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On Biblical Units of Measurements

John Byl, Ph.D.

Neither the Biblical unit of length (the cubit) nor the Biblical unit of volume (the bath) are known accurately. These two units are related in the account of Solomon's molten sea. Some time ago Gerry Bouw wrote an interesting article in connection with this.1 In it he raised a number of points that merit further discussion.

The Cubit

There is general agreement that the cubit was the length measured from the elbow to the tip of the extended middle finger. Although there have been various attempts to determine the precise length of the cubit, none are without problems. According to Powell, the best estimate for the cubit is 50 cm (19.7 inches) give or take 10%.2

The cubit was further subdivided into fingers, handbreadths, and spans. According to Powell (and to most commentators) these are probably structured into the system: 4 fingers to a handbreadth, 3 handbreadths to a span, and 2 spans to a cubit. This yields a handbreadth as 1/6 of a cubit. Bouw, on the other hand, takes a handbreadth to be 1/4 of a cubit. He bases this on a typical handbreadth of 4.5 inches, which would be about 1/4 of a cubit. However, this handbreadth presumably includes the thumb. The handbreadth as equivalent to 4 fingers implies that the thumb should be excluded: measure along the base of the four fingers. This yields about 3 to 3 1/2 inches, which is close to 1/6 of a cubit. It should be noted that Josephus also gives 24 fingers to the cubit,3 and 4 fingers to the handbreadth. The Septuagint translates the ”handbreadth” of Ex. 25:25 as “four fingers”. Thus, taking all of this into consideration, I take a handbreadth to be 1/6 of a cubit.

The Molten Sea

The measure of the bath is, if anything, even more uncertain than that of the cubit. Most estimates range from 20 to 47 litres.

The Bible seems to indicate a linkage between the cubit and the bath in the measurements of Solomon's “molten sea” (I Kings 7:23-26; II Chron. 4:2-5). These texts tell us that the “sea” was round, had a diameter (”from brim to brim”) of 10 cubits, a circumference of 30 cubits, a height of 5 cubits, and a thickness of a handbreadth (i.e., 1/6 cubit). Unfortunately, different values for the volume are given: 2000 baths in Kings and 3000 baths in Chronicles.

There are two other pertinent ancient sources for these numbers. The Septuagint version gives the same dimensions, except that it gives a circumference of 33 cubits in Kings and 30 cubits in Chronicles. In Kings no volume is given; in Chronicles it is stated to be 3000 measures. Josephus4 states that the sea was a hemisphere of 10 “feet” diameter holding 3000 baths.

All commentators agree that the top was circular. A radius of 5 cubits would thus yield 31.4 cubits. This can be reconciled with the 30 cubits by taking the numbers as rounded off (i.e., a precision of 1 significant digit rather than the 3 of the 31.4). It is evident that at least some of these numbers are rounded off since both the volumes and lengths are given to only one significant figure. Since the lengths are easier to measure, it seems natural to assume that the lengths are more precise than the volume.

Or, as Bouw and others have suggested, since the sea is stated to have a “brim like a cup,” the circumference may well have been measured beneath the brim. In this case the actual radius, omitting the brim, would be somewhat less than 5 cubits. Hence there need be no conflict. In this case the outer radius would be R = 30/2p = 4.77 cubits and the inner radius r = R - 1/6 = 4.61 cubits. The inner height would be h = 5 -1/6 = 4.83 cubits (assuming the bottom is as thick as the sides) or, perhaps, it might be the same as r.

What about the shape of the sea? This is critical if we are to relate the bath to the cubit. Although Josephus says it was a hemisphere, other commentators are divided as to whether it should be a cylinder or a hemisphere (or even a cone). The volumes for the various shapes would be: Vh = (2/3)p r3 = 205.2 cubes (i.e., cubic cubits); Vcyl = p r2 h = 322.5 cubes; VCone = Vcyl/3 = 107.5 cubes. Taking the cubit at 50 cm, one cube equals 125 litre. Then we can calculate the following estimates for the bath:

Volume Hemisphere Cylinder Cone
2000 baths 0.103 cube/12.9 lr 0.161 cube/20.1 lr 0.054 cube/6.8 lr
3000 baths 0.0684 cube/8.6 lr 0.1075 cube/13.4 lr 0.036 cube/4.5 lr

A possible uncertainty of 10% in the cubit corresponds to an uncertainty of 30% in the estimate of the bath. This uncertainty is further increased if we take into account that the number of baths (whether 2000 or 3000) may be rounded off to the nearest 100 (or even 1000). This could increase the uncertainty to as much as 55%.

If this is to be reconciled with estimates of the bath obtained through other means (i.e., at least 20 litres) then the only viable candidate is the cylinder at 2000 baths, with the hemisphere at 2000 baths and the cylinder at 3000 baths being the only others having even remote chances, within a 55% uncertainty range. (We note in passing that the 37 litre bath obtained by Bouw must be a miscalculation.)

The Shape of the Sea

What was the shape of the molten sea? Josephus states that the sea was a hemisphere. Also favouring the hemisphere is the fact that the height equals the radius. This must be considered as purely coincidental if it were a cylinder. Furthermore the phrase “round all about” suggests a hemisphere. For a hemisphere the 12 oxen with their hindparts underneath the sea would not add to the height of the top of the sea (which is for the priests to wash in), as would be the case for a cylinder (one would estimate that this would add at least a cubit). On these, and other, grounds Scott argues that the shape was hemispherical. On the other hand, Powell and Hognesius both favour a cylinder, although they give no strong grounds for their preference (other than this makes the numbers work out better).

All in all, I would conclude that the evidence favours a hemisphere but that a cylinder can't be conclusively ruled out.

2000 or 3000?

There has been much speculation as to how to reconcile the 2000 baths in Kings with the 3000 baths in Chronicles. Various theories have been advanced. One suggestion is that the author of Chronicles mistakenly assumed it was a cylinder whereas it was actually a hemisphere (the ratio of a hemisphere to a cylinder with the same radius and height is 2 to 3).5 However, since a hemisphere seems to yield too small a volume for the bath, Scott6 conjectures that the author of Kings used in error the formula for a sphere instead of that for a hemisphere, so that the actual volume was only 1000 baths. Naturally, these theories are unacceptable to anyone upholding Biblical inerrancy.

Hognesius7 suggests that the Chronicler assumed a cubit one handbreadth larger than the normal cubit (Ezek. 40:5 refers to a “long cubit” as one handbreadth longer than a common cubit). This would increase the volume by (7/6)3, or 59% (i.e., from 2000 baths to 3179, or roughly 3000). The obvious difficulty with this explanation is that the linear dimensions in Chronicles agree with those in Kings, demonstrating that the same cubit is meant. Thus one would have to argue that the Chronicler either did not know that the cubit in Kings was in fact shorter or that he deliberately exaggerates. Again, either possibility is unacceptable for inerrantists.

Using the large cubit ((7/6)x50 = 58.3 cm) would increase all the volumes in the Table by a factor of 59%. In particular, this would increase the bath (for the hemisphere at 2000 baths) to 20.5 litres; for the cylinder at 3000 baths it comes to 21.3 litres. Yet, if the cubit “of the old standard” were indeed that large this would increase the height of Goliath (6 cubits and a span, according to I Sam.17:4) from 10 feet 8 inches, already huge, to an incredible 12 feet 5 inches! (It is interesting to note that both Josephus and the Septuagint give Goliath's height as 4 cubits and a span (7 feet 4 inches); the Egyptian killed by Benaiah was 5 cubits tall (8 feet 2 inches or 9 feet 7 inches for large cubits) and, like Goliath, has “a spear like a weaver's beam” I Chron. 11:23).

It might be better to argue that the bath unit of the Chronicler was different from that of the author of Kings. This is in fact done by Powell. He suggests that the 3000 baths is likely the result of Astrological miscalculation, perhaps by misapplying the rule for the ratio (2:3) of liquid to dry capacity. The difficulty is that the ratio works the wrong way: 2000 liquid baths equals 1333 solid ones. Thus either the Chronicler made a mathematical blunder, as Powell suggests, or it was the author of Kings who applied the solid bath. In the latter case the actual value would be 3000 liquid baths (corresponding to 2000 solid baths).

It has been suggested that the discrepancy could be due to a copying error. It is of interest to note that in Kings there is mention of 20 measures (Hebrew: kor) of oil (I Kings 5:11), while the parallel passage in Chronicles refers to 20000 baths of oil (I Chron. 2:10). Elsewhere a kor is said to equal 10 baths (Ez. 45:14). How do we reconcile these? One could speculate that this is a copying error not found in the original manuscript.8 Could the same perhaps be true of the 2000 (or 3000) baths?

However, we need not resort to such conjectures. An easy resolution is to assume, as Bouw and others9 suggest, that the 2000 baths refers to the normal level whereas the 3000 baths refers to the maximum capacity. This implies that the actual capacity of the molten sea should be taken as 3000 baths. The 3000 figure has in its favour the fact that it is the one used by both the Septuagint and Josephus.

Another Linkage?

There is mention also of 10 “lavers” measuring 4 cubits each and containing 40 baths (I Kings 6:38). These were for rinsing off what was used for the burnt offering; the sea was for the priests to wash in (II Chron.4:6). These seem to have been round (I Kings 6:31), with a diameter of 4 cubits and a depth of at most 3 cubits (Josephus gives 4 cubits), the height of the frame (I Kings 6:27). Assuming a cylindrical shape, and a thickness of one handbreadth, this yields a bath of at most p(2- l/6)2(3- 1/6)/40 = 0.75 cubes = 93.5 litre. This seem much too large. Perhaps the actual depth of the lever was much less than 3 cubits; or the lever was normally only partially filled. In either case, this is of little help in determining the size of the bath.

Conclusion

There exists too much uncertainty regarding the length of the cubit and the shape of Solomon's “molten sea” for a precise determination of the size of the bath unit. The preferred figure of 3000 baths and a hemispherical shape suggests a bath of 8.6 litre, with an uncertainty of at least 30%. A cylindrical shape would give a bath of 13.4 litres.

These figures are significantly smaller than estimates of the bath obtained through other methods (primarily archaeological). It is, however, noteworthy that the homer (10 baths) was derived from the “armload”. Powell estimates that a donkey could carry about 90 kg. This would equal 90 litres of water, or 9 litres per bath, in excellent agreement with the 8.6 litre estimate based on the hemisphere and 3000 baths.

NOTES AND REFERENCES

1 Gerardus D. Bouw, 1992. “Biblical Units of Measurement”, The Biblical Astronomer, 2(62):10-14.

2 Marvin A. Powell, 1992. “Weights and Measures,” The Anchor Bible Dictionary, 6:897-908.

3 The Works of Josephus, (translated by W. Whiston, Hendrickson Pub. 1980), Antiquities of the Jews 3.6.3.

4 Josephus, op.cit., Antiquities 8.3.5.

5 For an account of these see Kjell Hognesius, 1994. “The Capacity of the Molten Sea in 2 Chronicles IV 5: A Suggestion,” Vetus Testamentum XLIV, 3:349-358.

6 R.B.Y. Scott, 1958. “The Hebrew Cubit”, Journal of Biblical Literature 77:205-214.

7 For an account of these see Kjell Hognesius, 1994. “The Capacity of the Molten Sea in 2 Chronicles IV 5: A Suggestion”, Vetus Testament XLIV, 3:349-358.

8 Actually, the 1 Kings reference refers to 20 baths of pure oil and designates them for Hiram's household. 2 Chronicles 2:10 states that those amounts (including 20,000 baths of oil—without the word ”pure”) are for Hiram's servants and laborers. (Ed)

9 This was suggested also by John W. Haley, 1874, Examination of the Alleged Discrepancies of the Bible (reprinted in 1977 by Baker Book House), p. 382.

Translated from WS2000 on 3 September 2005 by ws2html.