Each cusp has its own semiarc
A semidiurnal arc measures rotation from rising to upper culmination. Its length depends on the point’s declination and the observer’s latitude. Sky Degrees solves for the eleventh and twelfth cusps using one-third and two-thirds of each candidate point’s semiarc, with corresponding conditions below the horizon.
This differs from Alcabitius, which divides the Ascendant’s semiarc. Identical birth details can therefore produce different intermediate cusps while retaining the same astronomical Ascendant and Midheaven.
Compare positions before interpretations
Keep the birth instant, coordinates and zodiac fixed when switching systems. A planet can move from one numbered house to another because a boundary moved. Its zodiac longitude does not change merely because you selected Placidus.
Why a polar request can fail
Sky Degrees rejects Placidus at or beyond latitude 90° minus the calculation’s obliquity, north or south. With an obliquity of 23.4393°, that limit is 66.5607°. Some relevant points no longer rise and set normally. A failed construction is reported without substituting another house system.
A CONCRETE EXAMPLE
Worked geometry: unequal intervals near the Midheaven
A reproducible geometry check uses ARMC 100°, latitude 40° N and obliquity 23.4393°. ARMC is the meridian’s right ascension, not geographic longitude. The implementation returns MC 99.189513°, eleventh cusp 132.507284° and twelfth cusp 162.501965°.
The first interval is 33.317771°; the next is 29.994681°. These unequal ecliptic intervals are compatible with the time-based construction. The second cusp is 214.762346°: an illustrative planet at longitude 215° falls in house two, whereas the same longitude is still in house one with Koch in this check.
Read it in your own chart.
Keep the date, recorded time, location and zodiac visible as you compare results. Guest calculations need no account.
Create your free chartCommon questions
Is the Placidus tenth cusp the MC?
Yes, in this supported construction the tenth cusp is the true Midheaven. The fourth cusp is its opposite, the IC. Sky Degrees still records the axes independently.
Does Placidus make planetary positions more accurate?
It changes house boundaries, not the astronomical calculation of planetary longitude. Choosing a house system does not establish the accuracy of an astrological interpretation.
Calculation & interpretation
New personal calculations use Skyfield with JPL DE440 data and the site’s documented house and zodiac rules. The preserved Greenwich teaching chart has its own historical source label. Worked arithmetic and geometry examples are labelled separately. Astrological meanings are symbolic conventions, not established scientific predictions.
Birth time and place affect angles and houses. Unsupported or ambiguous inputs return an error rather than an invented chart. Personal results stay in browser state and do not create public result URLs.
Read the calculation settings guide