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Moon Sign Formula: Calculate Your Astrological Moon Sign by Hand

Updated on December 21, 2016
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TR Smith is a teacher and creator who uses mathematics in her line of work every day.

When people talk about their zodiac sign, e.g., "I'm an Aquarius," what they're usually referring to is their astrological sun sign. Your sun sign is the constellation the sun was passing through (from the vantage point of Earth) on the day you were born. But astrologers also calculate where other heavenly bodies are in relation to the 12 zodiac constellations. This means everyone has, among other things, a moon sign.

Whether or not you believe in astrology and the prediction of personal traits based on planetary position at time of birth, you may still find some fun in calculating your moon sign. The equation for finding your moon sign is more complicated than that of finding your sun sign since the moon revolves around the Earth as the Earth spins on its axis while revolving around the sun. Not only is its period much shorter, but the speed of its movement through the zodiac is not constant.

Nevertheless, if you know your birth date and time of birth, you can estimate your moon sign in several simple steps.

Sun Signs

Modern horoscopes are based on sun signs, given by these birthday ranges.

  • Aries: Mar 21 - Apr 20
  • Taurus: Apr 21 - May 21
  • Gemini: May 22 - Jun 21
  • Cancer: Jun 22 - Jul 22
  • Leo: Jul 23 - Aug 23
  • Virgo: Aug 24 - Sep 22
  • Libra: Sep 23 - Oct 23
  • Scorpio: Oct 24 - Nov 22
  • Sagittarius: Nov 23 - Dec 21
  • Capricorn: Dec 22 - Jan 20
  • Aquarius: Jan 21 - Feb 18
  • Pisces: Feb 19 - Mar 19

Basic Idea Behind the Moon Sign Formula

The basic astronomical principle behind calculating your moon sign is that the moon makes one full cycle through the zodiac belt once every 27.322 days on average. However, the moon does not move at a constant rate through all 360 degrees of the zodiac belt. Some days it moves as much as 15.3° and other days it moves as little as 11.8° from the vantage point of Earth.

In Astrology, the moon is the quickest of the heavenly bodies. In comparison, the sun completes the cycle once a year and Jupiter cycles through the zodiac every 12 years.

In the long run, all the planets and sun, and moon spend will spend an equal amount of time in each of the twelve zodiac signs -- Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces -- thus the amount of time they spend in a particular zodiac sign is 1/12 of the cycle length. The moon spends between 1.96 and 2.54 days in a sign, 2.27 days on average. This means it changes signs in the middle of day roughly every other day, so it's important to know the exact time of your birth, not just the date.

To calculate a person's moon sign, astrologers use an ephemeris, a table of the planetary positions for dates in the past and future. Ephemerides are calculated with complicated formulas from astronomy and celestial mechanics formulas, which we will not delve into here. Instead, we will use a simplified formula that still gives a pretty accurate moon sign.

Step 1

Convert your date and time of birth to the Greenwich Mean Time (GMT), also known as Coordinated Universal Time (UTC). To do this, you need to know your time zone in relation to GMT standard time and account for daylight savings time if it was in effect at your local time of birth.

For example, consider a person who was born July 6, 1980 at 3:00 PM local time in Washington DC. Since daylight savings time was in effect for this location, the real local time was 2:00 PM. Next we need to account for the fact that Washington DC is in a time zone 5 hours behind GMT, so the GMT time of birth was 7:00 PM July 6, 1980. Note that if a person was born around Midnight, the calendar day of birth can change when converting to GMT.

Step 2

Calculate the number of days between your date of birth (GMT) and January 23, 1921. This date has no particular significance other than the motion of the moon through the zodiac was at a high point at this time.

To count the number of days between two dates, you can use an online calculator, Excel spread sheet program, or an equation you can work out with a hand calculator. Some resources are linked on the left. For a person born July 6, 1980, the number of days between this birth date and January 23, 1921 is 21714 days.

Step 3

Convert your time of birth to the equivalent fraction of a day, and then add this number to the number of days you calculated in Step 2. Using the same example, a person born at 7:00 PM adds 19/24 = 0.71967, so the total number of days is 21714.71967. Call this number D. Keep at least 5 decimal places for better accuracy.

Step 4

Take the number you obtained in Step 3 and plug it into the expression

13.1762D + 12.0947cos(0.11403D)sin(0.11403(D+1)) - 6.627

where the cosine and sine functions are computed in radians. This equation is a simplified moon position formula adapted from ephemeris entries between 1921 and 1990. Plugging D = 21714.71967 into the formula above gives us 286117.23562.

Step 5

Take the number you obtained in Step 4 and divide by 360, but keep only the decimal part. Continuing with the example, we have 286117.23562 ÷ 360 = 794.77010. The decimal part is 0.7701.

Step 6

Multiply the decimal part you calculated above by 360. You will end up with a number between 0 and 359.999. Use the table below to convert that number to your moon sign. For example, 0.7701*360 ≈ 277.2, so our example person's moon sign is just barely in Taurus.

You can confirm with an astrological ephemeris that the moon sign of a person born on this date is actually on the cusp between Aries and Taurus. When the moon falls on the transition from one sign to another, the person is said to exhibit traits of both signs.

Value Obtained in Step 5
Your Moon Sign
0 - 29.999
30 - 59.999
60 - 89.999
90 - 119.999
120 - 149.999
150 - 179.999
180 - 209.999
210 - 239.999
240 - 269.999
270 - 299.999
300 - 329.999
330 - 359.999

Because the lunar cycle has a short period, and because the moon can pass from one zodiac sign to another in the middle of the day, your moon sign given by this approximation formula may differ by one sign. To get the most accurate moon positions, you should consult an ephemeris. For example, this approximation formula might say you are a Libra, while an ephemeris chart says you're a Virgo. This is more likely to happen when you are born at a time when the moon is near transition.

What If I Don't Know My Time of Birth?

Not everyone knows their time of birth, but that shouldn't stop you from getting something out of the formula. If your not sure about the time of day, or even the time zone, test the formula using your birthday at 12:00 AM GMT, and the following day at 12:00 AM at GMT. This will give you at most two zodiac signs, so you can narrow the range.

Interpreting Your Moon Sign

Now for the fun part! Whether or not you believe astrology can explain your fate, or consider it pseudoscience, it is nevertheless fun to see what your moon sign says about you. Here are the classic moon sign traits according to several astrology guides

Moon in Aries: You are a quick thinker but also have a quick temper. You are good in a crisis when it comes to taking fast action, but you have trouble remaining calm. You are impulsive and sometimes resort to insults, but at the same time you are an encouraging and supportive friend who believes in others abilities.

Moon in Taurus: You have a strong need for financial stability and do whatever it takes to secure your family's finance. This can manifest as being an honest workaholic on one extreme, to cheating on the other. You can be possessive, but are always faithful. You like to make people comfortable and comfort them.

Moon in Gemini: You are verbally expressive and tend to talk fast. You tend to embrace confrontation and are impatient with people who are not as smart as you. You get stressed out more easily than other signs, but you do not cave under the stress as badly as other signs. You are a skeptic and not particularly religious.

Moon in Cancer: You are emotional, but intuitive and sensitive to the needs of others. You are hard to fool. You have trouble letting go of the past and are less likely to move away from your hometown than other signs. People may describe you as moody and unpredictable, but really you just have a lot going on in your head.

Moon in Leo: You are good at acting confident even when you are not, and you like to encourage others and boost their confidence. You often feel alone and misunderstood. You have a penchant for the fine arts and dramatic arts. You worry about being liked and how many friends you have.

Moon in Virgo: You have a talent for the spoken and written word, and are good at making casual friends. You have a tendency to gossip and start fights with people close to you. Though you excel in school, you do not particularly like school. You prefer to experience life and learn first-hand.

Moon in Libra: You are diplomatic, but decisive. You have a flair for handling aggressive people and diffusing tension in situations. You tend to rationalize other people's bad actions and are prone to cognitive dissonance. People admire you for your steady character, but you may find yourself criticized for being superficial.

Moon in Scorpio: You have a lot of physical and mental energy, but tend to become jealous quickly over minor incidents. Yet you are good at putting on a smile and acting laid back. Your bottled emotions can spill out, confusing loved ones. You are easily provoked, but you are the first to stick up for the little guy.

Moon in Sagittarius: You maintain a positive outlook on life and bounce back quickly from hardship. People have difficulty relating to you. You are often conflicted by your needs for stability and adventure, and you get extremely impatient when situations do not make sufficient progress toward a resolution. You like intellectual challenges.

Moon in Capricorn: You react calmly in stressful situations. Some might say you are stone cold. You are ambitious and work hard to meet your goals, but you look down on people who fail to achieve their goals, or who don't set lofty goals for themselves. You prefer to be friends with the wealthy. You are generous with your money.

Moon in Aquarius: You tend to be a pushover and will accept any compromise in order to end a dispute. Because you are gentle, your friends and family behave gently toward you. Strangers may see you as an easy mark. You are intellectually curious, quick-witted, and inventive. You love learning and helping others learn.

Moon in Pisces: You are easily moved and have a penchant for literary writing and music. You give in to your vices too easily and have trouble resisting your impulses. You are creative, but not generous with your time. You are a loyal friend who keeps her judgments to herself. You prefer to let people discover their mistakes on their own.


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    • deecoleworld profile image

      deecoleworld 2 years ago from USA

      Why do you have convert your date and time of birth to Greenwich Mean Time (GMT)/Coordinated Universal Time (UTC)? Is there a reason for this?

      I am curious, what is your moon sign?

    • calculus-geometry profile image

      TR Smith 2 years ago from Germany

      Astrological and astronomical ephemerides are standardized to give the positions of heavenly bodies everyday at 12:00 AM UTC. Since I based my approximation formula off a standard astrological ephemeris, it's more accurate if you use your birth day and time converted to UTC. But since it's only an approximation, it won't hurt if you just use local time. You'll only be off by one sign at most. If you use a real ephemeris though, you'll need the UTC time.

      My moon sign is Sagittarius. Maybe I should put a poll on this hub. Thanks for your comment!

    • bottlerocketeer profile image

      bottlerocketeer 2 years ago from East Texas, USA

      Out of curiosity, would you consider one's astrological sign to be reflective of that person? Or do you consider it 'just for fun?' I only ask because you seem to be pretty well-informed on the subject, and I don't know if it is because you enjoy the calculation aspect of it (being a 'math person' like myself) or because you have personally invested the time to research it because you believe it can give insight into your life.

    • deecoleworld profile image

      deecoleworld 2 years ago from USA

      Ok I was just wondering, thank you for answering my question

    • calculus-geometry profile image

      TR Smith 2 years ago from Germany

      Mostly I was trying to see if I could find an approximation formula that was easy to work out, yet close to the ephemeris values most of the time. The "simplicity vs. accuracy" problem. I don't subscribe to astrology, but thought the formula might be useful for people who do.

    • Jay C OBrien profile image

      Jay C OBrien 2 years ago from Houston, TX USA

      Edgar Cayce is worth some research on astrology. See website: Edgar Cayce A.R.E. Cayce postulated a multiverse where Earth (our dimension) contains more free will that other dimensions.

      Here are some ideas about Cayce's Astrology.

      The word Astrology is a misnomer; it is actually Cayce’s Cosmology. Perhaps a better description would be: multi-dimensional life readings. The universe is actually a multi-verse through which the soul travels. The soul is an energy force, energy field or light body which passes through different dimensions for education and enlightenment. The light body is the sum total of all the sojourns through the various dimensions. The most recent dimensions travelled affect the light body the most. The dimensions were labeled with planetary names to distinguish one dimension from the other. The soul travels to different dimensions not to the material planets. Traditional aspects between planets in the birth chart give little or no clue to the most important planets (dimensions) which will exert the most influence as indicated by the readings.

      What do you think?

    • calculus-geometry profile image

      TR Smith 2 years ago from Germany

      I don't personally believe in any type of astrology or cosmology, but it sounds like a very interesting belief system. Thank you for reading!

    • pam170 profile image

      pam170 3 months ago

      Hello! I'm working on an astrology project and am trying to find a way in Python to calculate someone's moon sign so I don't have to scrape an astrology website. Through this search I came across this article. Thank you for sharing it! Is this a formula you created? If so, I'm curious how you created it! I don't know much about astrology or astronomy (this is a project I'm doing with a cousin, and she is the astrology person), and I've been trying to use a Python library called pyephem. But the constellations I've been getting haven't matched what I get from astrology websites. And I've been getting constellations that aren't in any astrology charts, e.g.:

      In [109]: ephem.constellation(ephem.Moon('1981/12/7'))

      Out[109]: ('Cet', 'Cetus')

      In [115]: ephem.constellation(ephem.Sun('1981/12/7'))

      Out[115]: ('Oph', 'Ophiuchus')

      Is this something you dealt with when you created your estimate? If so, any advice on how to deal with these discrepancies? Thank you!

    • calculus-geometry profile image

      TR Smith 3 months ago from Germany

      Hi Pam 170,

      I came up with the equation using regression to find the coefficients of a simple trig function that would best fit data in a hard copy ephemeris table I happened to have. I'm not an astronomer or astrologer and don't know the exact formulas. It just seemed like a fun thing to work out a simplified formula that a lay person could apply. The actual astronomical formulas are too complicated for practical use which is why they just make tables for people (like in the old days when people looked up logarithms and square roots in tables.)

      This might be of help too

    • pam170 profile image

      pam170 3 months ago

      Thank you for your reply! After a little reading on questions others had while using JPL's ephemeris data, I think using the ephemeris data is way beyond my ability. I can see why people use tables!

      If we get your permission, and if we use the equation under conditions you approve, would you be open to the idea of us using your equation to estimate moon signs? I was thinking of doing some tests to get an idea how good an estimation it would be: scraping an astrology website some number of times for randomly selected days, times, and locations, and comparing what the website says to what is returned by your equation. Or (if you haven't already said "No way! You can't use my equation."), do you already have something like a R-squared value that gives an idea of how well the line fits the data? Thank you!

    • calculus-geometry profile image

      TR Smith 3 months ago from Germany

      You can use the equation although I can't guarantee it will be as accurate as you need. It's usually off by several degrees but gets the right sign more than 90% of the time. If you prefer to get astrological signs from an ephemeris table, this is another good source

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