The Basics
D'ni numbers are based on characters for one, two, three, and four. These four digits are rotated counterclockwise and compounded to make higher numbers¹.
The numeral for five is a numeral one rotated 90° counterclockwise (in other words, 1x5). Six is 5+1, seven is 5+2, eight is 5+3, and nine is 5+4. Ten is a rotated numeral two (2x5). Fifteen is a rotated numeral three (3x5), and twenty is a rotated numeral four (4x5). The only numbers which do not follow that system are zero and twentyfive. Zero is a dot, and twentyfive can be written two ways: as an X when it's being shown as a single numeral, or onezero (10) when part of a numerical progression.
The reason why twentyfive can be written as 10 is because D'ni used base twentyfive mathematics, rather than base ten. In base ten, the places from right to left represent 1s, 10s, 100s, 1,000s, etcetera. In base twentyfive, from right to left, the places represent 1s, 25s, 625s, 15,625s, etcetera². As with Arabic based math, the D'ni wrote their numbers from right to left, with the far right place before the decimal point representing single digits, the next place to the left representing twentyfives, and so on.
Richard A. Watson (a.k.a. Rawa) mentioned that D'ni numbers might have been derived from a system of counting on one's fingers. Imagine counting on the fingers of your right hand, while using the fingers of the left hand to keep track of how many times you've reached five, and that appears to be the basis of D'ni numerical progression.
This chart shows some of the conversions from base 10 to base 25, and the D'ni notation for them. The first four numbers are places in D'ni mathematics, and the final three rows show some of the differences between how base 10 numbers are expressed in base 25. The fifth line is how Gehn wrote "233rd Age" in one of his journals. He used English for the journal and wrote "98rd Age". That doesn't make sense until you realize that he was simply transliterating the base 25 figure instead of converting it to base 10. Because of that, it appeared at first glance to be Age NinetyEight, which is wrong. It's really Age Two Hundred and ThirtyThree.
The strange notation in the seventh line is used because a single place in D'ni math can be from 0 to 24, which can't be expressed in Arabic notation. The parentheses are used to show that the two digits of 15 are both in the twentyfives place. Without them, the number would appear to be 1,150, instead of 1 in the 625s, 15 in the 25s, and 0 in the ones places.
Base 10 

Base 25 
D'ni 
1 
= 
1 
1 
25 
= 
10 
10 
625 
= 
100 
100 
15,625 
= 
1000 
1000 

233 
= 
98 
98 
700 
= 
130 
130 
1,000 
= 
1{15}0 
1%0 
¹To the D'ni, the rotation would have been clockwise, since their clocks ran in the opposite direction from ours.
²It worked for them, but for us, D'ni math is more than enough to induce headaches. At least for now, I can't even imagine trying to tackle D'ni fractions! This site has a working copy of Simon Riedl's D'ni calculator, so if you want to convert from Arabic notation to D'ni or viceversa, it can do it for you in a flash, with no mental trauma required.
The Numerals
This chart shows the basic D'ni numbers. We do not know any of their mathematic symbols, although we do have the symbols for period and and endash, which can be used for a point and a minus sign. The chart is read right to left, top to bottom, beginning with zero. The two additional numbers after the character for twentyfive are the cyclic zero symbol, and the infinity symbol. Cyclic zero is used in places where zero and another number overlap. An example of that would be a d'ni compass or timepiece.
D'ni Numerals 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
) 
! 
@ 
# 
$ 
% 
^ 
& 
* 
( 
[ 
] 
\ 
{ 
} 
 
= 
+ 
. 
 
The written or spoken words for D'ni numbers are a bit like Old English and German. In German, one does not say "twentyone"; instead, the number is "one and twenty". The main differences are that the D'ni said "twenty and one" and they began using that pattern after the number five. "Six" in D'ni is "five and one", or vagafa, and twelve is "ten and two", or nāgabrē. As you can guess, ga is the D'ni word for "and".
The names of D'ni months use a different system of numbers than normal. My own speculation is that they may be from a much older form of the Ronay language than the D'ni used, the way that month names in English use Latin numbers in some of their names: September, October, November, December are seven, eight, nine and ten respectively. When asked about it, Rawa refused to confirm or deny the theory. The second set of number names are only used in the calendar.
There are only ten months in the D'ni year, but I was able to extrapolate the words for eleven through fourteen from them. For fifteen through nineteen, I guessed the word for fifteen based on the observation that a and ē are converted to o in the regular words for one and two, and that the suffix for ten remains the same as the regular version. That means that the adjectives for fifteenth through nineteenth are conjectural. Since there is no example of how i would have been converted, I cannot guess the words for twenty through twentyfour. I colored all of my conjectural numbers blue to separate them from the confirmed numbers.
In the following chart, the words for the numbers in D'ni months are written below the regular number words.
D’ni number 
D'ni name 
D'ni Script 
English name 
Digit 
D'ni Script TTF 

Adjective 
Dn'i name 
D'ni Script 
0 
rūn 
rUn 
zero 
0 
0 

nothing, none 
rildil 
rilDil 
1 
fa
fo 
fa
fo 
one 
1 
1 

first 
faets 
faex 
2 
brē
bro 
brE
bro 
two 
2 
2 

second 
brēets 
brEex 
3 
sen
san 
sen
san 
three 
3 
3 

third 
senets 
senex 
4 
tor
tar 
tor
tar 
four 
4 
4 

fourth 
torets 
torex 
5 
vat
vot 
vat
vot 
five 
5 
5 

fifth 
vatets 
vatex 
6 
vagafa
vofo 
vagafa
vofo 
six 
6 
6 

sixth 
vagafaets 
vagafaex 
7 
vagabrē
vobro 
vagabrE
vobro 
seven 
7 
7 

seventh 
vagabrēets 
vagabrEex 
8 
vagasen
vosan 
vagasen
vosan 
eight 
8 
8 

eighth 
vagasenets 
vagasenex 
9 
vagator
votar 
vagato
votar 
nine 
9 
9 

ninth 
vagatorets 
vagatorex 
) 
nāvū
novū 
nAvU
novU 
ten 
10 
) 

tenth 
nāvūets 
nAvUex 
! 
nāgafa
nofo 
nAgafa
nofo 
eleven 
11 
! 

eleventh 
nāgafaets 
nAgafaex 
@ 
nāgabrē
nobro 
nAgabrE
nobro 
twelve 
12 
@ 

twelth 
nāgabrēets 
nAgabrEex 
# 
nāgasen
nosan 
nAgasen
nosan 
thirteen 
13 
# 

thirteenth 
nāgasenets 
nAgasenex 
$ 
nāgator
notar 
nAgator
notar 
fourteen 
14 
$ 

fourteenth 
nāgatorets 
nAgatorex 
% 
hēbor
hobor 
hEbor
hobor 
fifteen 
15 
% 

fifteenth 
hēborets 
hEborex 
^ 
hēgafa
hofo 
hEgafa
hofo 
sixteen 
16 
^ 

sixteenth 
hēgafaets 
hEgafaex 
& 
hēgabrē
hobro 
hEgabrE
hobro 
seventeen 
17 
& 

seventeenth 
hēgabrēets 
hEgabrEex 
* 
hēgasen
hosan 
hEgasen
hosan 
eighteen 
18 
* 

eighteenth 
hēgasenets 
hEgasenex 
( 
hēgator
hotar 
hEgator
hotar 
nineteen 
19 
( 

nineteenth 
hēgatorets 
hEgatorex 
[ 
rish 
riS 
twenty 
20 
[ 

twentieth 
rishets 
riSex 
] 
rigafa 
rigafa 
twentyone 
21 
] 

twentyfirst 
rigafaets 
rigafaex 
\ 
rigabrē 
rigabrE 
twentytwo 
22 
\ 

twentysecond 
rigabrēets 
rigabrEex 
{ 
rigasen 
rigasen 
twentythree 
23 
{ 

twentythird 
rigasenets 
rigasenex 
} 
rigator 
rigator 
twentyfour 
24 
} 

twentyfourth 
rigatorets 
rigatorex 
 
fasē
fosē 
fasE
fosE 
twentyfive 
25 
 

twentyfifth 
fasēets 
fasEex 
10 
fasē 
fasE 
twentyfive 
25 
10 




The names of places in written or spoken numbers
Just as we have words for the places in our base ten numerical notation, such as tens, hundreds, thousands, ten thousands, and so on, the D'ni had names for the places in their notation and they used suffixes to represent them.
Currently, we know words for up to six places, and so we can write the names of complex numbers at least up to 244,140,624. (Which — and I hope I get this right — should be rigatorblo, rigatormel, rigatorlan, rigatora, rigatorsērigator, and is written }}}}}} in D'ni numerals.)
To form a number, a suffix was attached to a root number, and single place numbers were added to bring the sum up to the desired value. As an example, 26 is fasēfa (25+1). 628 is farasen (625+3). 31,258 is brēlanvagasen (31,250+5+3). The highest value that can be expressed in any place is 24, so 624 is rigatorsērigator (600+24), which is }} in D'ni numerals.
Explorer Korov'ev of the Guild of Messengers suggested this example of how a complex number using D'ni notation would be laid out.
#^05!4 : 133,206,529 
Sum 
9,765,625s Place 
390,625s Place 
15,625s Place 
625s Place 
25s Place 
1s Place 

# 
^ 
0 
5 
! 
4 

nāgasenblo 
hēgafamel 

vatra 
nāgafasē 
tor 
133,206,529 = 
(13 x 25) 
+ (16 x 25) 
+ (0 x 25) 
+ (5 x 25) 
+ (11 x 25) 
+ 4 
sē : Combining form for multiples of 25.
fasē = 25. In D'ni notation, 1 x 25. Written as 10
brēsē = 50. In D'ni notation, 2 x 25. Written as 20
sensē = 75. In D'ni notation, 3 x 25. Written as 30
ra : Combining form for multiples of 625.
fara = 625. In D'ni notation, 1 x 625. Written as 100
brēra = 1,250. In D'ni notation, 2 x 625. Written as 200
senra = 1,875. In D'ni notation, 3 x 625. Written as 300
lan : Combining form for multiples of 15,625.
falan = 15,625. In D'ni notation, 1 x 15,625. Written as 1000
brēlan = 31,250. In D'ni notation, 2 x 15,625. Written as 2000
senlan = 46,875. In D'ni notation, 3 x 15,625. Written as 3000
mel : Combining form for multiples of 390,625.
famel = 390,625. In D'ni notation, 1 x 390,625. Written as 10000
brēmel = 781,250. In D'ni notation, 2 x 390,625. Written as 20000
senmel = 1,171,875. In D'ni notation, 3 x 390,625. Written as 30000
blo : Combining form for multiples of 9,765,625.
fablo = 9,765,625. In D'ni notation, 1 x 9,765,625. Written as 100000.
brēblo = 19,531,250. In D'ni notation, 2 x 9,765,625. Written as 200000.
senblo = 29,296,875. In D'ni notation, 3 x 9,765,625. Written as 300000.
Explorer Davide has made a Microsoft Excel script that converts base 10 numbers into base 25 and gives you the name of the result in D'ni. With a specific D'ni TrueType Font pack installed, it also shows the result in D'ni numbers. This is the second version of the file, and now includes a D'ni numeral to base 10 Arabic number converter.
Explorer Korov'ev made a similar file called DniNumbers2 in ODS format with more functions. His version also has a section to convert base 25 numbers into base 10. Of the two, Korov'ev's has more functions, and Davide's is easier to use. Both are excellently done.
D'ni Mathematics
Virtually nothing is known about D'ni mathematics. The DRC never released any documents that contained equations, or that dealt with the subject. All we have is semiofficial speculation.
Because of the lack of D'ni mathematic symbols, I'm going to fake a few for the purpose of examples. The math signs you will see are in no way official, and are just placeholders until such time as authentic ones are found.
I've spoken with Richard A. Watson about the subject briefly, and by his recollection, the D'ni may have used a system of notation in which the operands preceded the operators. The closest surface system to it is known as "Reverse Polish Notation." As an example, take this simple problem, 5 + 5 = 10.
Supposedly, the D'ni would have written it 5 5+, and we don't know yet how they would have displayed the result. Provisionally, I do so by displaying the result followed by an equality sign: 5 5+ 10=.
So, the problem might have looked something like this: 5 5 )
Let's take a slightly more complex problem, (9+9) x (124) = 144. The supposed D'ni system would not use brackets, because you apply the operands in the order they appear. The curly brackets in my example are just there to represent that numbers which are two digits in Arabic numerals are one digit in D'ni.
So, the problem would be written 9 9+ {12} 4x 5{19}=. It might look something like this: 9 9 @ 4 5(
In that example, nine and nine are followed by a sign to add the second nine, and then twelve and four are followed by a sign to subtract the four. Then comes a sign to multiply, and that gets applied to the results of the first two operations.
