Ancient Egyptian units of measure include units for length, area and volume.
Length [edit]
Units of length date back to at least the early dynastic period. In the Palermo stone, for instance, the level of the Nile river is recorded. During the reign of Pharaoh Djer the height of the river Nile was given as measuring 6 cubits and 1 palm. This is equivalent to approximately 320 cm (roughly 10 feet 6 inches).[1]
A third dynasty diagram shows how to construct an elliptical vault using simple measures along an arc. The ostracon depicting this diagram was found in the area of the Step Pyramid in Saqqara. A curve is divided into five sections and the height of the curve is given in cubits, palms and fingers in each of the sections.[2]
Lengths could be measured by cubit rods, examples of which have been found in the tombs of officials. Fourteen such rods, including one double cubit rod, were described and compared by Lepsius in 1865.[3] Two examples are known from the tomb of Maya – the treasurer of Tutankhamun – in Saqqara. Another was found in the tomb of Kha (TT8) in Thebes. These cubits are ca 52,5 cm long and are divided into seven palms, each palm is divided into four fingers and the fingers are further subdivided.[1]
Cubit rod from the Turin Museum.
For longer distances, such as land measurements, the Ancient Egyptians used rope. A scene in the tomb of Menna in Thebes shows surveyors measuring a plot of land using rope with knots ties at regular intervals. Similar scenes can be found in the tombs of Amenhotep-Sesi, Khaemhat and Djeserkareseneb. The balls of rope are also shown in New Kingdom statues of officials such as Senenmut, Amenemhet-Surer and Penanhor.[2]
Units of Length[1][2]
| Name |
Egyptian name |
Equivalent Egyptian values |
Metric Equivalent |
| Royal cubit |
meh niswt |
1 royal cubit = 7 palms = 28 fingers |
c. 52.5 cm |
| Short cubit |
meh nedjes |
1 short cubit = 6 palms = 24 fingers |
c. 45 cm |
| Remen |
remen |
1 remen = 5 palms = 20 fingers |
c. 37.5 cm |
| Djeser |
djeser |
1 djeser = 4 palms = 16 fingers |
c. 30 cm |
| Span (large) |
pedj-aa |
1 large span = 3.5 palms = 14 fingers |
c. 25 cm |
| Span (small) |
pedj-sheser |
1 small span = 3 palms = 12 fingers |
c. 22.5 cm |
| Fist |
|
1 fist = 6 fingers |
c. 10.75 cm |
| Hand |
|
1 hand = 5 fingers |
c. 9.38 cm |
| Palm |
shesep |
1 palm = 4 fingers |
c. 7.5 cm |
| Finger |
djeba |
1 finger = 1/4 palm |
c. 1.88 cm |
| Khet (rod) |
khet |
1 khet = 100 cubits |
c. 52.5 m |
| River measure |
iteru |
1 iteru = 20,000 cubits |
c. 10.5 km |
The records of areas of land date back to the early dynastic period. Gifts of land recorded in the Palermo stone are expressed in terms of kha, setat, etc. Further examples of units of area come from the mathematical papyri. Several problems in the Moscow Mathematical Papyrus for instance give the area of a rectangular plot of land (measured in setjats) and given a ratio for the lengths of the sides of the rectangles one is asked to compute the lengths of the sides.[1]
The setat was equal to one square khet, where a khet measured 100 cubits. The setat could be divided into strips one khet long and ten cubit wide (a Kha).[2][4]
Units of Area[1][2]
| Name |
Egyptian name |
Equivalent Egyptian values |
Metric Equivalent |
| Kha-ta |
kha-ta |
100,000 sq cubits |
27,565 square meters |
| Setat (setjat) |
setat |
1 square khet = 10,000 square cubits |
2,756½ square meters |
| Kha |
kha |
1000 square cubits = 1/10 setat |
275.65 square meters |
| Ta |
ta |
100 square cubits = 1/100 setat |
27.565 square meters |
| Shoulder (Remen) |
remen |
1/2 ta = 50 square cubits |
13.7 square meters |
| Heseb |
heseb |
1/2 remen = 25 square cubits |
6.8 square meters |
| Sa |
sa |
1/2 heseb = 12.5 square cubits |
3.4 square meters |
Volume, Capacity and Weight [edit]
Several problems in the mathematical papyri deal with volume questions. For example in RMP 42 the volume of a circular granary is computed as part of the problem and units of cubic cubits, khar, quadruple heqats and heqats are used.[1]
Problem 80 on the Rhind Mathematical Papyrus recorded how to divide grain (measured in heqats), a topic included in RMP 42 into smaller units called henu:
Problem 80 on the Rhind Mathematical Papyrus
The text states: As for vessels (debeh) used in measuring grain by the functionaries of the granary, done into henu : 1 hekat makes 10 [henu]; 1/2 makes 5 [henu]; 1/4 makes 2½ etc.[1]
Units of volume and capacity[1][2]
| Name |
Egyptian name |
Equivalent Egyptian values |
Metric Equivalent |
| Deny |
deny |
1 cubic cubit |
|
| Khar (sack) |
khar |
20 heqat (Middle Kingdom)
16 heqat (New Kingdom) [5] |
96.5 liters (Middle Kingdom)
76.8 liters (New Kingdom) [5] |
| quadruple heqat |
hekat-fedw |
4 heqat = 40 hinu |
19.2 liters |
| double heqat |
hekaty |
2 heqat = 20 hinu |
9.6 liters |
| Heqat (barrel) |
hekat |
10 hinu |
4.8 liters |
| Hinu (jar) |
hnw |
1/10 heqat = 32 ro |
.48 liters |
| Dja |
dja |
5/8 hinu = 20 ro [6] |
.3 liters |
| Ro |
r |
1/320 heqat |
.015 liters |
Weights were measured in terms of deben. This unit would have been equivalent to 13.6 grams in the Old Kingdom and Middle Kingdom. During the New Kingdom however it was equivalent to 91 grams. For smaller amounts the kite (1/10 of a deben) and the shematy (1/12 of a deben) were used.[2]
Units of weight [2]
| Name |
Egyptian name |
Equivalent Egyptian values |
Metric Equivalent |
| Deben |
dbn |
|
13.6 grams in the Old Kingdom and Middle Kingdom.
91 grams during the New Kingdom |
| Kite |
qd.t |
1/10 of a deben |
|
| Shematy |
shȝts |
1/12 of a deben |
|
The Egyptians divided their year (rnpt) into 365 days (hrw). The Egyptian calendar had 12 months (abd) of 30 days each, plus 5 epagomenal days.[1]
They divided their year into 3 seasons, named Akhet, Peret and Shemu. Akhet was the season of inundation. Peret was the season which saw the emergence of life after the inundation. The season of Shemu was named after the low water and included harvest time.[7]
Units of time[1][2]
| Name |
Egyptian name |
Equivalent Egyptian values |
| hour |
unut |
1 day = 24 hours |
| day |
hrw |
1 day = 1/30 month = 24 hours |
| month |
abd |
1 month = 30 days |
| Inundation season |
akhet |
Akhet = 4 months = 120 days |
| Emergence season |
peret |
Peret = 4 months = 120 days |
| Harvest season |
shemu |
Shemu = 4 months = 120 days |
| year |
renpet |
1 year = 365 days |
The introduction of equal length hours occurred in 127 BC. The Alexandrian scholar Claudius Ptolemaeus introduced the division of the hour into 60 minutes in the second century AD.
References [edit]
- ^ a b c d e f g h i j Clagett, Marshall (1999). Ancient Egyptian science, a Source Book. Volume Three: Ancient Egyptian Mathematics.. Philadelphia: American Philosophical Society. ISBN 978-0-87169-232-0.
- ^ a b c d e f g h i Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2007
- ^ Lepsius, Richard (1865). Die altaegyptische Elle und ihre Eintheilung (in German). Berlin: Dümmler.
- ^ Digital Egypt: Measuring area in Ancient Egypt
- ^ a b Katz, Victor J. (editor),Imhausen, Annette et.al. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press. 2007, p 17, ISBN 978-0-691-11485-9
- ^ T. Pommerening, Altagyptische Rezepturen metrologisch neu onterpretiert, Berichte zur Wissenschaftgeschichte 26 (2003) p. 1 - 16
- ^ Marshall Clagett, Ancient Egyptian Science: Calendars, clocks, and astronomy, 1989
External links [edit]
