Ascendant (Rising Sign) Calculator
Calculate your Ascendant (Rising Sign) — the zodiac sign rising on the eastern horizon at the exact moment of your birth. An accurate birth time and location are essential.
Formula
1. Julian Day Number (JD)
JD = ⌊365.25(Y+4716)⌋ + ⌊30.6001(M+1)⌋ + D + B − 1524.5
where B = 2 − ⌊Y/100⌋ + ⌊⌊Y/100⌋/4⌋ (Gregorian correction), and D includes the fractional UT hour.
2. Greenwich Mean Sidereal Time (GMST)
T = (JD − 2451545.0) / 36525
GMST = 280.46061837 + 360.98564736629 × (JD − 2451545) + 0.000387933T² − T³/38710000 (degrees)
3. Local Sidereal Time (LST)
LST = GMST + Geographic Longitude (degrees)
4. Obliquity of the Ecliptic (ε)
ε = 23.439291111° − 0.013004167°·T − 0.0000001639°·T² + 0.0000005036°·T³
5. Ascendant Ecliptic Longitude
ASC = arctan(−cos(LST) / (sin(ε)·tan(φ) + cos(ε)·sin(LST)))
where φ = geographic latitude. Quadrant correction applied based on LST quadrant.
6. Zodiac Sign
Sign = ⌊ASC / 30⌋ → index into the 12 zodiac signs (Aries = 0°, Taurus = 30°, … Pisces = 330°)
Assumptions & References
- Uses the Placidus / standard ecliptic Ascendant formula based on the intersection of the ecliptic with the eastern horizon.
- GMST formula follows the IAU 1982 / Meeus "Astronomical Algorithms" (2nd ed.) standard.
- Obliquity formula is the standard IAU expression truncated to 4th-order in T.
- Birth time must be the local clock time; the UTC offset must account for Daylight Saving Time if applicable.
- Calculation is unreliable at latitudes above ±66.5° (Arctic/Antarctic circles) because the ecliptic may not intersect the horizon in the usual way.
- No atmospheric refraction or topocentric corrections are applied.
- Longitude: East is positive, West is negative. Latitude: North is positive, South is negative.
- Reference: Jean Meeus, Astronomical Algorithms, Willmann-Bell, 1998, Chapters 12–13.