The division happens directly on the ecliptic
Unlike Alcabitius or Regiomontanus, Porphyry does not first divide an equatorial arc and project it onto the zodiac. It uses the zodiac longitudes of the angles themselves. Measure the appropriate forward arc, divide by three, and add those thirds to obtain the intermediate cusps.
For the upper quadrant in this implementation, the forward arc runs from the MC to the Ascendant. The complementary arc between Ascendant and IC completes the 180° half-circle. Opposite cusps are separated by 180°.
Equal thirds do not mean equal houses everywhere
If one angular quadrant spans 88.8°, each of its houses spans 29.6°. Its complementary quadrant spans 91.2°, producing 30.4° houses. Only a special arrangement with four 90° quadrants produces twelve equal 30° houses.
Check the angles before using the result
Sky Degrees requires the MC-to-Ascendant arc to be strictly between 0° and 180°. Degenerate or unsupported arrangements return an error. Porphyry is not an automatic fallback when another system fails, and high-latitude use is not guaranteed for every input.
A CONCRETE EXAMPLE
Worked trisection from two calculated angles
A geometry check at ARMC 100°, latitude 40° N and obliquity 23.4393° gives MC 99.189513° and Ascendant 187.988849°. Their forward separation is 88.799336°; dividing by three gives about 29.599779°.
Adding one and two thirds to the MC gives cusp eleven at 128.789292° and cusp twelve at 158.389071°. The complementary quadrant is 91.200664°, so its houses span about 30.400221°. The second cusp is consequently 218.389071°. All values are rounded after the calculation; they describe a geometry example, not a person’s life.
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 Porphyry the same as equal houses?
No. Equal houses add 30° repeatedly from the Ascendant. Porphyry separately trisects the arcs between the angles, which generally gives two alternating sets of house widths.
Can I estimate Porphyry cusps from a chart image?
Use numerical zodiac longitudes. A drawing can distort angular spacing, and rounded labels lose precision. The calculator’s cusp values provide a clearer comparison than measuring pixels.
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.
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