# Does 1st Kings say that pi = 3?

The construction of Solomon's temple includes a piece of furnishing described in 1 Kings 7:23 (ESV):

Then he made the sea of cast metal. It was round, ten cubits from brim to brim, and five cubits high, and a line of thirty cubits measured its circumference.

So if the `diameter = 10` cubits and the `circumference = 30` cubits, then `π = 3` by the equation `C = π * D`.

Of course, such an object does not exist since `π = 3.14159...` yet clearly the sea was constructed at some point. So how do we resolve this contradiction?

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Considering the range of widely spread explanations, and how some non-obvious and counterintuitive explanations are repeated over and over again, I think this is a very good question. – dancek Nov 12 '11 at 14:38
If it's good enough for the Indiana legislature it's good enough for me! – Affable Geek Mar 16 '12 at 13:27
...maybe I should come here more often if no one noticed and fixed the "3.141 4 9..." error for five months! -_- – El'endia Starman May 4 '12 at 4:14
@El'endia Starman: Weird. I guess I typed it from "memory" rather than copy-n-paste. Thanks. (Or maybe it was a clever ploy to prove that exactitude is over-rated. Yeah, that's it!) – Jon Ericson May 4 '12 at 4:31

It's hard to get inside the minds of people from other cultures, especially when we are separated by time as well as distance. And the main problem here is cultural: We have an expectation of greater precision than ancient people did. The other answers hint at this, but IMO they don't fully appreciate the divide between modern and ancient levels of precision.

There are several reasons we can't use the measurements in 1 Kings 7:23 to calculate pi:

• The other answers are on the right track regarding rounding. At the time the Tanakh was written, the decimal point had not been invented. So if the diameter were 9.55 cubits, there would simply be no way to record that except to round to the nearest cubit. This, however, does not prove the diameter was 9.55 cubits. We just can't know with any greater precision.

But there's more reasons for uncertainty:

• A cubit was not a uniform standard of distance. It was about the length of the forearm, from the elbow to the tip of the middle finger or from the elbow to the base of the hand. Moreover, arm length varies from person to person. How can we know whether the "line of 30 cubits" measuring the circumference uses the same cubit as the 10-cubit measurement across?
• Can we say for certain that the line of 30 cubits fit perfectly around the circumference with both ends touching and no overlap? The ESV translation above doesn't necessarily lead to that implication, though some others do.

Also note:

• Unlike passages that are meant to be instructional (e.g., Exodus 26:1-6), where specificity is relatively important, this one is merely descriptive. It doesn't need to be consulted by workers attempting to build the object according to spec. The object already existed.
• This passage is not a word problem from an early geometry textbook, where the reader's job is to calculate the value of pi. Its purpose is to describe an object in the temple. For that purpose, the round numbers "10 cubits" and "30 cubits" would give most people of the time a good idea of its size.

In conclusion:

There are many factors weighing against using the numbers in this passage as a precise mathematical equation. Our desire for decimal point accuracy misses the point of the Scripture, and says more about the modern world than it does about God.

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+1 for the conclusion alone. Pointing out the difference in genre between what was written and how some people try read it is also very appropriate. – Jon Ericson Nov 17 '11 at 23:50
For some more information about how pi was estimated in ancient times, see this article. The Egyptians apparently used an estimate of 22/7 (which I learned in grade school myself). Details of how they might have applied the knowledge to building pyramids can be found here. Of course, there are lots of strange theories about how the Egyptians might have learned to build the pyramids and most of them are bunk. ;-) – Jon Ericson Nov 18 '11 at 18:23

Many different explanations have been proposed. The best article I've read on the subject is The Number Pi in the Bible by Abarim Publications.

I'll begin with what I think is the obvious and correct explanation, then mention some other explanations (mentioned e.g. in the article above).

## 10 ≠ 10.0 (rather, "10" means (10.0 ± 0.5))

1 Kings 7:23 says nothing about the value of pi. It just mentions two values:

• a diameter of "10 cubits"
• a circumference of "30 cubits"

Now, imagine that the diameter was actually 9.55 cubits. The author would still probably have written "10 cubits" instead of going for the exact measure. You shouldn't be surprised that

``````30.0 / 9.55 = 3.1413…
``````

Which is quite near pi. Of course, "30" isn't exact either. Anyway, it's clear that for `x/y = pi`, we can have `x ≈ 30` and `y ≈ 10`. We can also calculate the possible range for pi:

``````x ∈ [29.5, 30.5[
y ∈ [9.5, 10.5[
pi = x/y ∈ ]2.80…, 3.21…[
``````

## Other explanations

There are many other explanations, which are in my opinion more complicated than the obvious one. Some of these might be true, but we don't need to assume so. Credits for much of the list goes to the article The Number Pi in the Bible.

• The rim of the sea was of a finite width. The diameter was measured on the outside, and the circumference on the inside.
• The top of the rim protrudes outside. The circumference is measured from the lower part while the diameter is measured from the top.
• The sea was actually oval-shaped, not circular.
• The verse includes a coded message in Hebrew, and by calculating numerical values and using some math we arrive at `pi = 3 * 111/106 = 3.1415…`.
• A range of unscientific explanations, such as...
• The Bible isn't a science textbook, so this is no problem!
• It's a miracle. The measurements are physically not possible, but God is above physics.
• Actually `pi = 3` as revealed by God, and we should adapt our man-made scientific ideas accordingly.
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That's a lovely rabbit hole you made me jump down. ;-) The article mentions that to an engineer, π ≈ 3, which is a pretty good summary. – Jon Ericson Nov 14 '11 at 23:07
By using the concept of Significant Figures, the math is correct. Heh... I guess, for that matter, whoever said the thing was a perfect circle anyway. "Round" is descriptive, not mathematical. – user6152 Nov 23 '14 at 3:54

To start with, compare the circle the diameter we're given would make with the circle the circumference we're given would make:

Since a circumference is π times the diameter, a 'pure' circle of 10 cubits in diameter as we describe the sea as having would be 10π cubits in circumference, or roughly 31.4 cubits.

Now, since the circumference attributed to our sea is only 30 cubits, it represents a smaller circle, which is 30/π or roughly 9.55 cubits in diameter.

Or to tabulate it:

``````Circle A:  ~9.55 cubits diameter,  30   cubits circumference
Circle B:  10    cubits diameter, ~31.4 cubits circumference
``````

Given that, we have two diameters differing by about .45 cubits (about eight inches on an 18-inch cubit--a sizable difference).

Since we know the sea was a physical object and not a circle bounded by an infinitesimal line, we can safely understand that the sea must be of some thickness; on this ground, it would not be unreasonable to take the shorter dimension as the inner measurement, and the longer dimension as the outer measurement, and see where that takes us.

Dividing the difference in the diameters in half, this would make the wall around our sea at least .225 cubits thick--i.e., about four inches on either end of the sea, assuming an eighteen-inch cubit.

Do we have any authority for assuming that this is the case and saying the sea was anything like four inches thick?

A couple of verses after this we have 1 Kings 7:26, which gives it to us outright:

Its thickness was a handbreadth, and its brim was made like the brim of a cup, like the flower of a lily. It held two thousand baths.

A handbreadth as a unit of measurement is generally given as between three and four inches.

(The 'Number Pi in the Bible' site linked elsewhere gives as its rebuttal to this sort of argument the statement "The writer makes sure that no question remains: both the diameter and the circumference are taken over-all." - though I'm not sure on what basis he sees that.)

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Welcome to Biblical Hermeneutics! This is a well-reasoned response. I too wonder why this explanation was so quickly dismissed in that article. – Jon Ericson Nov 17 '11 at 6:28
@MukeTever I don't understand what you're saying. If the circumference were 30 and the real diameter 9.55, then measuring the diameter on the inside of a .225-thick wall would yield 9.10. Can you clarify? – dancek Nov 18 '11 at 10:58
I'm starting to assume this is the brim-protruding-outside argument, which I think is the most believable one of those assuming exact values of 30.0 and 10.0. It's just worded in a way that I have a hard time understanding (ESL, sorry). – dancek Nov 18 '11 at 11:03
@Dancek The same argument could be used for a protruding brim; I just had in mind the thickness of the sea itself. The argument is probably the same for any shape that takes into account the thickness as well as the circumference and diameter given. – Muke Tever Nov 18 '11 at 14:01
(+1) This seems like the best answer to me. The diameter would be useful information if you wanted to fit the bowl through a door or something. The circumference would be more useful in referencing how much water it could hold. So, it seems reasonable to reference both, slightly different measurements in the way they were referenced. – Jas 3.1 Jul 14 '12 at 0:42

From a post by Cecil Adams, aka The Straight Dope

In 150 A.D. a Hebrew rabbi and scholar named Nehemiah attempted to explain away the anomaly in Chronicles by saying that the diameter of the tub was 10 cubits from outer rim to outer rim, whereas the 30 cubit circumference was measured around the inner rim. In other words, the difference between the biblical notion of pi and the actual value may be accounted for by the width of the tub's walls. How's that for tap dancing, eh?

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we don't even know what the real numerical value of pi is. When written out as a number, it will always be rounded. The question is: At which decimal place will you believe God's Word is true? The hundredth decimal place, the thousandth decimal place? I'm guessing for most, there will never be enough decimal places. For me pi = 3 is close enough.

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+1 for a common-sense answer though you haven't really added much that hasn't been said already ;) – Jack Douglas Jan 11 '13 at 14:45