Octal to Decimal Converter
Convert octal to decimal instantly with an exact base-8 to base-10 converter. Enter any valid octal integer to get its decimal value, positional powers-of-8 breakdown, digit count, verified examples, and conversion tables.
What Is an Octal to Decimal Converter?
An octal to decimal converter changes an integer written in the octal number system (base 8) into its equivalent decimal number system (base 10) value.
Octal uses only digits 0 through 7. Each digit occupies a position whose weight is a power of 8. Starting from the rightmost digit, those place values are 8⁰, 8¹, 8², 8³, and so on.
To convert manually, multiply each octal digit by its positional power of 8 and add all the resulting values. BinaryCon performs the same mathematical conversion using exact integer arithmetic.
Octal — Base 8
Uses digits 0–7 and positional values 1, 8, 64, 512, 4096, and beyond.
Decimal — Base 10
Uses digits 0–9 and is the everyday number system used for ordinary counting.
How to Use the Octal to Decimal Converter
Type a value such as 377. Valid octal input contains only
digits 0 through 7.
BinaryCon evaluates the octal place values and returns the exact decimal integer.
The result card displays the base-10 value in ordinary decimal notation.
For shorter inputs, the tool shows how each octal digit contributes a digit × power-of-8 term.
Use the decimal value in calculations, programming, permissions, coursework, or another converter.
Octal to Decimal Formula
If an octal number has digits
dₙ dₙ₋₁ ... d₁ d₀, its decimal value is:
The rightmost octal digit always uses 8⁰ = 1, the next digit uses 8¹ = 8, the next uses 8² = 64, and so on.
Worked Example: Convert Octal 377 to Decimal
Octal 377₈ has three digits.
7 × 8¹
7 × 8⁰ Evaluate the powers: 3 × 64 = 192
7 × 8 = 56
7 × 1 = 7 Add the results: 192 + 56 + 7 = 255 Therefore: 377₈ = 255₁₀
Example: Convert Octal 55 to Decimal
Octal to Decimal Conversion Table
| Octal | Decimal | Octal | Decimal |
|---|---|---|---|
0 | 0 | 10 | 8 |
1 | 1 | 11 | 9 |
2 | 2 | 12 | 10 |
3 | 3 | 13 | 11 |
4 | 4 | 14 | 12 |
5 | 5 | 15 | 13 |
6 | 6 | 16 | 14 |
7 | 7 | 17 | 15 |
20 | 16 | 40 | 32 |
77 | 63 | 100 | 64 |
177 | 127 | 200 | 128 |
377 | 255 | 400 | 256 |
777 | 511 | 1000 | 512 |
Important Powers of Eight
| Power | Decimal Value | Octal Benchmark |
|---|---|---|
| 8⁰ | 1 | 1 |
| 8¹ | 8 | 10 |
| 8² | 64 | 100 |
| 8³ | 512 | 1000 |
| 8⁴ | 4,096 | 10000 |
| 8⁵ | 32,768 | 100000 |
| 8⁶ | 262,144 | 1000000 |
Why Octal 10 Equals Decimal 8
In any positional number system, writing 10 means one unit of
the base and zero units of one.
This is why identical digit strings can have different numeric values when their bases are different.
Why Octal Cannot Contain 8 or 9
Octal is a base-8 system, so exactly eight digit values are available: 0, 1, 2, 3, 4, 5, 6, and 7.
Once the count moves past octal digit 7, a carry occurs:
10₈ = 8₁₀
11₈ = 9₁₀
Octal 755 in Decimal
Octal 755 is familiar because of Unix file permissions.
As an ordinary octal integer:
So the numeric decimal value of octal 755 is 493. In a permission context, however, the octal digits are usually more useful as separate three-bit permission groups than as a single decimal integer.
Octal, Decimal, and Binary Relationship
Octal is closely related to binary because every octal digit corresponds to three binary bits. Decimal has no such fixed-bit grouping relationship.
| Octal | Binary | Decimal |
|---|---|---|
| 0 | 000 | 0 |
| 1 | 001 | 1 |
| 2 | 010 | 2 |
| 3 | 011 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
Where Octal to Decimal Conversion Is Useful
Programming
Developers may encounter octal literals, masks, file modes, character escapes, or values from legacy systems.
Unix permissions
Octal permission values are often examined digit by digit, but converting them to decimal can still help when analyzing their numeric value.
Digital systems
Octal may appear as compact shorthand for binary data grouped into sets of three bits.
Computer science education
Octal-to-decimal exercises reinforce positional notation, powers of eight, and base conversion fundamentals.
Common Octal to Decimal Conversion Mistakes
Octal is base 8, so place values are powers of 8, not powers of 10.
The rightmost digit always has exponent zero: 8⁰ = 1.
Those digits do not exist in standard octal notation.
Octal 100 means 1×8², so its decimal value is 64.
Related BinaryCon Tools
Convert octal to binary or hexadecimal, reverse this conversion, or continue working with other number systems.
Octal to Decimal Converter FAQs
How do you convert octal to decimal?
Multiply each octal digit by the corresponding power of 8 and add the results. The rightmost digit uses 8⁰, the next uses 8¹, then 8², and so on.
What is octal 10 in decimal?
Octal 10 equals 8 decimal.
It represents 1×8¹ + 0×8⁰.
What is octal 12 in decimal?
Octal 12 equals decimal 10 because
1×8 + 2 = 10.
What is octal 55 in decimal?
Octal 55 equals decimal 45.
The calculation is 5×8 + 5 = 40 + 5.
What is octal 377 in decimal?
Octal 377 equals decimal 255:
3×64 + 7×8 + 7 = 192 + 56 + 7 = 255.
What is octal 1000 in decimal?
Octal 1000 equals decimal 512 because
it represents 1×8³.
What is octal 755 in decimal?
As a numeric octal integer, 755₈ equals
493 decimal: 7×64 + 5×8 + 5 = 493.
Can an octal number contain 8 or 9?
No. Valid standard octal digits are only 0 through 7. A value containing 8 or 9 must belong to another notation or contains an input error.
Why is 100 octal equal to 64 decimal?
In base 8, the digits in 100 represent
1×8² + 0×8¹ + 0×8⁰. Since 8² = 64, the decimal value is 64.
Can this converter handle very large octal integers?
Yes. The converter uses JavaScript BigInt to preserve exact integer precision rather than relying on ordinary floating-point numbers.
Does a leading zero change an octal integer?
Numerically, leading zeros do not change the value of an unsigned octal
integer. For example, 377 and 0377 both have
decimal value 255 when treated as base-8 numerals.
Is octal-to-decimal conversion exact?
Yes for integers. Each octal digit has an exact power-of-8 place value, so the equivalent decimal integer requires no approximation or rounding.
Does this calculator support octal fractions?
This page is designed for octal integers. Fractions use negative powers of eight to the right of the radix point and require separate fractional processing.
Convert Octal to Decimal Instantly
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