How To Use This Converter
Type a decimal number in the Decimal input field, or a Roman Numeral in the Roman field,
and press Enter or Return on your keyboard or keypad.
The other field will show the number you entered, converted to the other number system.
The Roman Numeral input field accepts capital and/or lowercase letters.
The Roman Numeral field displays results in capital letters.
TIP:Entry Errors
If the data you type into any Base field contains disallowed symbols for that field, the converter will notify you.
In that case, simply re-type valid data in the field of your choice and press Enter or Return.
TIP:Copy and Paste
You can Copy and Paste any of the fields by selecting the text in the field,
then pressing Control-C to copy, and Control-V to paste.

Roman Numerals

The Number System of Roman Numerals
The Roman Numeral system is the number system of ancient Rome. It is a decimal system, but it is not the modern
Decimal system of everyday use.
For its symbols, the Roman Numeral system uses the following seven letters from the Latin alphabet:
I, V, X, L, C, D, M
The ancient Romans wrote numerals with capital letters only, but in modern usage capital letters and lowercase letters are allowed.
The Roman Numeral symbols have the following decimal values:
I=1, V=5, X=10, L=50, C=100,D=500, M=1000
The symbols are written in additive (or subtractive) order from left to right. For example:
I=1, II=2, III=3, IV=4 (5-1)V=5, VI=6 (5+1), VII=7 (5+2)VIII=8 (5+3), IX=9 (10-1)
To represent large numbers the symbols are marked with an overline to indicate multiplication
by 1000:
I=1000,
V=5000,
X=10000,L=50000,
C=100000,
D=500000,M=1000000
To allow you to enter large Roman Numeral values into the converter, we use the underscore keyboard symbol
instead of the overline, to indicate multiplication by 1000.
For example, to represent decimal 158243, the converter writes:
_C_L_VMMMCCXLIII
Instead of the way it was written in ancient Rome:
CLVMMMCCXLIIIMaximum Input Length – Roman Numerals
The Roman Numeral input field is limited to a maximum of 2020 characters. That is sufficient to
represent the decimal number 999999999.

Radix-10

Decimal or Radix-10 Number System
Decimal is a Radix-10 positional notation number system. Radix-10 or Base-10 means that each Decimal "digit"
represents a multiple of increasing powers of 10, from right to left, such as:
... 10^{3}, 10^{2}, 10^{1}, 10^{0}
The valid Decimal symbols are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
For example, the Decimal number 927 represents the following numerical expression:
(9 x 10^{2}) + (2 x 10^{1}) + (7 x 10^{0})History of the Decimal Number System
The modern Decimal number system, known as the Hindu-Arabic number system, originated in India around the 9th century CE.
The system spread to the western world during the Middle Ages (1000 to 1300 CE) as a result of trade.
Some scholars attribute the first documented use of a Decimal system to China in the 1st century BCE.
Maximum Input Length – Decimal
The Decimal input field is limited to a maximum of 9 characters. That is sufficient to
represent the decimal number 999999999.

Roman Numeral Construction Rules

Additive Principle
Roman Numerals are written in sequential additive order from left to right.
Roman Numeral symbols have these values:
I=1, V=5, X=10, L=50, C=100,D=500, M=1000
So for example, the Roman Numeral MMVIII, is interpreted as the additive sequence:
1000 + 1000 + 5 + 3 = 2008Subtractive Principle
The Subtractive Principle dictates that when a symbol of smaller value comes before a
symbol of larger value, the smaller value is subtracted from the larger value,
and the result is added to the cumulative total.
For example, in the Roman Numeral MCMXLIV,
the symbol C (100) comes before M (1000),
so subtract C from M (1000-100=900), and
add the result (900) to the cumulative total.
Also, X (10) comes before L (50), so we
subtract X from L (50-10=40), and add the
result (40) to the cumulative total.
Finally, I (1) comes before V (5), so we
subtract I from V (5-1=4), and add the
result (4) to the cumulative total.
So the Roman Numeral MCMXLIV, is interpreted as the additive and subtractive sequence:
1000+(1000-100)+(50-10)+(5-1) = 1944Separate the Powers of Ten
As a rule, build the highest power of ten first, then add more Roman Numerals to the right
for each successively smaller power of ten.
For example, to build the Roman Numeral for decimal 3889, start
with 3000 (MMM), add 800 (DCCC),
add 80 (LXXX), and finally add 9 (IX)MMMDCCCLXXXIX