Navamsa (D9) and D10 Charts: How They Are Calculated

The navamsa (D9) and the dasamsa (D10) are divisional charts. A divisional chart cuts each zodiac sign into equal parts, and each part maps to a sign. Each planet then moves to the sign of the part that holds it. The D9 splits every 30° sign into 9 equal parts, each 3°20′ wide. Astrologers read it for marriage and for the inner strength of each planet. The D10 uses 10 parts of 3° per sign. It is read for career and status.

The one tricky step is where the count starts. Each sign has a type: movable, fixed or dual. Aries is movable, Taurus is fixed, Gemini is dual, and the pattern repeats. In the D9, the count for a movable sign begins at that same sign. For a fixed sign, it begins at the 9th sign from it. A dual sign begins at the 5th. In the D10, an odd sign begins at itself, and an even sign begins at the 9th sign from it. Odd signs are every other sign, starting with Aries. From the start sign, you count forward one sign per part.

Small parts make these charts sensitive to the birth time. Our sample chart is John Doe, born Aug 15, 1990, at 10:30 AM in New York. We stepped his birth time one second at a time. His D9 ascendant, the rising sign in that chart, changed from Gemini to Cancer at 10:30:20 AM. That is just 20 seconds after his recorded birth time.

What the D9 and D10 charts are for

Your main birth chart is the D1, also called the rasi chart. It puts each planet in one of 12 signs. A divisional chart zooms in on one area of life by cutting those signs into smaller parts. The API works out 16 of them, from D1 to D60 (VG-01).

Each chart response has a signifies field that says what the chart is for. For the D9, it lists two uses: the spouse, and how much real strength each planet has. For the D10, it says "profession and status." Neither chart uses new data. Both sort the D1 positions more finely, so a reading starts with the D1.

How the D9 (navamsa) is calculated

To place one planet in the D9, follow four steps:

1. Take the planet's sidereal sign and its degree inside that sign. Sidereal means measured against the fixed stars, the way Vedic astrology measures.

2. Find the part that holds that degree. Part 1 runs from 0° to 3°20′, part 2 from 3°20′ to 6°40′, and so on.

3. Find the start sign from the table below (VG-04).

4. Count forward from the start sign. Part 1 is the start sign, part 2 is the next sign, and so on.

You will also see the start given by element. Fire signs start from Aries, earth from Capricorn, air from Libra and water from Cancer. We ran all 12 signs through the core code. Both rules gave the same start sign every time.

Lay the 108 parts of the zodiac end to end. Their D9 signs run from Aries to Pisces nine times, with no break. We checked the middle of every part. So the D9 sign is just a count of 3°20′ steps from 0° Aries:

// longitude: the planet's sidereal longitude, from 0 to 360 degrees
function navamsaSign(longitude) {
  const step = Math.floor(longitude / (30 / 9)); // 0 to 107
  return (step % 12) + 1; // 1 is Aries, 12 is Pisces
}

The function needs one input that is hard to get right: an exact sidereal longitude. That means the right ayanamsa and the right time zone for the birth moment. The API does that work on every call.

Each D9 part is also exactly as wide as a nakshatra pada. A nakshatra is one of 27 star groups, and a pada is a quarter of one. So the 108 padas line up with the 108 D9 parts. For all 10 points in John's chart, the pada gave the same D9 sign as the API. The free nakshatra finder shows the Moon's pada for any birth.

How the D10 (dasamsa) is calculated

The D10 uses 10 parts of 3° each. Where the count starts turns on one question: is the sign odd or even (VG-02)? The odd signs are Aries, Gemini, Leo, Libra, Sagittarius and Aquarius, and each begins at itself. Each even sign begins at the 9th sign from itself. Then you count forward one sign per part, as in the D9.

Unlike the D9, the D10 is not one smooth cycle. The last part of each odd sign and the first part of the next sign get the same D10 sign. For example, the last 3° of Libra and the first 3° of Scorpio both map to Cancer. This join happens six times around the zodiac. On John's birth day in New York, one join made a single D10 ascendant window last 30 min 26 s.

Take care when you compare apps, because other D10 counts exist. One we found online starts every odd sign at Aries and every even sign at Capricorn. On John's chart, it gives a different D10 sign for 8 of 10 points, the ascendant included. Our rulebook marks these counts as school choices. Check which count an app uses before you test against it.

John Doe's chart, worked out

We sent our docs' sample chart to POST /v1/chart/D9 and POST /v1/chart/D10:

{
  "year": 1990, "month": 8, "day": 15,
  "hour": 10, "minute": 30,
  "latitude": 40.7128, "longitude": -74.006,
  "timezone": "America/New_York"
}

John Doe, born Aug 15, 1990, at 10:30 AM in New York.

The degrees come from POST /v1/planets, and we worked out the part numbers from them. The D9 and D10 signs are the API's own answers.

Take the ascendant. Virgo is a dual sign, so the D9 count starts at the 5th sign from it, Capricorn. Its 19°56′ falls in part 6, from 16°40′ to 20°00′. Count six signs: Capricorn, Aquarius, Pisces, Aries, Taurus, Gemini. The D9 ascendant is Gemini, the same as the API's answer.

For the D10, Virgo is even, so the count starts at the 9th sign from it, Taurus. Part 7 runs from 18° to 21°, and seven signs from Taurus is Scorpio. That matches too. All 10 points matched the API. None is vargottama, meaning its D1 and D9 signs match, which tradition reads as strength.

Accounts open on Nov 26, 2026. Join the launch list, and we will tell you when you can sign up and try these charts.

How far the birth time can move

John's ascendant sits under 4 arc minutes before part 6 ends at 20°00′. An arc minute is 1/60 of a degree. We stepped his birth time through the API, by minutes and then by seconds, until each chart changed:

What changes when the D9 ascendant flips? At 10:30:20 AM, no planet changed its D9 sign. But every planet moved one house, because D9 houses count from the D9 ascendant. Mars moved from the 7th house, the house of marriage, to the 6th.

The window length also changes through the day, because some signs rise faster than others. We timed every D9 ascendant window on John's birth day in New York. The shortest lasted 7 min 39 s, and the longest 17 min 1 s. The average was 13 min 18 s. John's window, 16 min 48 s, was longer than 81 of the day's 108.

The ayanamsa, the gap between the Western and Vedic zodiacs, can move it too. The API offers lahiri (the default), kp and raman. With kp, John's ascendant moves to 20°01′ of Virgo, so his D9 ascendant becomes Cancer. With raman, 5 of his 10 D9 signs change.

The divisional chart reference shows the full request and response for all 16 charts. The glossary has short definitions of the navamsa and the dasamsa.

What this means for your app

Ask for the birth time to the minute. Say why on the form: "A few minutes can change this chart." That gives people a reason to find a birth record.

When a time looks rounded, such as 10:30, mark the D9 and D10 ascendants and houses as uncertain. Planet signs are safer. John's Sun needs about 3.5 days to cross one D9 part.

To test the edges, call the chart at the given time and again 5 minutes either side. If the D9 ascendant changes, tell the user. And before you test against another app, match its ayanamsa and its D10 count.

Same rules, thin margins

Both charts rest on one idea: cut the sign into parts, then count from a start sign. The input is the hard part. In John's chart, 20 seconds moved the D9 ascendant. His Moon kept its D9 sign for more than 5 hours. Build your screens around that gap.