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Octal Calculator Perform octal (base-8) arithmetic with decimal, binary, and hex conversions.

Octal Calculator illustration
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Octal Calculator

Perform octal (base-8) arithmetic with decimal, binary, and hex conversions.

1

Choose Operation

Select add, subtract, multiply, or divide.

2

Enter Octal Numbers

Type numbers using digits 0-7 only.

3

View Multi-Base Results

See the result in octal, decimal, binary, and hexadecimal.

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What Is Octal Calculator?

An octal calculator performs arithmetic on base-8 numbers, which use only the digits 0 through 7. The octal system has historical significance in computing — it was widely used in early minicomputers and mainframes because each octal digit represents exactly 3 binary bits, making conversion straightforward. Today, octal remains relevant in Unix/Linux file permissions (chmod 755), some programming contexts, and as an intermediate between binary and more complex bases. This calculator performs addition, subtraction, multiplication, and integer division on octal numbers, displaying results in all four common bases (octal, decimal, binary, hexadecimal) for easy cross-reference.

Why Use Octal Calculator?

  • Dedicated octal arithmetic operations
  • Real-time decimal preview of octal inputs
  • Multi-base output (octal, decimal, binary, hex)
  • Essential for Unix file permission calculations
  • Clean, simple interface for base-8 work

Common Use Cases

Linux Administration

Calculate file permissions using octal notation (chmod 755, 644, etc.).

Legacy Systems

Work with older computing systems that use octal representation.

Computer Science Education

Learn base-8 arithmetic and its relationship to binary.

Digital Systems

Work with systems where 3-bit groupings are natural.

Technical Guide

Octal (base-8) uses digits 0-7, where each digit represents exactly 3 binary bits: 0=000, 1=001, 2=010, ..., 7=111. Arithmetic follows standard positional notation rules: carry occurs when a column sum reaches 8. The most common modern use is Unix file permissions, where three octal digits represent owner/group/other permissions (read=4, write=2, execute=1, summed per category). The calculator parses octal strings using parseInt(value, 8), validates that only digits 0-7 are present, performs integer operations, and formats results using toString(8) for octal, toString(2) for binary, and toString(16) for hex output.

Tips & Best Practices

  • 1
    Each octal digit maps to exactly 3 binary bits
  • 2
    Unix permissions: 7=rwx, 6=rw-, 5=r-x, 4=r--, 0=---
  • 3
    Only digits 0-7 are valid in octal
  • 4
    Octal 10 = decimal 8 (not ten!)
  • 5
    Converting between octal and binary: group binary digits in threes

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Frequently Asked Questions

Q What digits are valid in octal?
Only 0, 1, 2, 3, 4, 5, 6, and 7. The digits 8 and 9 do not exist in base-8.
Q Why is octal used for file permissions?
Unix file permissions have three groups of three bits (owner, group, other), and each 3-bit group maps perfectly to one octal digit. So rwxr-xr-- = 754 in octal.
Q How do I convert octal to decimal?
Multiply each digit by 8 raised to its position power. For example, octal 17 = 1×8¹ + 7×8⁰ = 8 + 7 = 15 in decimal.
Q Is octal still used in modern computing?
While less common than hex, octal is still used for Unix/Linux file permissions, some C/C++ literal notations (prefixed with 0), and legacy system interfaces.
Q How does octal relate to binary?
Each octal digit = exactly 3 binary bits. To convert, group binary digits in sets of three from right to left and replace each group with its octal equivalent.

About This Tool

Octal Calculator is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.