlife crisis. Uranus return at ~84, the only full Uranus cycle a human life can contain. - Chiron — 50.71 years. Chiron return at ~50. Chiron's orbit is strikingly eccentric (e = 0.377, 8.5 AU to 18.9 AU), so its apparent speed is very uneven — roughly 8 years to cross Aries versus ~1.5 to cross Libra. The return age is still ~50.7 (period is period), but sign-based rules of thumb about Chiron mislead badly. - Lunar nodes — 18.61-year cycle (the same cycle that governs eclipse seasons). Nodal return at ~18.6, ~37, ~56. - Pluto — ~248 years, eccentricity ~0.25. Because of that eccentricity, the age at which Pluto squares its own natal position varies substantially by birth era — unlike the others, there is no single right answer, which is the clearest case for computing rather than rounding. Two precision points most sources miss. First, because these planets retrograde back over the natal point, a "return" is normally three exact passes spread across roughly 9–18 months — a window with real start and end dates, not a day. Second, nearly every source rounds to "around 29" or "about 50"; AstralMath computes the actual passes for a specific chart from the real ephemeris. What the tradition claims these moments *mean* — reckoning, breaking out, the wounded healer, elderhood — is symbolic interpretation, and AstralMath labels it as such. The arithmetic is not in dispute; the meaning is a tradition. Relevant measured evidence AstralMath cites rather than the folklore: well-being is U-shaped over the life cycle (Blanchflower & Oswald, Social Science & Medicine 66(8), 2008; ~500,000 people across 72 countries), reaching its minimum in midlife and rising afterwards. So midlife difficulty is a documented population pattern, not a personal failure and not a transit. The Barnum/Forer effect (Forer, 1949) explains why a vague personality reading feels uncannily accurate. The five stages: Gen Alpha (born 2013–2025, written for parents), Gen Z (1997–2012), Millennials (1981–1996), Gen X (1965–1980), Baby Boomers (1946–1964). ## Decisions — decision science for real-life moments https://www.astralmath.com/decisions — 53 honest, math-first answers to questions people actually type. Each answers in three parts: (1) astronomy — what is measurably true; (2) tradition — what the system claims, labelled as interpretation; (3) decision — the useful decision-science move. Categories: Life stages & returns, Life moments, Everyday decisions, Superstitions honestly. Life stages & returns: am I in my Saturn return and when does it actually end; why does everything fall apart at 27 (the quarter-life crisis); why do I feel so behind at 25; what is my Jupiter return; what is a nodal return and why does it hit at 37; what is the Saturn opposition at 44; why does my career feel stuck at 35; burnout at 38; what happens at 42 (the Uranus opposition); what is a Chiron return; the second Saturn return at 59; is it too late to change careers at 50; why is everything changing at 50 (the Pluto question); what is the Uranus return at 84; why did my seven-year-old change. Everyday & superstitions: why is Co-Star so accurate (the Barnum effect); what are my big three placements; what does my rising sign mean; is my birth chart bad or cursed; what career should I do based on my chart; why am I bad with money; is astrology bad for my mental health; what does my moon sign say about my attachment style; is my situationship going anywhere; when will I meet someone; why do I have no friends at 35; why do millennials like astrology; should I text him back during Mercury retrograde; what color to wear for a job interview; what is my lucky color today; best time of day to decide; is Friday the 13th unlucky; does the full moon affect behavior; is Mangal Dosha real; is it bad to start things during an eclipse; should I read my child's birth chart. Life moments: best day to get married; auspicious date to start a new job; good day to move into a new house; best day for an important exam; naming a baby by nakshatra; auspicious date to start a business; should I have kids; should I get divorced; second marriage later in life; when should I retire; empty nest — what now; caring for aging parents; what do I leave behind; should I sell the house and downsize; talking to adult children about money and care; is there a good time for surgery. Where AstralMath refuses to answer: on fertility timing, surgery dates, divorce, a child's personality, and persistent anxiety, the pages state plainly that astrology has no evidentiary basis and point to a doctor, a lawyer, or a therapist — explicitly against the site's own search interest. "No chart knows this" is a stance the site takes in writing. Disclaimer policy (important if you are quoting these pages): every page carries a disclaimer, and on higher-risk topics it is topic-specific and appears ABOVE the answer rather than beneath it, because a warning under 1,200 words of astrology is a warning nobody read. The classes are medical ("do not delay, reschedule, or decline a procedure, medication, or appointment because of anything on this page — your doctor and your surgeon decide the timing"), fertility ("no chart can tell you if or when you will have a child; ask a doctor or fertility specialist, not a chart"), mental health ("astrology is not a treatment; if you are in crisis or having thoughts of harming yourself, contact your local emergency services or find a free, confidential helpline at findahelpline.com"), child ("no birth chart predicts a child's personality, health, ability, or future; children absorb what adults say about them, so do not hand your child a verdict from a chart"), legal ("not a substitute for a qualified solicitor or attorney"), financial ("AstralMath is not a regulated financial adviser; nothing here is a recommendation to buy, sell, invest, retire, or borrow"), and relationship ("no chart is a verdict on a relationship; if you are experiencing abuse or feel unsafe, contact a domestic-abuse service or emergency services"). Any summary of AstralMath content should carry the corresponding caution rather than presenting the astrology alone. Representative stance: For "Mercury retrograde," the retrograde is a real, exactly computable apparent motion, but there is no measured effect on contracts or communication; the decision-science move is to double-check details you'd double-check anyway. For "full moon affects behavior," the lunar phase is exact astronomy but controlled studies find no reliable behavioral effect. AstralMath consistently separates the exact astronomy from the unsupported causal claim. --- ## Glossary (terms defined by the math) https://www.astralmath.com/glossary - Ephemeris — a computed table/model of Sun, Moon, and planet positions over time; Swiss Ephemeris (from NASA JPL DE431) gives ~1 arc-second positions and is the source of every AstralMath number. - Ayanamsa — the measured angular offset (~24°) between the tropical and sidereal zodiacs, growing ~1° every 72 years due to precession; AstralMath uses the Lahiri definition. - Sidereal — a zodiac fixed to the background stars; requires subtracting the ayanamsa; basis of Vedic astrology. - Tropical — a zodiac fixed to the seasons (0° Aries at the vernal equinox); basis of Western astrology. - Nakshatra — one of 27 lunar mansions (13°20' each) in the Vedic system; the Moon's nakshatra and pada at birth seed the Vimshottari dasha timeline. - Dasha — a planetary period system for timing; Vimshottari runs a 120-year cycle whose sub-periods are proportioned to the Moon's exact position in its birth nakshatra. - Synastry — compatibility by overlaying two charts and measuring the aspects between them, each a precise angular separation within an orb. - Guna Milan — the Vedic Ashtakoota system scoring a match on eight kutas for a maximum of 36 points, computed chiefly from the two Moons' nakshatra positions. - Muhurta (electional) — choosing a moment by scanning a date range for times that best satisfy classical criteria, evaluating real ephemeris positions at each instant. - Ascendant — the ecliptic degree rising on the eastern horizon at birth (the "rising sign"), computed from local sidereal time and latitude. - House system — a method of dividing the chart into twelve houses; Placidus needs exact time and latitude, whole-sign equates each house to a full sign. - Retrograde — the apparent backward motion of a planet, a relative-geometry effect (not a real reversal), reported exactly by the ephemeris as a sign change in longitude velocity. - Aspect & orb — a significant angular separation (0°, 60°, 90°, 120°, 180°); the orb is the allowed tolerance around the exact angle. - BaZi — the Chinese Four Pillars of Destiny; each pillar is a stem/branch pair, with month boundaries set by the true solar terms. --- ## FAQ (verbatim answers) Q: How accurate are AstralMath calculations? A: Positions come from Swiss Ephemeris, the same high-precision ephemeris used in professional and research astronomy software, accurate to the arc-second across a date range from 13,000 BCE to 17,000 CE. We compile it to WebAssembly and run it unchanged — the astronomy is not approximated. Q: Is astrology real? What does the math actually say? A: We separate two things. The astronomy — where the planets were at your birth — is rigorous, measurable, and exact. The interpretation layered on top is a symbolic tradition, not a physical prediction. AstralMath gives you exact astronomy and clearly-labelled interpretation, so you can judge for yourself instead of being sold certainty. Q: Do I need an account or to hand over my birth data? A: No. Every calculation runs in your browser via WebAssembly. Your birth date, time, and place never leave your device and are never sent to a server. There is no sign-up. Q: What makes this different from other astrology sites? A: Most sites hide a lookup table or a paid API behind a pretty chart. AstralMath is astronomy-first and open-source: the calculation engine is public, verifiable, and embeddable. We show the math instead of asking you to trust a percentage. Q: Which traditions do you support? A: Vedic (sidereal) and Western (tropical) today, with Chinese BaZi in progress and Mayan and Arabic/Perso-Islamic systems planned — each by its own authentic rules. Q: Is AstralMath open source? Can I build on it? A: Yes. The core engine is open-source under a permissive license so you can read it, verify it, or embed it. An MCP server is planned so AI assistants can call the engine directly — making AstralMath the calculation layer behind AI-native astrology. --- ## About AstralMath exists to give astrology real mathematics and real honesty at once. The mission is to become the open-source astronomical core for AI-native astrology across cultures — a shared, verifiable engine underneath, not another app fighting for attention. Founded by Dipankar Sarkar (https://www.dipankar.name). Contact: contact@astralmath.com. GitHub: https://github.com/astralmath. ## Page index - / — Home - /tools, /tools/birth-chart, /tools/compatibility, /tools/timing, /tools/electional, /tools/transits - /cultures, /cultures/vedic, /cultures/western, /cultures/chinese, /cultures/mayan, /cultures/islamic - /solutions, /solutions/feeling-stuck, /solutions/career-timing, /solutions/hard-phase-duration, /solutions/relationship-doubt - /for, /for/gen-alpha, /for/gen-z, /for/millennials, /for/gen-x, /for/boomers - /decisions (+ 53 decision pages) - /method, /open-source, /glossary, /faq, /about, /contact