Ancient Egyptian units of measurement
Encyclopedia
Length
Units of length date back to at least the early dynastic periodEarly Dynastic Period of Egypt
The Archaic or Early Dynastic Period of Egypt immediately follows the unification of Lower and Upper Egypt c. 3100 BC. It is generally taken to include the First and Second Dynasties, lasting from the Protodynastic Period of Egypt until about 2686 BC, or the beginning of the Old Kingdom...
. In the Palermo stone
Palermo stone
The Palermo Stone is a large fragment of a stele known as the Royal Annals of the Old Kingdom of Ancient Egypt. It contains records of the kings of Egypt from the first dynasty through the fifth dynasty....
for instance the level of the Nile
Nile
The Nile is a major north-flowing river in North Africa, generally regarded as the longest river in the world. It is long. It runs through the ten countries of Sudan, South Sudan, Burundi, Rwanda, Democratic Republic of the Congo, Tanzania, Kenya, Ethiopia, Uganda and Egypt.The Nile has two major...
river is recorded. During the reign of Pharaoh
Pharaoh
Pharaoh is a title used in many modern discussions of the ancient Egyptian rulers of all periods. The title originates in the term "pr-aa" which means "great house" and describes the royal palace...
Djer
Djer
Djer was the second or third pharaoh of the first dynasty of Egypt, which dates from approximately 3100 BC. Some scholars, however, debate whether the first pharaoh, Menes or Narmer, and Hor-Aha might have been different rulers. If they were separate rulers, this would make Djer the third pharaoh...
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
Third dynasty of Egypt
For the Sumerian Renaissance, see Third Dynasty of Ur.The Third Dynasty of ancient Egypt is the first dynasty of the Old Kingdom. Other dynasties of the Old Kingdom include the Fourth, Fifth and Sixth...
diagram shows how to construct an elliptical vault using simple measures along an arc. The ostracon
Ostracon
An ostracon is a piece of pottery , usually broken off from a vase or other earthenware vessel. In archaeology, ostraca may contain scratched-in words or other forms of writing which may give clues as to the time when the piece was in use...
depicting this diagram was found in the area of the Step Pyramid
Step pyramid
Step pyramids are structures which characterized several cultures throughout history, in several locations throughout the world. These pyramids typically are large and made of several layers of stone...
in Saqqara
Saqqara
Saqqara is a vast, ancient burial ground in Egypt, serving as the necropolis for the Ancient Egyptian capital, Memphis. Saqqara features numerous pyramids, including the world famous Step pyramid of Djoser, sometimes referred to as the Step Tomb due to its rectangular base, as well as a number of...
. 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
Cubit
The cubit is a traditional unit of length, based on the length of the forearm. Cubits of various lengths were employed in many parts of the world in Antiquity, in the Middle Ages and into Early Modern Times....
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
Maya (Egyptian)
Maya was the Overseer of the Treasury during the reign of Pharaoh Tutankhamun, Ay and Horemheb of the eighteenth dynasty of Ancient Egypt. He was also an important official and was noted for restoring the burials of several earlier Pharaohs in the Royal Necropolis in the years following the deaths...
- the treasurer of Tutankhamun
Tutankhamun
Tutankhamun , Egyptian , ; approx. 1341 BC – 1323 BC) was an Egyptian pharaoh of the 18th dynasty , during the period of Egyptian history known as the New Kingdom...
- in Saqqara
Saqqara
Saqqara is a vast, ancient burial ground in Egypt, serving as the necropolis for the Ancient Egyptian capital, Memphis. Saqqara features numerous pyramids, including the world famous Step pyramid of Djoser, sometimes referred to as the Step Tomb due to its rectangular base, as well as a number of...
. Another was found in the tomb of Kha (TT8
TT8
TT8 or Theban Tomb 8 was the site of one of the greatest archaeological discoveries in ancient Egypt. This New Kingdom era tomb was one of the few tombs of Ancient Egypt's nobility to have survived intact down through the centuries - it was only discovered by Arthur Weigall and Ernesto Schiaparelli...
) in Thebes
Thebes, Egypt
Thebes is the Greek name for a city in Ancient Egypt located about 800 km south of the Mediterranean, on the east bank of the river Nile within the modern city of Luxor. The Theban Necropolis is situated nearby on the west bank of the Nile.-History:...
. 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.
For longer distances, such as land measurements, the Ancient Egyptians used rope. A scene in the tomb of Menna
Menna
The Ancient Egyptian artisan Menna was "Scribe of the Fields of the Lord of the Two Lands", probably during the reign of Thutmose IV during the 18th dynasty. He was buried in a well decorated tomb, located in the Sheikh Abd el-Qurna district of the Maadi, opposite Luxor, in Egypt.-External links:*...
in Thebes
Thebes, Egypt
Thebes is the Greek name for a city in Ancient Egypt located about 800 km south of the Mediterranean, on the east bank of the river Nile within the modern city of Luxor. The Theban Necropolis is situated nearby on the west bank of the Nile.-History:...
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
New Kingdom
The New Kingdom of Egypt, also referred to as the Egyptian Empire is the period in ancient Egyptian history between the 16th century BC and the 11th century BC, covering the Eighteenth, Nineteenth, and Twentieth Dynasties of Egypt....
statues of officials such as Senenmut
Senenmut
Senenmut was an 18th dynasty ancient Egyptian architect and government official. His name translates literally as "mother's brother."- Family :...
, Amenemhet-Surer and Penanhor.
| Name | |Egyptian name | |Equivalent Egyptian values | |Metric Equivalent |
|---|---|---|---|
| Royal cubit | |
1 royal cubit = 7 palms = 28 fingers | c. 52.5 cm |
| Standard cubit | |
1 standard cubit = 6 palms = 24 fingers | c. 45 cm |
| Remen | |
1 remen = 5 palms = 20 fingers | c. 37.5 cm |
| Djeser | |
1 djeser = 4 palms = 16 fingers | c. 30 cm |
| Span (large) | |
1 large span = 3.5 palms = 14 fingers | c. 25 cm |
| Span (small) | |
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 | |
1 palm = 4 fingers | c. 7.5 cm |
| Finger | |
1 finger = 1/4 palm | c. 1.88 cm |
| Khet (rod) | |
1 khet = 100 cubits | c. 52.5 m |
| River measure | |
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 stonePalermo stone
The Palermo Stone is a large fragment of a stele known as the Royal Annals of the Old Kingdom of Ancient Egypt. It contains records of the kings of Egypt from the first dynasty through the fifth dynasty....
are expressed in terms of kha, setat, etc. Further examples of units of area come from the mathematical papyri
Papyrus
Papyrus is a thick paper-like material produced from the pith of the papyrus plant, Cyperus papyrus, a wetland sedge that was once abundant in the Nile Delta of Egypt....
. Several problems in the Moscow Mathematical Papyrus
Moscow Mathematical Papyrus
The Moscow Mathematical Papyrus is an ancient Egyptian mathematical papyrus, also called the Golenishchev Mathematical Papyrus, after its first owner, Egyptologist Vladimir Golenishchev. Golenishchev bought the papyrus in 1892 or 1893 in Thebes...
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).
| Name | |Egyptian name | |Equivalent Egyptian values | |Metric Equivalent |
|---|---|---|---|
| Kha-ta | |
100,000 sq cubits | 27,565 square meters |
| Setat (setjat) | |
1 square khet = 10,000 square cubits | 2,756½ square meters |
| 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) | |
1/2 ta = 50 square cubits | 13.7 square meters |
| Heseb | |
1/2 remen = 25 square cubits | 6.8 square meters |
| Sa | |
1/2 heseb = 12.5 square cubits | 3.4 square meters |
Volume, Capacity and Weight
Several problems in the mathematical papyriPapyrus
Papyrus is a thick paper-like material produced from the pith of the papyrus plant, Cyperus papyrus, a wetland sedge that was once abundant in the Nile Delta of Egypt....
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
Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus , is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1650 BC...
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 [henu]; 1/2 makes 5 [henu]; 1/4 makes 2½ etc.
| Name | |Egyptian name | |Equivalent Egyptian values | |Metric Equivalent |
|---|---|---|---|
| Deny | deny | 1 cubic cubit | |
| Khar (sack) | |
20 heqat (Middle Kingdom Middle Kingdom Middle Kingdom may refer to:*China, traditional translation of its common name, Zhōngguó *Middle Kingdom of Egypt*Middle kingdoms of India... ) 16 heqat (New Kingdom New Kingdom The New Kingdom of Egypt, also referred to as the Egyptian Empire is the period in ancient Egyptian history between the 16th century BC and the 11th century BC, covering the Eighteenth, Nineteenth, and Twentieth Dynasties of Egypt.... ) |
96.5 liters (Middle Kingdom Middle Kingdom Middle Kingdom may refer to:*China, traditional translation of its common name, Zhōngguó *Middle Kingdom of Egypt*Middle kingdoms of India... ) 76.8 liters (New Kingdom New Kingdom The New Kingdom of Egypt, also referred to as the Egyptian Empire is the period in ancient Egyptian history between the 16th century BC and the 11th century BC, covering the Eighteenth, Nineteenth, and Twentieth Dynasties of Egypt.... ) |
| quadruple heqat | |
4 heqat = 40 hinu | 19.2 liters |
| double heqat | hekaty | 2 heqat = 20 hinu | 9.6 liters |
| Heqat (barrel) | |
10 hinu | 4.8 liters |
| Hinu (jar) | |
1/10 heqat = 32 ro | .48 liters |
| Dja | dja | 5/8 hinu = 20 ro | .3 liters |
| Ro | |
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
Old Kingdom
Old Kingdom is the name given to the period in the 3rd millennium BC when Egypt attained its first continuous peak of civilization in complexity and achievement – the first of three so-called "Kingdom" periods, which mark the high points of civilization in the lower Nile Valley .The term itself was...
and Middle Kingdom
Middle Kingdom
Middle Kingdom may refer to:*China, traditional translation of its common name, Zhōngguó *Middle Kingdom of Egypt*Middle kingdoms of India...
. During the New Kingdom
New Kingdom
The New Kingdom of Egypt, also referred to as the Egyptian Empire is the period in ancient Egyptian history between the 16th century BC and the 11th century BC, covering the Eighteenth, Nineteenth, and Twentieth Dynasties of Egypt....
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.
| Name | |Egyptian name | |Equivalent Egyptian values | |Metric Equivalent |
|---|---|---|---|
| Deben | |
13.6 grams in the Old Kingdom Old Kingdom Old Kingdom is the name given to the period in the 3rd millennium BC when Egypt attained its first continuous peak of civilization in complexity and achievement – the first of three so-called "Kingdom" periods, which mark the high points of civilization in the lower Nile Valley .The term itself was... and Middle Kingdom Middle Kingdom Middle Kingdom may refer to:*China, traditional translation of its common name, Zhōngguó *Middle Kingdom of Egypt*Middle kingdoms of India... . 91 grams during the New Kingdom New Kingdom The New Kingdom of Egypt, also referred to as the Egyptian Empire is the period in ancient Egyptian history between the 16th century BC and the 11th century BC, covering the Eighteenth, Nineteenth, and Twentieth Dynasties of Egypt.... |
|
| Kite | |
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 calendarEgyptian calendar
The ancient civil Egyptian calendar had a year that was 360 days long and was divided into 12 months of 30 days each, plus five extra days at the end of the year. The months were divided into three weeks of ten days each...
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.
| Name | |Egyptian name | |Equivalent Egyptian values |
|---|---|---|
| hour | |
1 day = 24 hours |
| day | |
1 day = 1/30 month = 24 hours |
| month | |
1 month = 30 days |
| Inundation season | |
Akhet = 4 months = 120 days |
| Emergence season | |
Peret = 4 months = 120 days |
| Harvest season | |
Shemu = 4 months = 120 days |
| year | |
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.
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.
