Numbers and Measurements

Numbers and Measurements

Middle Egyptian uses a decimal system — without zero. Each power of ten has its own sign, and the scribe repeats each sign as many times as needed. Numbers are almost always written in numerals rather than in words.

Hieroglyphs	English	Value
	one	1
	ten	10
	hundred	100
	thousand	1000
	ten thousand	10000
	hundred thousand	100000
	million	1000000

Thus the number 1,234,567 (one million two hundred thirty-four thousand five hundred sixty-seven) is represented as follows:

The signs are always arranged from largest to smallest, and the small signs (1, 10, 100) are grouped in “square” groups of two to four. In transliteration one simply writes the number in numerals: mḥ 30 “30 cubits”.

For very large numbers multiplication was sometimes used: 4 × 100,000 + 7 × 10,000 = 470,000. The sign for a million is mostly used in an imprecise sense: “a great many”, “millions”. There was no zero: in accounts an empty space was left, or the word nfrw “lack” was written.

Cardinal Numbers

Cardinal numbers (“one, two, three”) are grammatically singular nouns. Only “one” is usually written out in words; the names of the other numbers are known to us mainly from Coptic. The numbers 1–10 and the tens 10–30 have a masculine and a feminine form.

The names of the numbers:

The other numbers are compounded from these names: mḏw-wꜥ “eleven”, ḫꜣ ḫmnw-št ḥmw-sjsw “one thousand eight hundred forty-six”. Above 10,000 one counts in ten-thousands: djw ḏbꜥ “five ten-thousands” = 50,000.

The relief clearly shows how the tens are written: the sign mḏ is written once for each ten, and the signs are arranged in rows of three, one above the other, to fill the writing square (quadrat). Thus 60 is written as two rows of three hobbles, not as a single sequence of six. The same principle applies to all signs: they are arranged by the aesthetic consideration of filling the square, not in one long line.

1. Structure of lists: the noun followed by the number

Usually the noun comes before the number, mostly in the singular — as in accounts: “year, 20”. Presumably in speech the number was pronounced first.

Hieroglyphs	Transliteration	English
	mmj 7	“Seven giraffes”
	ḥb.t 3	“Three ritual books”
	t 10 ḥ(n)q.t ds 2	“Ten loaves [and] two jugs [of] beer”
	rnp.t 20	“20 years”
	sp.w 4	“4 times”

In the last example the noun is plural — this too is possible.

2. Number with a demonstrative pronoun

The number is a singular noun, so the demonstrative pronoun is singular and agrees in gender with the noun. The exceptions are 100 and 1,000: with them the pronoun agrees with the number itself — feminine for 100 (št), masculine for 1,000 (ḫꜣ).

Hieroglyphs	Transliteration	English
	pꜣ pr 3	“these three houses”
	tꜣ dp.t 3	“these three boats”
	tꜣ bꜣk 100	“these 100 servants”
	pꜣ t 1000	“these 1000 loaves”

3. Number before the noun

With large numbers (1,000, a million) the number sometimes comes before the noun, and they are joined by m or by the indirect genitive (n(.jj)):

Hieroglyphs	Transliteration	English
	ḫꜣ m sbj	“[A] thousand rebels”
	ḥḥ n(.jj)sp	“[A] million times”

4. wꜥ “one”

wꜥ (feminine wꜥ.t) usually comes after the noun and agrees with it in gender. It also comes before it, joined by n(.jj) — and at a later stage this is a way of expressing the indefinite: “a certain dog”. wꜥ m + plural means “one of”. wꜥ is also used in the sense “sole, unique”.

Hieroglyphs	Transliteration	English
	mjw wꜥ	“one cat”
	wꜥ n(.jj) ṯsm	“[a] dog”
	wꜥ m ẖrd.w	“one of [the] children”
	nṯr wꜥ	“[the] unique god”

5. sp sn “twice”

The phrase sp sn (“twice”; also transliterated sp 2) is used in writing as a repetition mark: it tells the reader to read what precedes it twice. It is not itself pronounced — it is a purely graphic mark, like the repeat sign in musical notation. Its position varies with the scope of the repetition:

• After a word — the word is said twice, usually for emphasis: ꜥšꜣ sp sn = ꜥšꜣ ꜥšꜣ “much, much”, that is, “very often”.

• After a phrase or sentence — the whole phrase is said twice: jnk ꜣs.t sp sn = “I am Isis! I am Isis!”.

• Within a word (after the 12th Dynasty) — it replaces doubled consonants in reduplicated verbs: sk sp sn = sksk “to destroy” (from skj “to perish”).

Hieroglyphs	Transliteration	English
	ꜥšꜣ sp sn	“very often”
	jnk ꜣs.t sp sn	“I [am] Isis! I [am] Isis!”

In transliteration one usually writes sp sn or sp 2, and in translation — one repeats the word or phrase.

Ordinal Numbers

Ordinal numbers indicate order in a series: first, second, third, and so on. In Middle Egyptian the word for “first” is special: it is a nisba form derived from the preposition tp “upon” and agrees with the noun in gender.

Examples:

Hieroglyphs	Transliteration	Gender	English
	m sp tp.jj	Masculine	“On [the] first occasion”
	ḥm.t=f tp.(jj)t	Feminine	“His first wife”

“second” to “ninth” – the ending nw (feminine: nw.t) is added, attached directly to the numeral, either below it or immediately after it.

Examples:

Hieroglyphs	Transliteration	Gender	English
	pr=f 4-nw	Masculine	“His fourth house”
	5-nw n ḥꜣb	Masculine	“[The] 5th festival”

The ordinal number is an adjective, so it usually comes after the noun. Sometimes it comes before it, and then the noun follows in apposition or is joined by n(.jj): snw.t=f jꜣ.t “his second office” (literally: “his second, the office”).

Ordinal numbers from ten upward were written by combining the word mḥ “the one completing” (feminine: mḥ.t) with the numerals after it.

mḥ is a participle of the verb mḥ “to fill”: sbꜣ mḥ-12 = “the gate completing the 12”, rnp.t mḥ.t-12 = “the year completing the 12”.

Examples:

	Hieroglyphs
sbꜣ mḥ-12 n(.jj)ḥw.t-nṯr	Transliteration
“[The] twelfth gate of [the] temple”	English
“[The] twelfth gate of [the] temple”	English

	Hieroglyphs
prj.t mḥ.t-14	Transliteration
“[The] fourteenth procession”	English
“[The] fourteenth procession”	English

Hours of the day and night:

Hours are counted with ordinal numbers:

	Hieroglyphs
wnw.t mḥ.t-10 n.t hrw	Transliteration
“[The] tenth hour of the day”	English
“[The] 10th hour of [the] day”	English

	Hieroglyphs
wnw.t 4-nw.t n.t grḥ	Transliteration
“[The] fourth hour of [the] night”	English
“[The] 4th hour of [the] night”	English

Fractions

A fraction is written with the word r “part”, with the denominator below it. The numerator is always 1: r-5 = ⅕.

Examples:

Hieroglyphs	Transliteration	Translation	Hieroglyphs	Transliteration	Translation
	r-5	⅕		r-244	1/244

In addition, there are four special fractions: ½ (gs ), ¼ (r-4 ), ⅔ (r.wj ), ¾ (ḫmt-r.w )

Except for ⅔ and ¾, the numerator of every fraction is 1. To write any other fraction, several fractions are added together.

Example — adding fractions:

Hieroglyphs	Transliteration	Value
	5 gs r-7 r-14	5 + 1/2 + 1/7 + 1/14 = 5 5/7

The numerator of every fraction is 1, so a larger value is obtained by adding several fractions: a half, plus a seventh, plus one fourteenth — together five sevenths.

Writing the common fractions:

Hieroglyphs	Transliteration	Fraction
gs	gs	1/2
	r-4	1/4
	r.wj	2/3
	ḫmt-r.w	3/4
	r-5	1/5
	r-244	1/244

The number is written below r, and its digits are grouped as usual: r-4 = four strokes in two rows.

Dates

Years were not counted from a fixed point but by the regnal years of the ruling king. A full date therefore begins with the regnal year and ends with the king's name.

Structure of the Egyptian calendar:

Hieroglyphs	Transliteration	Unit of time	Breakdown
	rnp.t	Year	3 seasons
	tr	Season	4 months
	ꜣbd	Month	30 days
	hrw	Day	24 hours (12 of day and 12 of night)
	wnw.t	Hour
	ꜣ.t	Moment

The day began at sunrise. Until the New Kingdom, hours were not of fixed length: in winter the daytime hours were shorter than the night hours, and in summer the reverse.

Structure of the year:

Hieroglyphs	Transliteration	Season name	Breakdown
	ꜣḫ.t	Akhet — the season of inundation	Mid-July – mid-November
	pr.t	Peret — the season of growing	Mid-November – mid-March
	šmw	Shemu — the season of harvest	Mid-March – mid-July

3 seasons × 4 months × 30 days = 360 days. At the end of the year (after the fourth month of šmw) five days were added — ḥr(j).w-rnp.t “those above the year” — the birthdays of Osiris, Horus, Seth, Isis and Nephthys.

Dates in Middle Egyptian:

Structure of a date:

Regnal year → month number (within the season, 1–4) → season name → day number → king's name

The regnal year is written ḥꜣ.t-sp (some read rnp.t-ḥsb), followed by the number.

Special terms:

Hieroglyphs	Transliteration	Meaning
	sw	Written to mark the day, instead of hrw
	tpj	Instead of “month 1” (written: tpj + season name)
	ꜥrqj	Special term for the last day of a month → instead of sw 30

Example (regnal year in red, month number + season name in blue, day number in green, king's name in black):

	Hieroglyphs
ḥꜣ.t-sp 2, ꜣbd 3 ꜣḫ.t, sw 1 ḫr ḥm n(.jj) nsw-bj.tj N(j)-mꜣꜥ.t-Rꜥ	Transliteration
“Regnal year 2, third month of the inundation season (Akhet), day 1, under the Majesty of the King of Upper and Lower Egypt, Amenemhat III (Ni-maat-Re)”	English
“Regnal year 2, third month of inundation, day one under [the] Majesty of [the] King of Upper and Lower Egypt, Ammenemes III”	English

More examples (tpj instead of “month 1”, ꜥrqj instead of “day 30”):

	Hieroglyphs
tpj šmw 16	Transliteration
“First month of the harvest, day 16”	English
“First (month) of Harvest, (day) 16”	English

	Hieroglyphs
ḥꜣ.t-sp 24 ꜣbd 2 pr.t ꜥrqj	Transliteration
“Year 24, second month of the growing season, last day”	English
“Year 24, second (month) of Growing, last (day)”	English

The use of tpj “first” and ꜥrqj “last” shows that numbers in dates were pronounced as ordinals: “the third month of the inundation, the seventh day”.

Measurements

Middle Egyptian developed varied systems of measurement for length, area, volume and weight. These systems arose from the needs of agricultural life along the Nile: dividing land, trading grain and liquids, and measuring building materials.

In the examples above we saw that in measures the thing measured comes first, then the unit of measure, then the number — with both nouns in the singular: ḥ(n)q.t ds 100 “100 jars of beer” (literally: “beer, jar, 100”).

Structure: name of the material/dimension → unit of measure → number

To state an object's dimensions (length and width), the suffix pronoun matching the gender of the noun is used (=f for masculine, =s for feminine).

• ꜣw → “length”

• wsḫ → “width”

Hieroglyphs	Transliteration	Gender	English
	m ꜣw=f	Masculine	“In its (masc.) length”
	m ꜣw=s	Feminine	“In its (fem.) length”
	m wsḫ=f	Masculine	“In its (masc.) width”
	m wsḫ=s	Feminine	“In its (fem.) width”

Length and Width

The basic unit of length and width is the cubit mḥ , the length of the forearm from the elbow to the tip of the middle finger — about 52.5 centimeters. Smaller and larger units are derived from it.

Structure:

[Genitive construction] the subject → measure + number → m → type of measurement (length/width) + suffix pronoun agreeing in gender

Example:

	Hieroglyphs
dp.t n(.jj)t mḥ-120 m ꜣw=s mḥ-40 m wsḫ=s	Transliteration
“a boat 120 cubits long and 40 cubits wide”	English
“[A] boat 120 cubits long [and] 40 cubits wide”	English

Here the suffix pronoun =s is used because dp.t “boat” is feminine.

Area

The basic unit of area is the sṯꜣ.t “aroura”: an area of 100 × 100 cubits (about 2,750 m², roughly two-thirds of an acre). The Egyptians viewed it as 100 strips of 1 × 100 cubits; hence the strip itself is called mḥ-tꜣ “land-cubit” (1/100 aroura), and 10 arouras are called ḫꜣ-tꜣ “land-thousand”.

Structure:

the subject → measure + number

Example:

	Hieroglyphs
ꜣḥ.wt nfr.(w)t sṯꜣ.t-24	Transliteration
“24 arouras [of] good farmland”	English
“24 arouras [of] good arable land”	English

Volume

Two systems of volume were used — one for liquid measure and one for dry measure.

Liquid → two common measures:

• hnw → “hin”, the basic measure (about 0.48 liter)

• ds → “jar”, used mainly for beer; volume unknown

Structure: the liquid → measure + number

Example:

	Hieroglyphs
ḥnq.t hnw-47	Transliteration
“47 hin [of] beer”	English
“47 hins [of] beer”	English

Dry → four common measures:

The basic measure for grain is the ḥqꜣ.t “heqat” (about 4.8 liters) = 10 hnw.

Structure: the material → measure + number

Examples:

Hieroglyphs	Transliteration	English
	jt šmꜥ ḥqꜣ.t-645	“645 heqats [of] Upper Egyptian barley”
	ḥqꜣ.t 88½	“88½ heqat”

Weight

The unit of weight is the dbn “deben”. In the Middle Kingdom it weighed only about 13.6 grams and had no subdivisions. At the end of the 12th Dynasty its value rose to about 91 grams, and two subdivisions were added:

Hieroglyphs	Transliteration	Measure
	dbn	~ 91 grams
	qd.t	~ 9.1 grams (1/10 dbn)
	šnꜥ.tj	~ 7.5 grams (1/12 dbn)

šnꜥ.tj “ring” is the earlier subdivision; after the 18th Dynasty qd.t took its place.

Structure: the material → measure + number

Example:

	Hieroglyphs
ḥmt, dbn-47 qd.t-5	Transliteration
“47 deben and 5 kite (qd.t) [of] copper”	English
“47 deben [and] 5 qite (qd.t) [of] copper”	English

Chapter New Vocabulary

Hieroglyphs	Transliteration	Type	English
	ꜣs.t	Proper noun	Isis
	wsḫ	Noun	Width
	mmj	Noun	Giraffe
	mḥ	Verb	To fill, complete
	N(j)-mꜣꜥ.t-Rꜥ	Proper noun	Nimaatre (Ammenemes III)
	nsw-bj.tj	Noun	King of Upper and Lower Egypt
	ḥꜣ.t-sp	Noun	Regnal year
	ḥb.t	Noun	Ritual book
	ḥmt	Noun	Copper
	sbꜣ	Noun	Gate; star
	skj	Verb	To perish
	sṯꜣ.t	Noun	Aroura (land measure)
	šmꜥ	Noun	Upper Egypt
	ds	Noun	Jug