Enter a base-10 number or a base-9 number into the calculator to convert between base 10 and base 9.

Base 9 Calculator

Enter one value to calculate the other

Base 9 Formula

The following formula is used to calculate the base 10 (decimal) value of a base 9 number.

N_{10} = \sum (d_n \cdot 9^n)

Variables:

  • N10 is the value in base 10 (decimal)
  • d is a digit in the base 9 number (0–8)
  • n is the position of the digit in the base 9 number, starting from 0 on the right

To calculate the base 10 value of a base 9 number, multiply each base 9 digit by 9 raised to the power of its position, then sum the results.

What is a Base 9?

Base 9, also known as nonary, is a numeral system that uses nine as its base. It uses digits from 0 to 8. It’s a positional numeral system, meaning the position of a digit in a number determines its value. For example, in the base 9 number 123, the 1 represents 81 (9^2), the 2 represents 18 (9^1), and the 3 represents 3 (9^0).

How to Convert a Base 9 Number to Base 10?

The following steps outline how to convert a base 9 number to base 10 using the formula: N10 = ∑ (d · 9n).

  1. First, determine the digit (d) in the base 9 number (0–8).
  2. Next, determine the position of the digit (n) in the base 9 number, starting from 0 on the right.
  3. Next, calculate the value of (9^n).
  4. Multiply the digit (d) by the value of (9^n).
  5. Repeat steps 1-4 for each digit in the base 9 number.
  6. Finally, sum up all the results from step 4 to get the base 10 (decimal) value.

Example Problem:

Use the following variables as an example problem to test your knowledge.

digit (d) = 7

position of the digit (n) = 2

Calculate the base 10 value contributed by this digit (d · 9n). (If it is the only nonzero digit, the corresponding base 9 number would be 7009.)