Derivative Houses Calculator — Count the Houses From Any Point

What a derivative house is

Your natal houses count from the Ascendant. A derivative, or rotated, house frame instead counts from another point, making that point the new first house. The sixth house from your Moon, for instance, is its daily-work house, and the fourth from your Moon is its home.

This is how astrologers answer questions about the houses of a house, or the chart of another person. To read your mother, you might turn the wheel to the Lord of the fourth and use her houses. To study your work life as the Moon sees it, you count from the Moon.

The rotation is rigid. Every cusp swings by the same amount so the chosen base degree lands exactly on the new first cusp, and the twelve houses keep their widths. Nothing is recast; the same sky is simply renumbered.

How the rotated frame is built

We take the longitude of the base point you select and compute how far it sits from the natal first cusp. That difference becomes a uniform shift applied to all twelve cusps, carrying the base degree onto the new Ascendant of the derived frame.

With the cusps rotated, every body is re-housed by testing its longitude against the new boundaries. The base point itself always lands on the first cusp, by construction, which is the check our automated test confirms.

Because this operates on the cusps you already have, it is exact and reversible. Set the base to the Ascendant and the derived frame collapses back onto your natal houses, a built-in identity check.

What you get back

Choose a base point and the tool returns, for every body:

• Its ordinary natal house.
• Its house counted from the base point.
• The base degree carried onto the new first cusp.
• A table comparing both house numbers at a glance.
• Fifteen base options from planets to angles and the Part of Fortune.

Reading a rotated chart

Pick the base that matches your question. To understand your emotional life and daily rhythm, count from the Moon. To study another person, turn the wheel to the ruling planet of the house that signifies them, and read their houses from it.

Then look at where the bodies pile up in the derived frame. A cluster in the fifth house from the Moon colours your moods with play and creativity; the same bodies in the twelfth from the Moon would colour them with withdrawal and privacy.

Read the derived lord too. The sign on the first cusp of the rotated frame, and its ruler, describe the overall tone of living life from that base point.

Use derivatives lightly and honestly. They are a lens, not a separate chart, and they are most useful when you keep one clear question in mind rather than renumbering everything at once.

A worked example: counting from the Moon

Take the chart our verification script measures for 1 January 2000 at 17:30 UT in London. The Moon sits at 226.1 degrees, in the fifth natal house. Rotate the wheel to make the Moon the first house.

In the derived frame the Sun and Mercury, both in the sixth natal house, move into the third from the Moon. The Sun shares that third house with Mercury, so the light of the chart and its messenger both colour the Moon's communication and immediate world.

Mars, in the eighth house natally, falls into the fourth from the Moon, and Jupiter and Saturn, both in the tenth, move together into the sixth from the Moon. Venus stays with the Moon in the derived first, and Pluto lands in the second from the Moon.

Each re-numbering follows from the single rotation that parks the Moon on the new cusp, and the whole row set is reproduced by an automated check. Change the base to the Sun, the Ascendant, or the Part of Fortune and watch the same bodies re-home.

What this tool does not claim

A derivative frame is a renumbering of one chart, not an independent chart. It shares the same planets and aspects, so treat its houses as a perspective on the natal wheel rather than a new set of facts.

Counting from a point is an interpretive convention with traditional roots, especially for the Moon and for signifying other people. Its usefulness is a matter of craft and consensus, not of measurement.

The cusps are rotated rather than recast, so this keeps the natal house widths. Some practitioners prefer to recast a relocation-style frame when studying another person; that is a different technique than the derived houses shown here.

Derivative houses beside twelfth-parts and relocation

The derivative frame and the twelfth-part share one core. The twelfth-part asks which sign a point occupies when the wheel is turned to a base; the derivative frame asks which house every body occupies under the same turning.

Relocation is different. It recasts fresh angles for a new place on Earth, while a derivative frame keeps your chart and simply renumbers its houses from a chosen point. Use relocation for a place, and derivatives for a perspective.

For the ordinary house assignments behind all of this, cast the full natal chart and read the houses before you start rotating them.

Our method in one line

Cusps from sub-arcsecond astronomy (VSOP87/ELP via astronomy-engine) in Porphyry quadrant houses (whole-sign available on every chart) houses are rotated by a uniform shift that carries the chosen base degree onto the first cusp, then every body is re-housed. The worked-example rows are reproduced by an automated check. Reviewed by Dr. Amara Osei, Astronomy Reviewer.