Octal to Decimal Converter

Convert octal (base-8) numbers to decimal (base-10) instantly with a step-by-step calculation breakdown. Supports batch conversion and reverse direction.

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Octal → Decimal

Common Octal to Decimal Values

10
= 8
77
= 63
100
= 64
144
= 100
377
= 255
644
= 420
755
= 493
777
= 511
1000
= 512
1777
= 1023
3777
= 2047
7777
= 4095

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Bidirectional

Convert octal to decimal and decimal back to octal. Click the Swap button to switch direction instantly.

Step-by-Step

See the full positional notation calculation showing how each octal digit contributes to the decimal result.

Batch Conversion

Convert multiple octal values at once. Enter space or comma-separated values for fast bulk conversion.

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Frequently Asked Questions

How do I convert octal to decimal?
Multiply each octal digit by 8 raised to the power of its position (starting from 0 on the right), then add all values together. For example, octal 175 = (1×8²) + (7×8¹) + (5×8&sup0;) = 64 + 56 + 5 = 125 in decimal.
What is the octal number system?
The octal number system is base-8, using digits 0 through 7. It was historically popular in computing because each octal digit represents exactly 3 binary bits. It's still used today in Unix/Linux file permissions (chmod 755), some programming languages (0o prefix in Python), and legacy systems.
What is octal 777 in decimal?
Octal 777 in decimal is 511. The calculation: (7×64) + (7×8) + (7×1) = 448 + 56 + 7 = 511. In Unix, chmod 777 grants full read, write, and execute permissions to owner, group, and others.
What is the difference between octal and decimal?
Decimal is base-10 (digits 0-9), the standard number system used in everyday life. Octal is base-8 (digits 0-7), used primarily in computing. Each place value in decimal is a power of 10, while in octal it's a power of 8. For example, 10 in decimal is ten, but 10 in octal equals eight.
Can I convert decimal back to octal?
Yes! Click the "Swap Direction" button to switch to Decimal → Octal mode. To manually convert, divide the decimal number by 8 repeatedly, recording each remainder. Read the remainders bottom-to-top. For example, 125 ÷ 8 = 15 r5, 15 ÷ 8 = 1 r7, 1 ÷ 8 = 0 r1, so 125 = octal 175.