Birth Chart Calculator
Calculate your astrological birth chart including Sun sign, Moon sign, and Ascendant (Rising sign) based on your birth date, time, and location coordinates.
Formulas Used
Julian Day Number (JDN):
JD = ⌊365.25(Y+4716)⌋ + ⌊30.6001(M+1)⌋ + D + h/24 + B − 1524.5
where B = 2 − ⌊Y/100⌋ + ⌊⌊Y/100⌋/4⌋ (Gregorian correction)
Julian Centuries from J2000.0:
T = (JD − 2451545.0) / 36525
Sun Longitude:
L₀ = 280.46646° + 36000.76983°·T (mean longitude)
M = 357.52911° + 35999.05029°·T (mean anomaly)
C = (1.914602 − 0.004817T)sin M + 0.019993 sin 2M + 0.000289 sin 3M
λ☉ = L₀ + C
Moon Longitude:
L′ = 218.3165° + 481267.8813°·T (mean longitude)
Perturbation terms summed from Meeus Table 47a
λ☽ = L′ + Σ corrections
Ascendant:
θ₀ = 280.46061837° + 360.98564736629°·(JD − 2451545) (GMST)
LST = θ₀ + λ (local sidereal time)
ASC = atan2(−cos LST, sin LST·cos ε + tan φ·sin ε)
where ε = 23.439291° − 0.013004°·T (obliquity), φ = latitude
Zodiac Sign: sign index = ⌊λ / 30⌋ (0=Aries … 11=Pisces)
Assumptions & References
- Sun and Moon positions use low-precision truncated series accurate to ≈ 0.5–1° (sufficient for sign determination).
- Ascendant uses the standard spherical-trigonometry formula with GMST from IAU 1982.
- House cusps use the Equal House system (each house = 30° from ASC); Placidus requires iterative solving not shown here.
- No planetary positions (Mercury–Pluto) are computed; full ephemeris requires VSOP87 or JPL data.
- UTC offset must be entered manually; daylight saving time is not auto-detected.
- Longitude: East positive, West negative (standard geographic convention).
- Valid date range: approximately 1900–2100 CE.
- Reference: Jean Meeus, Astronomical Algorithms, 2nd ed. (1998), Chapters 22, 25, 47.
- GMST formula: IAU 1982 / Meeus Chapter 12.