Mental Molad Method

By Ari Meir Brodsky

Kislev 5767 – December 2006 (Updated Sivan 5770 –May 2010)

INTRODUCTION

Have you ever found yourself at a Shabbaton in some far away place, on the morning of Birkat HaChodesh, and realized that no one remembered to bring a calendar with the molad listing? Or have you ever simply wondered, when the Gabbai announces the molad, how that time was calculated?

Partly as a result of these situations and curiosities, I’ve developed my own Mental Molad Method. In no more than five minutes, I can easily determine the time of the molad without having to write anything down, and certainly without a calculator. If I think of it in advance, I may work it out on Friday night. But most months it’s my activity during the Haftara on Shabbat morning… when I realize “Birkat HaChodesh is coming, and we need to know the molad!”

If you take a few minutes now and learn the Mental Molad Method, you too will be able to calculate the molad on the spot. There are only a couple of facts you need to remember, and the rest is simple arithmetic that you can do in your mind. I’ve specifically designed the method to include certain shortcuts to make the arithmetic easier… you’ll see as we go along!

Here’s the idea: You start by remembering a certain “reference molad”, that is, the molad of some particular month in the past that you can use as a starting point. Then you just multiply the number of elapsed months since the reference molad by the “monthly molad remainder”, and add that result to the reference molad, and you get the molad of the upcoming month. That’s it – it’s that simple! Now let’s fill in the details.

STEP 1: THE REFERENCE MOLAD

In theory, you can start with any “reference molad” you want. If you happen to remember the previous month’s molad you can use that as a reference, but I never do. The “reference molad” that I remember is:

The molad for the month of Marcheshvan 5765 was on Thursday morning at 2:00 a.m. exactly, with no minutes and no chalakim.

The reason for using that particular molad as a reference is that it’s easy to remember – no minutes and no chalakim! Incidentally, that was a very unusual occurrence. I wrote about it in my essay on 5765, “How is this year different from all other years?” (See item W.3 at http://individual.utoronto.ca/aribrodsky/5765.html) It happens only about once every 87 years.

STEP 2: NUMBER OF ELAPSED MONTHS

You will need to determine how many months have elapsed since the reference molad. A year can have either 12 or 13 months, so you need to know that 5765 and 5768 were Jewish leap years with 13 months each (and so will be 5771), but the intervening years are regular years with 12 months each. So just add up the number of months elapsed from Marcheshvan 5765 until the month whose molad you’re determining.

STEP 3: MONTHLY MOLAD REMAINDER

When we calculate the time of the molad, all we care about is the position of the molad during the course of the week. We can ignore any complete weeks that have elapsed. So the 28 days each month that make up 4 full weeks don’t matter to us at all. This makes it easier to work with the “monthly molad remainder” – the length of time that we must add to one molad to determine the next one, ignoring the full weeks. I consider the computationally simplest version of the monthly molad remainder to be:

The monthly molad remainder is:

1 ½ days, ¾ of an hour, minus 1 minute, plus 1 chelek

STEP 4: DO THE ARITHMETIC

Now you have to multiply the number of elapsed months from step 2 by the monthly molad remainder in step 3, and add the result to the reference molad from step 1. Do this step by step, starting with the days, and then moving on to hours and chalakim. It’s true that the fractions can be frustrating, but if you take a few moments and double-check your calculation you shouldn’t have trouble. And multiplying by ¾ of an hour really is easier than having to multiply by 44 minutes, which would be the alternative. (An even number of elapsed months is easier to work with than an odd number, and if the number of months is a multiple of 4, then you get really lucky.)

As you do the arithmetic, don’t forget these helpful hints:

a) Whole weeks don’t matter, so if you get (for example) 39 days, drop the 5 weeks and just keep 4 days.

b) There are 24 hours in a day, in case you forgot. Make sure to keep track of “a.m.” and “p.m.” carefully as you add the hours.

c) 18 chalakim make up a minute, so if you have more than 18 chalakim turn them into minutes and just keep the remainder as chalakim.

EXAMPLE

Let’s do an example. Suppose you want to calculate the molad for Kislev 5767. That’s what happened at the Yavneh Shabbaton I attended recently, where I explained this method to several people.

Step 1 – we start with our reference molad of “Thursday morning at 2:00 a.m.” for Marcheshvan 5765.

Step 2 – how many months have elapsed from our reference molad (Marcheshvan 5765) to the desired molad (Kislev 5767)? 5765 was a leap year, so from Marcheshvan 5765 to Marcheshvan 5766 was 13 months. 5766 was a regular year, so from Marcheshvan 5766 to Marcheshvan 5767 was another 12 months. Add one more month to get to Kislev 5767, and our total is 26 months.

Step 3 – we know the monthly molad remainder is “1 ½ days, ¾ of an hour, minus 1 minute, plus 1 chelek”.

Step 4 – we need to multiply 26 months times “1 ½ days, ¾ of an hour, minus 1 minute, plus 1 chelek”, and add the result to our reference molad of “Thursday morning at 2:00 a.m.”

Here we go:

26 times 1 ½ days is 39 days. 35 days don’t matter because they are 5 full weeks, so we’re left with 4 days. Add these 4 days to “Thursday 2:00 a.m.” and you get to “Monday 2:00 a.m.”
26 times ¾ of an hour gives 19 ½ hours. Add the 19 ½ hours to our previous result of “Monday 2:00 a.m.” and you get “Monday 9:30 p.m.”
We now have to subtract 26 times 1 minute. From “Monday 9:30 p.m.” we subtract 26 minutes, leaving us with “Monday 9:04 p.m.”
We then add 26 times 1 chelek. Remember that 18 chalakim make up one minute, so 26 chalakim is the same as 1 minute and 8 chalakim. From “Monday 9:04 p.m.” we add 1 minute and 8 chalakim, giving us “Monday 9:05 p.m. and 8 chalakim”. That’s the molad for Kislev 5767, as we announced on the Shabbat preceding Rosh Chodesh.

YOUR CHALLENGE

Some time between now and the next Birkat HaChodesh, use this Mental Molad Method to calculate the next month’s molad. Share your calculation with all your friends and impress them. And when the Gabbai gets up to announce the molad, you’ll know exactly what he’s going to say before he says anything! Or even better, you never know when you’ll be able to save the day (or the month) because no one present has a calendar with the molad listing!

CREDITS AND SOURCES

All the basics of calculating the molad come from Rambam (Maimonides), Mishne Torah, Hilkhot Kiddush HaChodesh, chapter 6. The only ideas that are my own are:

a) Taking Marcheshvan 5765 as the reference molad because of its simplicity;

b) Restating the monthly molad remainder as “1 ½ days, ¾ of an hour, minus 1 minute, plus 1 chelek”, rather than the usual “1 day, 12 hours, 44 minutes and 1 chelek”, in order to simplify the multiplication arithmetic. As bad as fractions are, you really don’t want to multiply by 44, especially on Shabbat.

Thanks to EH, NL, SG, and SW for their discussions with me at the Yavneh Shabbaton, which prompted me to write this up. Thanks also to DJ for correcting a typo.

Comments or corrections are welcome. Send them to ari.brodsky@utoronto.ca.

© Copyright 5767/2006 by Ari Meir Brodsky. All rights reserved. Permission is given to copy, forward or print this document for personal use, provided this copyright notice is included. You may not print or distribute this document or any part of it for profit or for commercial purposes. For any other form of distribution please request permission by e-mail to ari.brodsky@utoronto.ca.