Vigesimal (Base 20) to Decimal (Base 10) Converter
Convert vigesimal numbers to decimal.
CF (base 20) = 255 (base 10)
Digits in base 20: 0 to 9 and A to J. Digits in base 10: 0 to 9.
How to convert Vigesimal to Decimal
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 20 the place values, from the right, are 200 = 1, 201 = 20, 202 = 400 and so on.
To get from base 20 to decimal, multiply each digit by 20 raised to the power of its position, counting from 0 on the right, and add the results.
The method
decimal value = each digit × its place value, all added upplace values in base 20: 1, 20, 400, 8000, 160000, and so ondigits in base 20: 0 to 9 and A to Jdigits in base 10: 0 to 9
Worked example 1: 25 from vigesimal to decimal
25 (base 20) = 2 × 201 + 5 × 200= 40 + 5= 4525 (base 20) = 45 (base 10)
Letters stand for values from 10 up: A = 10, B = 11, C = 12 and so on. Digits that are 0 add nothing to the sum, so they are left out of the expansion.
Worked example 2: CF from vigesimal to decimal
CF (base 20) = 12 × 201 + 15 × 200= 240 + 15= 255CF (base 20) = 255 (base 10)
Worked example 3: 2A0 from vigesimal to decimal
2A0 (base 20) = 2 × 202 + 10 × 201= 800 + 200= 1,0002A0 (base 20) = 1000 (base 10)
Need the other direction? Open the Decimal to Vigesimal converter.
Vigesimal to Decimal examples
The decimal number 255 is written CF in vigesimal and 255 in decimal.
| Vigesimal | Decimal |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 7 | 7 |
| 8 | 8 |
| A | 10 |
| F | 15 |
| G | 16 |
| 1C | 32 |
| 34 | 64 |
| 50 | 100 |
| CF | 255 |
| 2A0 | 1000 |
Where Vigesimal to Decimal comes up
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.
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.
Going to a smaller base spreads the same value over more digits, so the result is longer. The number 255 needs 2 digits in vigesimal and 3 in decimal.
Vigesimal to Decimal FAQ
How do I convert vigesimal to decimal?
Multiply each base 20 digit by 20 raised to the power of its position, counting from 0 on the right, then add everything up.
Which digits does vigesimal use?
Base 20 uses the digits 0 to 9 and A to J. For example, K is not a valid digit in base 20. Letters are not case sensitive on this converter, and results are shown in capitals.
Will the decimal number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 1.3 decimal digits for every vigesimal digit. The number 255 needs 2 digits in vigesimal and 3 in decimal.
What is CF in decimal?
CF in vigesimal is 255 in decimal. 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.