Octal Calculator

The Octal Calculator performs arithmetic operations on octal (base 8) numbers. Octal uses only the digits 0-7, and each octal digit maps to exactly three binary bits. It is common in computing — most famously for Unix and Linux file permissions like chmod 755.

One digit, three bits. Because 8 = 2³, a single octal digit stands in for three binary digits, which makes octal a tidy shorthand for grouping bits — exactly how permission triplets work.

Common Use Cases

File Permissions

Work out Unix permission values such as 755 or 644 when setting access with chmod.

Bit Grouping

Represent binary data compactly by clustering bits into groups of three for clearer reading.

Learning & Homework

Verify octal arithmetic and base-conversion exercises for computer science coursework.

How to Use the Octal Calculator

Enter the First Number

Type the first octal number using only the digits 0-7. Input validation blocks invalid digits like 8 or 9. The 0o prefix is added for you.

Choose an Operator

Select an arithmetic operator: addition (+), subtraction (−), multiplication (×), division (÷), or modulo (%).

Enter the Second Number

Type the second octal value into the lower field, again using only valid octal digits 0-7.

Calculate & Read Results

Click Calculate or press Enter. The result is shown in binary, octal, decimal, and hexadecimal at once, each with a one-click copy button.

Quick start: Tap a Try examples chip to load a ready-made octal expression, then change the operands to watch the result update across all four bases.

Features

Supported Arithmetic Operations

The Octal tab supports the five core arithmetic operators. Each row below shows a worked octal example with its decimal equivalent.

Operator	Name	Example (octal)	Decimal
`+`	Addition	17 + 5 = 24	15 + 5 = 20
`−`	Subtraction	77 − 33 = 44	63 − 27 = 36
`×`	Multiplication	12 × 3 = 36	10 × 3 = 30
`÷`	Division	100 ÷ 4 = 20	64 ÷ 4 = 16
`%`	Modulo	17 % 5 = 2	15 % 5 = 0

What the Tool Gives You

Results in Four Bases

Every answer appears at once in binary, octal, decimal, and hexadecimal — no manual conversion required.

Large-Number Support

BigInt arithmetic keeps even long octal values exact instead of rounding them.

Input Validation

Only valid octal digits 0–7 are accepted, so invalid entries are caught before you calculate.

Quick Examples

One-tap example expressions for common octal calculations, plus a built-in operator reference panel.

Need bitwise operations? AND, OR, XOR, and shifts act on raw bits and live on the Binary tab. The Octal tab focuses on the five arithmetic operators.

Frequently Asked Questions

What is octal?

Octal is a base-8 number system using the digits 0-7. Each octal digit represents exactly 3 binary bits. For example, octal 17 equals decimal 15 (1 × 8 + 7).

Why is octal used?

Octal is a compact way to represent binary data. It is most commonly used in Unix/Linux file permissions (such as chmod 755) and in some programming contexts where grouping bits in threes is convenient.

How do I convert octal to decimal?

Multiply each digit by its place value (powers of 8) and add them. For example: 17₈ = 1 × 8¹ + 7 × 8⁰ = 8 + 7 = 15₁₀.

What does chmod 755 mean?

Each octal digit sets one permission group: 755 means rwxr-xr-x — the owner can read, write, and execute, while group and others can read and execute. The digit 7 is 4 + 2 + 1 (read + write + execute).