Birth Chart Calculator

How the Birth Chart Calculator works

A birth chart, or natal chart, is a map of the sky at the moment of birth as seen from the birthplace. Western astrology reads the Sun sign from the date alone, but the Moon changes sign every two to three days and the rising sign every two hours or so, so those need the time and place. Together the Sun, Moon and rising sign are often called the "big three".

How the birth chart calculator works

The time you enter is converted to Universal Time using the offset, then to a day count from the start of 2000. The positions of the Sun, Moon and planets come from their orbital elements, the same method astronomers use for quick ephemeris work, including the main corrections for the Moon's wobbles and the pull between Jupiter and Saturn. Each position is an ecliptic longitude from 0° to 360°, split into twelve 30° signs starting from 0° Aries.

For the rising sign, the calculator works out the local sidereal time at the birthplace, then finds the point of the zodiac crossing the eastern horizon. The Midheaven is the point due south at its highest. These are the two angles that need an accurate time and place.

The formula

Each position starts from the body's mean anomaly M, which grows steadily with the day count. The formula then solves Kepler's equation, E = M + e sin E, for an orbit of eccentricity e, and turns the result into an ecliptic longitude. The ascendant formula is ASC = atan2(cos RAMC, −(sin RAMC cos ε + tan φ sin ε)), where RAMC is the sidereal angle overhead, ε the 23.44° tilt of the Earth's axis and φ the birth latitude. The Midheaven is MC = atan2(sin RAMC, cos RAMC cos ε).

Worked examples

Example 1: London, 15 June 1990, 08:30, UTC+1. Sun 23° 57′ Gemini, Moon 12° 49′ Pisces, rising sign 7° 51′ Leo, Midheaven 17° 01′ Aries. Three planets sit in Capricorn, so the element balance leans to Earth: Fire 1, Earth 4, Air 2, Water 2.

Example 2: New York, 20 January 1985, 23:15, UTC−5. Sun 1° 04′ Aquarius, Moon 1° 57′ Aquarius, rising sign 16° 01′ Libra, Midheaven 18° 40′ Cancer. The Sun had entered Aquarius only about a day earlier; one day sooner and this chart would have a Capricorn Sun.

How many hours does each rising sign last? Roughly two on average, but at London's latitude signs such as Pisces and Aries rise in under an hour while Virgo and Libra take nearly three.

Accuracy you can expect

A birth time that is 15 minutes out moves the ascendant by about 4°, which can change the rising sign. The Moon moves about half a degree an hour, so the calculator flags a Moon within 1° of a sign boundary.

Getting the inputs right

UTC offset. Use the offset in force on the birth date, including daylight saving. UK summer is +1, US Eastern summer −4 and winter −5, India +5.5. Old records sometimes used local mean time, which differs slightly.

Latitude and longitude. Use decimal degrees: north and east are positive, south and west are negative. A city centre is close enough; a few kilometres barely moves the chart.

Coordinates and standard UTC offsets for common birthplaces (add 1 hour in summer time)

Sydney and Auckland add summer time from October to April. Most other cities outside Europe and North America do not use it today, but rules change, so check the birth year.

Tips and pitfalls

This uses the tropical zodiac. Western astrology ties 0° Aries to the March equinox. Vedic astrology uses the sidereal zodiac, which is about 24° behind today, so most signs shift back one.

Pluto is not included. Its orbit needs a separate long-series model, and it moves so slowly that everyone born within the same 12 to 30 years shares its sign.

Polar births are not supported. Above about 66° latitude some signs never rise, so the ascendant breaks down. The calculator limits latitude to ±66°.

How to read the result

The first lines give the big three, each with its degree in the sign. The planets follow, then the element balance. The table lists every point with its exact ecliptic longitude.

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