# 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 8^{0}. The digit that is one position from the right is equal to the digit times 8^{1}.

### Octal to Decimal Formula

The octal to decimal formula can be expressed as:

decimal number_{10} = (d_{0} × 8^{0}) + (d_{1} × 8^{1}) + … + (d_{n – 1} × 8^{n – 1})

When using the formula, d_{0} is the octal digit furthest to the right, d_{1} 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 number_{10} = (7 × 8^{2}) + (3 × 8^{1}) + (0 × 8^{0})

decimal number_{10} = 448 + 24 + 0

decimal number_{10} = 472

## Octal to Decimal Conversion Table

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