Octal Calculator
Perform octal (base-8) arithmetic and convert between octal, decimal, binary and hex.
About Octal Calculator
Octal (base-8) uses digits 0–7. Each octal digit maps to exactly three binary digits, making it a compact notation for binary data. Arithmetic in octal works the same as decimal — carry at 8 instead of 10. To perform arithmetic, the calculator converts both operands to decimal, applies the operation, and converts the result back to octal, binary and hexadecimal.
Formula
Octal to Decimal
decimal = Σ(digit_i × 8^i) for i from 0 to n-1
- digit_i
- The ith octal digit (from the right, 0-indexed)
- i
- Position index
Worked example
With the default values below, Octal Calculator returns Result (Octal) of 24. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Octal Number A
- 17
- Operationone of Add (+), Subtract (−), Multiply (×), Divide (÷), Convert only
- Add (+)
- Octal Number B
- 5
Results
- Result (Octal)
- 24
- Result (Decimal)
- 20
- Result (Binary)
- 10100
- Result (Hex)
- 14
Step by step
- 1Operation
- 2Decimal values
- 3Result (decimal)= 20
- 4Result (octal)= 24
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is octal useful?
Each octal digit corresponds to exactly three binary bits, so octal is a concise way to represent binary data. It is used in Unix file permissions (e.g. 755) and some legacy computing contexts.
How do I convert octal to decimal by hand?
Multiply each digit by 8 raised to its position (rightmost is position 0) and sum: 17₈ = 1×8¹ + 7×8⁰ = 8 + 7 = 15.