Octal to Decimal Converter

Enter an octal number below to convert it to decimal.

Decimal Number:

Steps to Convert to Decimal

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How to Convert Octal to Decimal

The octal number system is a base 8 number system that uses eight digits, from 0 to 7. The decimal number system, on the other hand, is a base 10 number system that uses ten digits, 0 to 9.

When working with octal numbers, you’ll often need to convert the number to its decimal value, considering the decimal system is most commonly used.

The base 8 system is often used in legacy computing applications because a single octal digit can represent three binary bits, which are cleanly divisible in 6, 12, 24, and 36-bit computer systems. Most modern computer systems, however, are 16, 32, or 64-bit systems, which are cleanly divisible into base 16 numbers.

Therefore, the hexadecimal system is more commonly used today.

To convert an octal number to a decimal number, you can use the positional notation method. To use this method, multiply each octal digit number starting from the rightmost number, moving to the left by 8 to the power of n, where n is the distance from the right.

So, reading the octal number from right to left, the furthest digit to the right is equal to the digit times 8⁰. The digit that is one position from the right is equal to the digit times 8¹.

Octal to Decimal Formula

The octal to decimal formula can be expressed as:

decimal number₁₀ = (d₀ × 8⁰) + (d₁ × 8¹) + … + (d_{n – 1} × 8^{n – 1})

When using the formula, d₀ is the octal digit furthest to the right, d₁ is the digit one position from the right, and d_{n – 1} is the digit furthest to the left.

For example, let’s convert the octal number 730 to decimal.

decimal number₁₀ = (7 × 8²) + (3 × 8¹) + (0 × 8⁰)
decimal number₁₀ = 448 + 24 + 0
decimal number₁₀ = 472

Octal to Decimal Conversion Table

The table below shows octal numbers and the equivalent decimal number values.

Octal numbers converted to the equivalent decimal values
Octal Number	Decimal Number
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
10	8
11	9
12	10
13	11
14	12
15	13
16	14
17	15
20	16
21	17
22	18
23	19
24	20
25	21
26	22
27	23
30	24
31	25
32	26
33	27
34	28
35	29
36	30
37	31
40	32
100	64
200	128
400	256
1000	512
2000	1024
4000	2048

Frequently Asked Questions

When would you convert from octal to decimal?

You would convert from octal to decimal when you are working in legacy computing applications and need to convert a base 8 number to one that is more easily readable.

Why is there no 9 in octal?

There is no 9 in octal because each digit represents a power of 8, and so the “ones” digit only contains numbers 0-7.

How do you know if a number is octal or decimal?

By just looking at a number, one cannot tell if it is octal or decimal unless it has a prefix. The prefix for an octal number is “0o” and is most often used when working with octal numbers in computing applications.