Decimal (Base 10) to Vigesimal (Base 20) Converter
Convert decimal numbers to vigesimal.
255 (base 10) = CF (base 20)
Digits in base 10: 0 to 9. Digits in base 20: 0 to 9 and A to J.
How to convert Decimal to Vigesimal
Every positional number system works the same way: a digit is worth its own value times the base raised to the power of its position. In base 10 the place values, from the right, are 100 = 1, 101 = 10, 102 = 100 and so on.
To get from decimal to base 20, divide the number by 20 over and over. Every remainder is one digit of the answer, starting with the last digit, so you read the remainders from the bottom up.
The method
divide by 20, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to firstdigits in base 10: 0 to 9digits in base 20: 0 to 9 and A to J
Worked example 1: 45 from decimal to vigesimal
45 ÷ 20 = 2 remainder 52 ÷ 20 = 0 remainder 2Read the remainders from the bottom up: 2545 (base 10) = 25 (base 20)
Letters stand for values from 10 up: A = 10, B = 11, C = 12 and so on. Remainders come out last digit first, which is why you read them from the bottom up.
Worked example 2: 255 from decimal to vigesimal
255 ÷ 20 = 12 remainder 15 (F)12 ÷ 20 = 0 remainder 12 (C)Read the remainders from the bottom up: CF255 (base 10) = CF (base 20)
Worked example 3: 1000 from decimal to vigesimal
1,000 ÷ 20 = 50 remainder 050 ÷ 20 = 2 remainder 10 (A)2 ÷ 20 = 0 remainder 2Read the remainders from the bottom up: 2A01000 (base 10) = 2A0 (base 20)
Need the other direction? Open the Vigesimal to Decimal converter.
Decimal to Vigesimal examples
The decimal number 255 is written 255 in decimal and CF in vigesimal.
| Decimal | Vigesimal |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 7 | 7 |
| 8 | 8 |
| 10 | A |
| 15 | F |
| 16 | G |
| 32 | 1C |
| 64 | 34 |
| 100 | 50 |
| 255 | CF |
| 1000 | 2A0 |
Where Decimal to Vigesimal comes up
Decimal is the base 10 system everyone learns first, with the digits 0 to 9. It is the form people read: prices, measurements, ages and IDs. It is also the base we calculate in by hand, which is why the worked steps on this page pass through decimal.
Vigesimal counts in twenties, with the digits 0 to 9 and A to J. The Maya wrote numbers in a base 20 system, and French still says quatre-vingts, four twenties, for 80.
Going to a larger base packs more value into each digit, so the result is shorter. The number 255 needs 3 digits in decimal and 2 in vigesimal.
Decimal to Vigesimal FAQ
How do I convert decimal to vigesimal?
Divide the decimal number by 20, write down the remainder, and repeat with the quotient until it reaches 0. The remainders, read from last to first, are the base 20 number.
Which digits does decimal use?
Base 10 uses the digits 0 to 9. For example, A is not a valid digit in base 10.
Will the vigesimal number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.77 vigesimal digits for every decimal digit. The number 255 needs 3 digits in decimal and 2 in vigesimal.
What is 255 in vigesimal?
255 in decimal is CF in vigesimal. Both are the decimal number 255.
Can I convert negative numbers or fractions?
The converter handles whole numbers, and a leading minus sign works for negatives. Fractions use a different method, where you repeatedly multiply the fractional part by the new base, and they are not supported here.