Octal to Decimal Converter

Enter an octal number below to convert it to decimal.

Decimal Number:

Steps to Convert to Decimal

Learn how we calculated this below

How to Convert Octal to Decimal

The octal number system is a base 8 number system since it uses just eight digits, 0 to 7. On the other hand, decimal is a base 10 number system since it uses ten digits, 0 to 9.

When working with octal numbers, you’ll often need to convert the number to its decimal value since most people use the decimal system.

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, so the hexadecimal system is more commonly used today.

To convert an octal number to a decimal, you can use the positional notation method. To use this method, multiply each octal digit number from the rightmost number 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