Convert between decimal and octal with this base 8 calculator and see the converted value plus step-by-step conversion details shown below.
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Base 8 Formula
The base 8 calculator converts between decimal numbers and octal numbers. Octal, also called base 8, uses only the digits 0 through 7.
To convert an octal number to decimal, multiply each octal digit by a power of 8 based on its position, then add the results.
- Decimal is the base 10 value.
- d is an octal digit from 0 to 7.
- n is the position of the digit, counted from right to left starting at 0.
- 8 is the base used by octal numbers.
To convert a decimal number to octal, repeatedly divide the decimal number by 8 and record each remainder. The octal result is the remainders read from last to first.
- Decimal is the number being divided at each step.
- Quotient is the whole-number result after dividing by 8.
- Remainder is the digit used in the octal result.
If you enter a decimal value, the calculator returns the equivalent octal value. If you enter an octal value, the calculator expands each digit by powers of 8 and returns the decimal value.
Octal Place Values and Common Conversions
Use these tables to check how octal digits are weighted and to compare common decimal and octal values.
| Octal place | Power of 8 | Decimal value |
|---|---|---|
| 1s place | 80 | 1 |
| 8s place | 81 | 8 |
| 64s place | 82 | 64 |
| 512s place | 83 | 512 |
| 4096s place | 84 | 4096 |
| Decimal | Octal | Note |
|---|---|---|
| 8 | 10 | One group of 8 |
| 16 | 20 | Two groups of 8 |
| 64 | 100 | One group of 64 |
| 255 | 377 | Common 8-bit maximum |
Example Problems
Example 1: Convert octal 157 to decimal
Break the octal number into place values:
So, octal 157 equals decimal 111.
Example 2: Convert decimal 100 to octal
Divide by 8 and track the remainders:
- 100 ÷ 8 = 12 remainder 4
- 12 ÷ 8 = 1 remainder 4
- 1 ÷ 8 = 0 remainder 1
Read the remainders from bottom to top:
FAQ
What digits are allowed in base 8?
Base 8 uses the digits 0, 1, 2, 3, 4, 5, 6, and 7. The digits 8 and 9 are not valid in an octal number because each place represents powers of 8.
Why does octal 10 equal decimal 8?
In octal, 10 means one group of 8 and zero 1s. It does not mean ten in decimal. The value is calculated as 1 × 81 + 0 × 80, which equals 8.
How do you know which field to fill in?
Enter exactly one value. If you enter a decimal number, the calculator finds the octal value. If you enter an octal number, the calculator finds the decimal value. Leave the other field blank so the calculator knows which conversion to perform.
