Did the Bible get the value of Pi wrong?

This is a popular issue some sceptics raise with the passages of 1 Kings 7:23-26 and 2 Chronicles 4:2-5 which describes the so called Copper Sea, a large water basin made out of copper for the Jerusalem temple. Specifically the math in 1 Kings 7:23 and 2 Chronicles 4:2 where it says that the Sea was circular in shape, with 10 cubits (ca 4.5 meters) from brim to brim, yet it took a measuring line of 30 cubits (ca 13.5 meters) to go around it. The arguments goes that if you have a circle with a diameter of 10 units, the circumference would be 10 x π or ca 31.415 units around. Hence, it would seem the Bible wrongly defines the value of π as 3, rather than approximately 3,14159…

Read all of the text

This accusation is easily defeated when looking at the context. The text is not meant to define any mathematical constants. It is just a description of the design of the copper basin, and context shows it is not a perfect cylinder. In 1 Kings 7:26 we can read:

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.

So we learn an interesting facts. The top part of the Copper Sea was shaped like “the brim of a cup”. How are those shaped?

An ancient cup with a jutting brim

If you look up how ancient Israelite cups were made you can clearly see what is meant. It is very common that the brim juts out.
A lily flower

It also says it’s like a lily flower. As you can see, the edges of lilies are bent outward.

The Copper Sea was obviously designed with a ‘lip’ jutting out, so if you measured from one side to the other across it, it would be 10 cubits wide. But if you measured around the narrow part below the brim, it would not be as wide, and thus the circumference would be less than 31,415 cubits, or 30 cubits.

Some calculations

From this extra information we can do some calculations. The width of the Sea below the brim would be 30 / π cubits, or 9,55 cubits (ca 4,2 meters). This is about 30 cm narrower than at the brim, meaning the brim juts out 15 cm on all sides. The verse also tells us that the thickness of the basin wall was one handbreadth. One handbreadth is about 1/6 cubit, or 7,5 cm. Hence the inner diameter of the neck would be 15 cm less than 4,2 meters, or 4,05 meters. That makes the inner area 12,72 m².

How much did it contain?

Verse 23 says that the Sea was 5 cubits high, which equals 2,25 meters. This also indicates that it was not a simple cylinder, because then it would only have a maximum inner volume of  28,68 m³ holding a maximum of 28.687 liters, give or take. The problem is that in 1 Kings 7:26 is is said to contain 2000 Bath measures, and in 2 chronicles 4:5 it is said to contain 3000. First of all is this a contradiction? No, of course not. If it contains 3000 then it contains 2000 as well. The 3000 measure is probably just the max volume, and the 2000 measure the amount they usually filled it with. But how much is that? A Bath measure is estimated to be about 22 liters, so 3000 bath measures equals 66.000 liters. That is more than the 28.687 liters a cylinder of that size would contain. So we can understand that the overall shape was not a perfect cylinder. A clue is found in verse 2 Chronicles 4:4:

It stood on twelve oxen, three facing north, three facing west, three facing south, and three facing east. The sea was set on them, and all their rear parts were inward.

If the bottom of the basin was circular, it would be really difficult to balance it on the backs of twelve copper oxen placed in lines of 3. A square shape would be much more logical. If the lower part of the basin was a square or cubic shape which transitions into a lily-like opening. By trying a few measurements and using geometric formulas to calculate the volume, I came up with measurements that produce a very accurate result and an aesthetically pleasing basin.

Schematic of the Copper Sea

This model consists of a cubic base section 2 cubits (90cm) high, a truncated pyramid middle section one cubit high and a cylindrical top section 2 cubits high. Here are the calculations on the inner volume.

The structure would be 15 cm wider on the outside. The inner width of the base section is 16 cubits, which is 7,2 meters.  7,2 x 7,2 x 0,9 is 46,6 m³.

The truncated pyramid is calculated with the formula V = 1/3 x H x (A² + B² + AB).  The height H is 0.45. The Base width A is 6,75 and since the top area is a circle rather than a square, the equivalent base width B is the square root of the area 12.88, which is 3,58. 1/3 x 0,45 x (45,5 + 12,88 + 6,75 x 3,58) = 12.38m³.

The cylinder part has an area of 12.88 m², times 0.9 m, which is 11,59m³.

That equals a total volume of 70 m³. This design could easily contain 66.000 liters of water.

That should put this issue to a rest.