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Ancient Egyptian units of measure include units for length, area and volume.

Length

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).

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.

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. 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 Royal cubit = 7 palms x 4 fingers = 28 fingers

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.

Units of Length

Name	Egyptian name	Equivalent Egyptian values	Metric Equivalent
Royal cubit	meh niswt	1 royal cubit = 7 palms = 28 fingers	c. 52.5 cm
Standard cubit	meh nedjes	1 standard 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

Area

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.

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).

Units of Area

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

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.

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:

The text states: As for vessels (debeh) used in measuring grain by the functionaries of the granary, done into henu : 1 hekat makes 10 ; 1/2 makes 5 ; 1/4 makes 2½ etc.

Units of volume and capacity

Name	Egyptian name	Equivalent Egyptian values	Metric Equivalent
Deny	deny	1 cubic cubit
Khar (sack)	khar	20 heqat (Middle Kingdom) 16 heqat (New Kingdom)	96.5 liters (Middle Kingdom) 76.8 liters (New Kingdom)
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	.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.

Units of weight

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

Time

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.

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.

Units of time

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

1. ^ Clagett, Marshall (1999). Ancient Egyptian science, a Source Book. Volume Three: Ancient Egyptian Mathematics. Philadelphia: American Philosophical Society. ISBN 978-0-87169-232-0.
2. ^ Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2007
3. Lepsius, Richard (1865). Die altaegyptische Elle und ihre Eintheilung (in German). Berlin: Dümmler.
4. Digital Egypt: Measuring area in Ancient Egypt
5. ^ 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
6. T. Pommerening, Altagyptische Rezepturen metrologisch neu onterpretiert, Berichte zur Wissenschaftgeschichte 26 (2003) p. 1 - 16
7. Marshall Clagett, Ancient Egyptian Science: Calendars, clocks, and astronomy, 1989

External links

• Egyptian ceremonial ruler showing fingers, palms, hands, fists, feet, remen
• Cubit divided into fingers and hands
• Modern replica of Egyptian ruler
• Measuring length in Ancient Egypt Page by Digitalegypt (University College London).
• Irrational numbers and pyramids Article by Gay Robins and C.C.D.Shute
• Introduction to Egyptian mathematics Page contains photographs of Maya's cubit rod from the Louvre and land surveying scenes from the tomb of Menna.

• Ancient currencies
• Obsolete units of measure
• Systems of units