Introduction to Natal Chart Calculation
– Written by Philip Graves – 14 Jan 2004
– Reformatted for WordPress, June 8th, 2016
To calculate a natal figure manually you need to know the date, time zone and location of birth. Follow this procedure:
Calculating the Local Sidereal Time
1. Express the time of birth using the 24-hour clock. Look up the co-ordinates and (if you are not sure of it) also the time zone of the place of birth in the atlas database at astro.com. Then correct the time of the subject’s birth to Greenwich Mean Time, as follows:
If the time zone is:
|International Date Line||Add 12 hours|
|Bering (Samoa)||Add 11 hours|
|Hawaiian||Add 10½ hours|
|Alaska-Hawaii||Add 10 hours|
|Yukon||Add 9 hours|
|Pacific||Add 8 hours|
|Mountain||Add 7 hours|
|Central||Add 6 hours|
|Eastern||Add 5 hours|
|Atlantic||Add 4 hours|
|Newfoundland||Add 3½ hours|
|Brazil Zone 2||Add 3 hours|
|Azores||Add 2 hours|
|West Africa||Add 1 hour|
|Central European||Deduct 1 hour|
|Eastern European||Deduct 2 hours|
|Baghdad||Deduct 3 hours|
|Indian time||Deduct 5½ hours|
|North Sumatra (Burma)||Deduct 6½ hours|
|South Sumatra||Deduct 7 hours|
|Java||Deduct 7½ hours|
|China Coast||Deduct 8 hours|
|Japan||Deduct 9 hours|
|South Australia||Deduct 9½ hours|
|Guam||Deduct 10 hours|
|New Zealand||Deduct 12 hours|
If daylight savings or summer time was in operation at the time of year concerned, deduct one hour.
You now have established the GMT-corrected time of birth. In some cases the time zone correction will also have changed the date; adopt any changed date and the changed time from now on.
2. Open a suitable printed or online ephemeris book. Turn to the year, month and date concerned. Look at the column marked ‘SID. TIME’, which shows the sidereal time (by the 24-hour clock) at Greenwich at midnight the start of that day. Add ten seconds to it for every hour of the GMT-corrected time after midnight that the subject was born. Then add the time of birth itself.
3. If the subject was born to the west of Greenwich, shown by the ‘W’ next to a co-ordinate, then for every whole degree west, deduct four minutes, but for every three whole degrees west, add two seconds; for every minute of a degree west, deduct four seconds. If the subject was born to the east of Greenwich, shown by the ‘E’ next to a co-ordinate, then for every whole degree east add four minutes, but for every three whole degrees east, deduct two seconds; for every minute of a degree east, add four seconds.
4. If the resultant local sidereal time at birth exceeds 24 hours, deduct 24 hours; if it is below 0 hours, add 24 hours.
5. Convert the seconds of this time to the nearest whole decimal point of a minute, as follows:
00-05 seconds = .0
06-11 seconds = .1
12-17 seconds = .2
18-23 seconds = .3
24-29 seconds = .4
20-35 seconds = .5
36-41 seconds = .6
42-47 seconds = .7
48-53 seconds = .8
54-59 seconds = .9
Calculating the House Cusps
1. Turn to the table of houses you have access to and wish to use; and select, in turn, the two latitudes closest to the latitude of your birth: we shall call the nearest one to the north n, and the nearest one to the south s.
2. For the first latitude, n, scroll down to the two listed sidereal times that are closest to the local sidereal time of birth that you calculated above, and note them down, calling the nearest before a and the nearest after b. Divide by four (or by whatever value represents the difference in minutes between a and b) the difference in minutes between a and the local sidereal time at birth. This should be easy since you have already converted the seconds of the local sidereal time into decimal points of minutes. Call the result, which will be a number between 0 and 1, f, as it is the fraction of the difference in sidereal time between a and b that corresponds to the local sidereal time at birth.
3. Note from the table the positions by sign, degree and minute of the MC, 11th house cusp, 12th house cusp, Ascendant, 2nd house cusp and third house cusp for both a and b.
4. Then for each of these six cusps in turn, deduct its position at sidereal time a from its position at sidereal time b, to give you the difference in minutes d; then multiply d by f and add the resultant number of minutes to the position of the cusp at a. Having done this for all six cusps, you have the exact position of the six house cusps concerned at your time and date and longitude of birth had you been born at latitude n.
5. Repeat steps 2. to 4. for the second latitude, s.
6. For each in turn of the six house cusps whose positions by sign, degree and minute you have now calculated for your exact local sidereal time at both latitudes, deduct its position at s from its position at n to give you the cusp position difference c in minutes of a degree for that particular cusp. In some cases the result will be a negative (minus) figure; this is correct, so don’t attempt to change its value to positive. Please note that there will be no difference in the position of the MC (10th house cusp) as this is constant for a given local sidereal time regardless of latitude.
7. Deduct the whole degrees of latitude s from those of latitude n to give you the difference in degrees between the two, and multiply this by sixty to give the difference in minutes, which we shall call m.
8. Divide by m the difference in minutes between s and the latitude of the place of birth; we shall call the resulting fraction, which will be a number between 0 and 1, l, since it represents the proportion of the difference in latitudes between s and n that corresponds with the latitude of the birth place.
9. For each cusp in turn, multiply its c by l and add the resultant number of minutes of a degree to the position of the cusp at s, to give the exact position of the cusp in signs, degrees and minutes for the time and place of birth. Where its c was a negative value, the position for the cusp at the exact birthplace will be before the position at s. Where its c was a positive value, the position of the cusp at the exact birthplace will be after the position at s.
10. To find the remaining six house cusps, add 180º to each of the six you have found, to find the one opposite it. This is a simple matter of changing the sign to the opposite sign. Thus, the IC (4th house cusp) can be taken from the MC (10th house cusp); the 5th house cusp can be taken from the 11th house cusp; the 6th house cusp can be taken from the 12th house cusp; the Descendant (7th house cusp) can be taken from the Ascendant (1st house cusp); the 8th house cusp can be taken from the 2nd house cusp; and the 9th house cusp can be taken from the third house cusp.
Calculating the Planetary Placements
1. Turn in the ephemeris you are using to the year, month and date of the GMT-corrected time of birth. Look at the figures for the positions of the Sun, Moon, planets and North Node at the start of the day (the row bearing the day’s date) and those for the end of the day (the row immediately beneath, bearing the following day’s date).
2. For each factor concerned (eg Sun), in order to make working (and eventual aspect and transit calculation) easier, convert the minutes of degrees (the two figures to the right of the central two-letter sign abbreviation) at both the start and the end of the day to the nearest whole decimal point of a degree, as follows:
00-05 minutes = .0
06-11 minutes = .1
12-17 minutes = .2
18-23 minutes = .3
24-29 minutes = .4
20-35 minutes = .5
36-41 minutes = .6
42-47 minutes = .7
48-53 minutes = .8
54-59 minutes = .9
3. Then subtract the position at the start of the day from that at the end of the day to work out the number of degrees (to the nearest decimal point) the factor will have moved by during the whole 24 hour day. [If the factor was in retrograde motion, this figure will be negative. Don’t worry if so: keep it as a minus number.]
In working out this difference, remember that there are thirty degrees in every sign, expressed to the nearest whole decimal place from 0.0º to 29.9º. If there was a change of sign from the start to the end of the day, add 30º to the degrees figure for the sign which is the later of the two in the normal direct-motion zodiac, regardless of the direction of the change between the signs (ie forward if in direct motion; backward if in retrograde motion) performed by the factor concerned during that day.
4. Next, calculate the amount of this total movement that will have occurred by the exact time of day you are looking up. To do this, express the time of day you are looking up as a fraction of 24 hours – for example, 8 p.m. = 20/24 (or, better still, as a fraction of the 1440 minutes in each day – for example, 6:37 a.m. = 397/1440); then multiply this time fraction by the total movement during the day which you already calculated in 4. above. Express the result to the nearest decimal point of a degree. If the factor was in retrograde motion, again, this figure will be negative, which is correct if so: do not attempt to invert its polarity to positive!
5. Finally, add this result to the position of the factor at the start of the day, as directly read from the ephemeris. This will give you the closest possible estimate as to the exact position of the factor at the time of day you are looking up. [If the figure you are adding is a negative value (a minus number) because the factor was in retrograde motion, then the sum which you are effectively performing is a subtraction of the negative sum’s positive equivalent! Adding a minus number is the same thing as subtracting a plus number.] Repeat this process with all the listed factors whose positions you wanted to know, from the Sun through to the Moon’s North Node, so that you know the sign and degree (to the nearest decimal point) positions for all of them.
6. Insert the Sun, Moon and planets in whichever house they fall into based on the positions of the house cusps you already calculated. A house starts at its cusp and continues until the next cusp after. If, however, one of them is located within the last three degrees of a house, then its influence will be as powerful in the next house as in the house it is in; while if it is within the last two degrees, it will be more powerful in the next house, but some residual influence of the house it is in will persist.
Calculating the aspects
1. Convert the sign and degree placements for each of the chart factors in turn into absolute degrees of the zodiac. Take the number of degrees (and tenths) as your starting point, then make the following additions according to the sign: for Aries, 0º; for Taurus, 30º; for Gemini, 60º; for Cancer, 90º; for Leo, 120º; for Virgo, 150º; for Libra, 180º; for Scorpio, 210º; for Sagittarius, 240º; for Capricorn, 270º; for Aquarius, 300º; for Pisces, 330º. Thus, for example, 19.7º Scorpio becomes 229.7º.
2. Draw up an x-y grid with columns on the x-axis and rows on the y-axis labelled with the Sun, the Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, the Ascendant, the Midheaven and any other factors you want to include, and write their absolute degree positions (still to the nearest decimal point) alongside in each case.
3. Then, take a calculator, and for each box in your new-made aspect grid (except duplicates) subtract the lower number of degrees of the two factors under consideration from the higher one. If the number that results is greater than 180º, scrap the result, add 360º to the lower figure, and try again treating it as the higher figure and subtracting the original higher figure from it. You will then get the nearest distance in degrees between the two factors in every case, accurate to approximately one tenth of a degree. Write the resulting number into the appropriate box; then move on to the next box on your grid. For example, if you have the Sun at 229.7º and the Moon at 314.3º, deduct the Sun figure from the Moon one, to give you 84.6º – and write this angle of separation into the box where the Sun on one axis of your grid meets the Moon on the other.
4. When you have finished filling in the grid with all the angles between your natal chart factors, look up each in turn against the table of aspect types on the Aspects 2 page, and see if it falls into the range of any of them or not. If it does, that is the type of aspect present between those two factors. In our example, 84.6º falls into the range of the square, so you can note down on your piece of paper that the aspect Sun square Moon is in the natal chart. Make a note of the orb of proximity that you are having to allow.
5. Continue until you have worked out all the aspects in the chart and their orbs of proximity.
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