True to the centralized and administrative nature of the pharaonic state, ancient Egypt had an official system of weights and measures, valid throughout the country, which did not show really significant changes until the Late period. This regulated system comprised three main subsystems that enforced capacity, length, and weight. Measures of capacity were the most complex, with regard to dry goods and fluids. For the food staples (bread and beer), a measure of “baking ratio” expressed the proportion between the fixed quantity of cereals and the size of loaves or the strength of beer. From the measures of length, the measures of area and volume were derived, as well as the more specific measure of a monument's external batter (upward and backward slope). Measures of weight (and some of capacity) were adapted for the valuation of goods, as a kind of notional “money.”
The present-day equivalents of the measures in each category are known by calculating the average capacity, length, or weight of ancient measuring objects now in museums. This method is more accurate than trusting any one object, since many, worn with use, no longer retain their original length or shape; in fact, ancient technology was not always capable of manufacturing exact measures.
In ancient Egypt, some offices or temples retained “official” standard measures that could be checked when controversy arose—for example, stone rulers were less subject to contraction and expansion (from humidity) than their wooden counterparts of daily use. Apart from such natural factors as heat and humidity, measures were probably often altered deliberately or deemed to be unreliable. When collecting the grain due him in a distant village, a land proprietor of the eleventh dynasty felt it safer to send his own grain measure with his collectors, to prevent being cheated.
Before discussing the units of measures, it is important to say that an elementary universal measure is just the number resulting from counting goods. In fact, ancient Egyptian economic documents frequently record such figures, expressing quantities of a product counted either by the piece or by a usual grouping of pieces: bunches or garlands of flowers, clusters of dates, mrw-bundles of vegetables, nḫ-bundles of flax, handfuls of reeds, and even censersful or altarsful of incense.
Ancient Egyptians had an elaborate system of measures of capacity, chiefly used, however, for measuring cereals and other dry goods, not fluids, as the very word “capacity” would seem to suggest.
In this system, the basic unit was the ḥḳʒt (or “bushel”), of 4.805 liters (about 5 quarts). In the Old and Middle Kingdoms, 10 ẖʒr made the larger unit khar (or “sack”), of 48.05 liters (about 50 quarts). By the beginning of the New Kingdom, the value of the khar was increased to the equivalent of 16 heqat (76.88 liters or 80 quarts), expressed as 4 fourfold-heqat, each of 19.22 liters (20 quarts). This increase did not reflect an economic crisis, but the change of a decimal system to a binary system, which was probably intended to make accounting easier. Thenceforward, the fourfold-heqat was no more understood as being made up of four heqat but as a unit in its own right—the fourth of the khar, best known as an ἰpt, the Coptic form of ancient Egyptian ipet (“measure,” whose name but not the value was borrowed in Hebrew as ephah). Smaller quantities were expressed as fractions of oipe, more precisely as one of the fractions of the geometric progression 1/2, 1/4 (the former heqat), 1/8, 1/16, 1/32, and 1/64. The latter quantity (0.30 liter, just under a pint) was divisible into 5 rʒ (“parts”) of 0.06 liter each (3 ounces), reflecting the ancient division of the heqat into 80, and of the fourfold-ḥḳʒt into 320 rʒ. Should the need arise, quantities even smaller could be expressed in fractions of ro. Contrary to these fractions, written in the ordinary Egyptian way (any given number under the hieroglyph figuring a mouth expresses a fraction, with this number as the denominator and 1 as the numerator), the fractions of ἰpt from 1/2 to 1/64 were written by the various parts of the hieroglyph wḏʒt (“sound” or “complete eye,” the symbol of completeness). Known as the “Horus Eye notation,” it was obviously a mnemonic device and had for its basis the Egyptian myth in which the god Horus had had his eye taken out by his brother Seth, before it was restored to him by Thoth, god of knowledge, mathematics, and fair accounting. (See Figure 1.)
The basic measure for fluids was the ḥnw, of 1/10 (1/40 oipe) or 0.48 liter (a pint), made up of 32 (“parts”), each of 0.06 liter (0.5 ounce). The name of this measure, the ḥnw, is best known under its Coptic form hin, later borrowed in Hebrew to name a measure of capacity about twelve times larger. Besides the hin, Egyptians used a large variety of vessels for specific products
(beer, wine, etc.) or specific kinds of products (liquids, oils, etc.), although each had a more or less fixed capacity (which we but rarely know), their diversity shows that these vessels were not true units of measure. In fact, their use indicates the mere counting pieces of a product, so economic records frequently express totals of products in “various vessels.” Among the best known of such kinds of containers, one can quote the large storage vessel mnἰ or mnt (“jar” of 20 or 30 hin [9.6 or 14.4 liters]), the small mehtet (of 1 hin), and the smaller bas (1/2 hin), a (1/4 hin), and pgʒ (1/8 hin) used for the presentation of offerings.
The “Baking Ratio.”
A measure called psw (from the Egyptian verb pes, “to cook”), commonly translated as “baking ratio,” was used for expressing the number either of loaves or of hin of beer made from an ἰpt of grain. For loaves, this expressed a size (the greater the “baking ratio,” the smaller the loaf) and for beer, a quality (the greater the “baking ratio,” the weaker the beer). The purpose of this kind of measurement, which can be compared with our units for alcohol or our calories, was to allow the accountants to estimate the quantities of grain to be issued from the granaries either to prepare a divine offering or to feed a known number of people for a fixed period of time: the court, a party of workmen engaged in a monument's construction, or an army going abroad.
The basic unit was the cubit, expressing the length of the forearm, from the elbow (Lat., cubitus) to the tip of the fingers (0.523 meter/18 inches). The measure was made up of 7 palms (the hand's width without the thumb), with each palm comprising 4 fingers, each of 1.86 centimeters (0.75 inch). Lesser lengths were measured in fractions of the finger. For the New Kingdom, votive cubits found in tombs bear inscriptions naming other measures not known elsewhere: apart from the cubit of 7 palms, here called royal cubit, there are the small cubit of 6 palms (44.82 cm), the rmn of 5 palms (37.35 cm), the dsr of 4 palms (29.88 cm), the great span of 3.5 palms (26.14 cm), the small span of 3 palms (22.41 cm), the dopple or double palm (14.94 cm), and the fist of 1.5 palm or 6 fingers (11.20 cm). Apart from the cubit, Egyptians of the New Kingdom sometimes used, for measuring the progress in the excavation of a tomb, a larger unit, called nebi (“pole”), a term that would survive in Egypt under its Greek transcription ναύβιον; its length has been estimated to 1 1/4 cubits (65.3 centimeters) by some but by others to about 70 centimeters divided in 7 parts of 10 centimeters each.
Land surveying needed a longer unit than the cubit, the ḫt n nwḥ (“rod of cord”), or more simply ḫt (“rod”) of 100 cubits (52.30 meters/160 feet), since the measure of a land-measuring rope was 100 cubits long, stretched between two rods driven in the ground. Journeying needed a still larger unit, the ἰtrw (“river”), which measured 20,000 cubits (10.46 kilometers/6.5 miles). As proven by a variant of its name, ἰtrw n sḳdwt (“ἰtrw of towing”), it originally expressed the length of a day's towing of a boat along the Nile. Modern scholarship sometimes translates ἰtrw by schoene, since it is roughly equivalent to the Attic schoene of 10,656 meters or 10.656 kilometers. From the twelfth dynasty (Karnak White Chapel of Senwosret I), the Egyptians officially estimated the length of their country from Elephantine in the south to Behedet (Tell el-Balamun) at 106 ἰtrw (1,108.76 kilometers/670 miles), divided into 86 ἰtrw for Upper Egypt and 20 ἰtrw for Lower Egypt—the border between the two being at the town of Per-Hapy (to the south of today's Old Cairo). Notwithstanding the etymology of ἰtrw, which refers to the Nile as Egypt's primary route, the ἰtrw also measured land distances.
Ancient classical writers, such as Diodorus Siculus, expressed more than once an admiration for the Egyptians' geometrical knowledge, which was based on the need to take new measures of their fields each year, once the Nile flood retreated. The basic measure of area was the sṯt, commonly known as aroura (from the Greek ἄρονρα, “field,” “land”), a square of land of 100 by 100 cubits or 1 ḫt by 1 ḫt (2,735.29 square meters). Multiples and submultiples were not defined by squaring multiples or submultiples (as we would do), but by multiplying or dividing the width, while retaining the length as 100 cubits (implying that fields were always thought to be set in rows, along a road or a canal, on which their widths abutted).
As a measure of volume proper, we know only of the dnἰt, which was a cubic cubit (0.143 cubic meters). This measure was used exclusively for measuring the progress made by workers in the excavation of a tomb. From such texts as the Rhind Mathematical Papyrus, scribes clearly knew how to calculate volumes from linear measures—even volumes like cylindrical granaries or truncated pyramids—but they neglected to give a name to the resulting cubic units.
The sḳd expressed the slope (or batter) of a masonry massive—like a pyramid—by giving the length in palms of the horizontal basis of a right-angled triangle of 1 cubit height, whose hypotenuse was a section of the expected or measured slope. In Old Kingdom construction, there is an obvious trend to use mainly a sḳd of 5 1/2 palms or 5 1/4 palms, corresponding to slopes of 51°51′ and 53°7′ as exemplified, respectively, by the pyramids of Khufu and Khafre.
Ancient Egypt's basic unit of weight was the dbn (according to Akkadian sources, pronounced tiban). The etymology suggests it to have been originally a metal ring. From 13 grams during the Old Kingdom, its weight was increased to 91 grams (7 × 13 grams) during the Middle Kingdom. In the New Kingdom, it was divided into 10 ḳdt (Coptic, qite) of 9.1 grams each, with lesser weights expressed as fractions of ḳdt.
Ancient Egyptians never used coins for exchanging goods. The first known coins in Egypt were made by the thirtieth dynasty pharaohs only to pay their Greek mercenaries. The dbn (see above) and other units of weight were used as notional units of value (similar to the term “pound”), allowing parity for the bartering of goods, by reducing them to a common scale. According to the value of the goods thus exchanged, these units (from the rarest to the commonest) could be a dbn of gold, silver, or copper. During the New Kingdom, gold was probably double the value of silver; and silver, originally one hundred times the value of copper in the nineteenth dynasty, became only sixty times its worth in the twentieth. As a standard of value, gold was never used at all, and silver was rarely used at Deir el-Medina, the community that provided most of this data. [For an expanded discussion, see PRICES AND PAYMENT.]
- Gardiner, Alan H. The Wilbour Papyrus, vol. 2: Commentary. London, 1948, pp. 59–65. Assesses the measuring system in use at the end of the New Kingdom.
- Gardiner, Alan H. Egyptian Grammar. Being an Introduction to the Study of Hieroglyphs. 3d ed. Oxford, 1973, section 266. The classical presentation of the ancient Egyptian system of weights and measures.
- Helck, Wolfgang. “Maße und Gewichte (pharaonische Zt.).” In Lexikon der Ägyptologie, 3: 1199–1209. Wiesbaden, 1980. A short but comprehensive statement of the known facts.
- James, T. G. H. The Hekanakhte Papers and Other Early Middle Kingdom Documents. Publications of the Metropolitan Museum of Art Egyptian Expedition, 19. New York, 1962. Appendix C, pp. 115–118, discusses the measurement system of a rural area in the eleventh dynasty.
- Janssen, Jac. J. Commodity Prices from the Ramessid Period. An Economic Study of the Village of Necropolis Workmen at Thebes. Leiden, 1975. Presents the problem of ancient Egyptian “money” in chapter 1, pp. 101–111.
- Robins, Gay, and Charles Shute. The Rhind Mathematical Papyrus. London, 1987. A short but comprehensive presentation of ancient Egyptian mathematics, geometry, and metrology, as expressed in the most important ancient Egyptian treatise on these matters (Rhind Mathematical Papyrus, British Museum 10057–10058).