Biblical value of pi

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The Bible seems to claim that the value of π (pi) is 3.

1 Kings 7:23 Bible-icon.png says:

23 And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.

An almost identical passage in 2 Chronicles 4:2 Bible-icon.png says:

2 Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.


Atheists sometimes use this passage to demonstrate that the Bible contains a mathematical error, despite the fact that it is supposedly divinely inspired and inerrant. Since the circumference of a circle is π times its diameter, a circular sea could only be ten cubits across and thirty cubits around if π = 30 cubits ÷ 10 cubits = 3, rather than the true value 3.14159265....

Apologetic response

Unfortunately, this claim is easily refuted in a few different ways.

  1. The Bible doesn't claim that the sea was a perfect circle, only that it was "round"; it could have been slightly ellipical and 10 cubits was its longer dimension.
  2. The 30 cubit measurement may have been the interior circumference while 10 cubits was the diameter from one outside edge to the other. That is, the thickness of the "brim" accounts for the discrepancy.
  3. The diameter of a circle with circumference 30 cubits would be approximately 9.55 cubits, which rounds to 10 cubits.
  4. More generally, the passage only implies the wrong value for π if you assume (probably unwisely) that the numbers given are accurate to more than two significant figures (i.e., that they equal 10.0 and 30.0, respectively, when rounded to the nearest tenth). Otherwise, there is quite a large range of possible values implied. If the numbers are only accurate to the nearest unit — surely an acceptable assumption — the implied value could be anything from 2.81 (≈29.5/10.499) to 3.21 (≈30.499/9.5), a range that clearly contains the true value of π. (In other words, the measurements can both be correct, and the shape perfectly circular, if the numbers are simply being reported to the nearest unit.)


While some atheists like to cite this as a demonstration against strict Biblical literalists, as we could certainly expect greater precision if the words of the Bible come directly from a god, the argument tends to be viewed as trivial. This argument is certainly vastly overshadowed by the wealth of other errors, contradictions, ambiguities and atrocities contained in the Bible.

It is also worth noting that the cubit itself was an inherently ambiguous unit, being based on the length of the human forearm. Our ancient friends simply did not possess the accuracy of measurement that we do today.

v · d Arguments against the existence of god
Existential arguments   Argument from nonbelief · Who created God? · Turtles all the way down · Problem of non-God objects · Argument from incompatible attributes · No-reason argument · Santa Claus argument · Can God create a rock so heavy that he can't lift it? · Outsider test
Arguments from the Bible   Failed Prophecy · Biblical contradictions
Evidentiary arguments   Attributes of God · Inefficacy of prayer
Reasonableness arguments   Occam's Razor · Outsider test · Argument from locality · Argument from inconsistent revelations
Other arguments   Emotional pleas
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