Calculate base 10 and base 9 conversions by entering one number to find the equivalent value in the other numeral system with steps shown.
- Base 8 Calculator
- Binary Coded Decimal Calculator
- Log Base 2 Calculator
- Exponent Calculator
- All Math and Numbers Calculators
Base 9 Calculator Formula
The calculator converts whole numbers between base 10 and base 9. Base 9 uses only the digits 0 through 8. Each place value is a power of 9.
Base 9 to Base 10
N_{10} = d_n*9^n + d_{n-1}*9^{n-1} + ... + d_1*9^1 + d_0*9^0- N10 is the value of the number in base 10.
- d is a digit in the base 9 number.
- n is the highest place-value position, counting from 0 on the right.
- 9 is the base.
Base 10 to Base 9
N_{10} = q*9 + r- N10 is the base 10 number being converted.
- q is the quotient after dividing by 9.
- r is the remainder, which becomes a base 9 digit.
To convert from base 10 to base 9, divide the number by 9 repeatedly and record the remainders. Read the remainders from last to first to get the base 9 number.
To convert from base 9 to base 10, multiply each digit by its place value and add the results. Negative numbers keep the same negative sign after conversion.
Base 9 Place Values and Common Conversions
Use these tables to check the size of each place in a base 9 number and to compare common base 10 and base 9 values.
| Base 9 place | Power of 9 | Base 10 value |
|---|---|---|
| 1s place | 90 | 1 |
| 9s place | 91 | 9 |
| 81s place | 92 | 81 |
| 729s place | 93 | 729 |
| 6561s place | 94 | 6561 |
| Base 10 | Base 9 | Note |
|---|---|---|
| 8 | 8 | Largest single digit in base 9 |
| 9 | 10 | One group of 9 and zero 1s |
| 10 | 11 | One 9 and one 1 |
| 80 | 88 | Last two-digit base 9 number |
| 81 | 100 | One group of 81 |
Example Problems
Example 1: Convert 125 from base 10 to base 9
Divide by 9 and keep the remainders:
- 125 ÷ 9 = 13 remainder 8
- 13 ÷ 9 = 1 remainder 4
- 1 ÷ 9 = 0 remainder 1
Read the remainders from last to first:
12510 = 1489
Example 2: Convert 572 from base 9 to base 10
Expand the number using powers of 9:
5729 = 5×92 + 7×91 + 2×90
5729 = 5×81 + 7×9 + 2×1
5729 = 405 + 63 + 2 = 470
5729 = 47010
FAQ
What digits are allowed in base 9?
Base 9 allows the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8. The digit 9 is not valid in base 9 because 9 is written as 109.
Why does 10 in base 9 equal 9 in base 10?
In base 9, the number 10 means one group of 9 and zero ones. So 109 equals 910, not ten in base 10.
Can base 9 numbers be negative?
Yes. A negative sign can be placed before a base 9 number. The digits are converted the same way as a positive number, and the negative sign is kept in the final result.
