Natal Chart House System Calculator
Calculate the 12 astrological house cusps using various house systems based on your birth date, time, and geographic location.
Formulas Used
Julian Date: JD = JDN − 0.5 + UTC_hour/24, where JDN uses the proleptic Gregorian calendar formula.
Julian Centuries: T = (JD − 2451545.0) / 36525
GMST (°): 280.46061837 + 360.98564736629 × (JD − 2451545) + 0.000387933T² − T³/38710000
LST (°): GMST + Geographic Longitude
Obliquity ε (°): 23.439291111 − 0.013004167T − 0.0000001639T² + 0.0000000503611T³
Ascendant: Asc = atan2(−cos(LST), sin(LST)·cos(ε) + tan(φ)·sin(ε))
Midheaven (MC): MC = atan2(tan(LST), cos(ε))
Placidus: Intermediate cusps found iteratively by trisecting the diurnal/nocturnal semi-arc: SA = arccos(−tan(φ)·tan(δ)). Cusps H11/H12 at 1/3 and 2/3 of upper semi-arc; H2/H3 at 1/3 and 2/3 of lower semi-arc.
Koch: Trisects the semi-arc of the MC degree using oblique ascension: OA_cusp = OA_MC ± (n/3)·SA_MC, then converts back to ecliptic longitude.
Equal House: Each cusp = Asc + n × 30°.
Whole Sign: Each house = one complete zodiac sign (30°), starting from the sign containing the Ascendant.
Campanus: Trisects the prime vertical. Great circle through N/S horizon poles and prime vertical point at angle θ intersects the ecliptic.
Regiomontanus: tan(λ) = sin(ΔRA) / (cos(ΔRA)·sin(ε) − tan(φ)·cos(ε)), where ΔRA = angle along equator from RAMC.
Assumptions & References
- Birth time is entered as local clock time; UTC offset must be provided manually (including DST if applicable).
- GMST formula: IAU 1982 / Astronomical Almanac (accurate to ~0.1″ over ±1 century from J2000).
- Obliquity formula: IAU 1980 (Lieske et al.), valid for dates within a few centuries of J2000.
- Placidus and Koch systems are mathematically undefined at latitudes above ~66.5° (Arctic/Antarctic circles) due to circumpolar conditions.
- Placidus iteration converges within 50 steps to better than 0.0001° for non-circumpolar latitudes.
- Opposite house cusps (H4/H10, H1/H7, etc.) are always exactly 180° apart.
- All ecliptic longitudes are tropical (referenced to the vernal equinox of date).
- References: Holden, R.W. (1977) The Elements of House Division; Campion, N. (1994) The Practical Astrologer; Meeus, J. (1998) Astronomical Algorithms, 2nd ed.