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Calculator

Welcome to our Convert Octal to Decimal page.

This converter will convert from octal numbers to decimal, or from decimal numbers to octal (base 8).

Our converter will also show you detailed working out so you can create your own worked examples!

How It Works

Here is our octal conversion calculator which will help you to convert octal to decimal and decimal to octal.

The converter will also show you the formula and working out you need to convert between units.

Convert Octal to Decimal Calculator - How It Works...

Step 1) Choose which calculator you want - octal to decimal or decimal to octal

Step 2) Type in the number you want to convert.

Step 3) Click the Convert button and the answer will be displayed.

How to convert octal to decimal

To convert an octal number (base-8) to the decimal (base-10) number system, we need to use octal place value to add the base-10 value of each digit.

In the octal place value system, each time you move a place to the left, the value increases eight-fold.

In octal, the digit values go from zero to seven; numbers 8 and 9 are not allowed!

This table above shows the number 326,107 in the octal number system.

1) Convert 275 from octal to decimal.

Step 1) Write down the place value of each digit.

8^{2} |
8^{1} |
8^{0} |
---|---|---|

64 | 8 | 1 |

2 | 7 | 5 |

Step 2) Add up the place value of each digit.

64x2 + 8x7 + 1x5

= 128 + 56 + 5 = 189

So 275 in octal is equal to 189.

2) Convert 3250 from octal into decimal.

Step 1) Write down the place value of each digit.

8^{3} |
8^{2} |
8^{1} |
8^{0} |
---|---|---|---|

512 | 64 | 8 | 1 |

3 | 2 | 5 | 0 |

Step 2) Add up the place value of each digit.

512x3 + 64x2 + 8x5 + 1x0

1536 + 128 + 40 + 0 = 1704

So 3250 in octal is equal to 1704.

How to convert from decimal to octal

To convert a decimal number (base-10) to the octal (base-8) number system, we need to change the decimal base-10 place value into octal base-8 place value.

We can do this in different ways by using division and looking at quotients and remainders.

The best way to see this is to look at some worked examples .

Example 1) Convert 139 from decimal to octal.

Step 1) Look at what octal place values we need.

The powers of 8 are 1, 8, 64, 512, 4096, ...

Our value is just 139, so the powers of 8 we need are 1, 8 and 64 (up to 8^{2}).

Step 2) Divide 139 by the highest place value number.

So we now divide 139 by 64 = 2 r. 11

The quotient tells us what number goes into with the place value of 64, which is 2.

8^{2} |
8^{1} |
8^{0} |
---|---|---|

64 | 8 | 1 |

2 | ? | ? |

Step 3) We now divide the remainder by the next (lower) power of 8.

So we have 11 ÷ 8 = 1 r. 3

The quotient us what number goes with the place value of 8, which is 1.

8^{2} |
8^{1} |
8^{0} |
---|---|---|

64 | 8 | 1 |

2 | 1 | ? |

Step 4) Divide the remainder by the next (lower) power of 8.

So we have 3 ÷ 1 = 3

This tells us which number goes with the place value of 1s which is 3.

8^{2} |
8^{1} |
8^{0} |
---|---|---|

64 | 8 | 1 |

2 | 1 | 3 |

Step 5) Put your place value parts together.

Our number 139 = 64x2 + 8x1 + 1x3.

So our octal answer is 213.

Example 2) Convert 946 from decimal to octal.

Step 1) Look at what octal place values we need.

The powers of 8 are 1, 8, 64, 512, 4096, ...

Our value is just 946, so the powers of 8 we need are 1, 8, 64 and 512(up to 8^{3}).

Step 2) Divide 946 by the highest place value number.

So we now divide 946 by 512 = 1 r. 434

The quotient tells us what number goes into with the place value of 512, which is 1.

8^{3} |
8^{2} |
8^{1} |
8^{0} |
---|---|---|---|

512 | 64 | 8 | 1 |

1 | ? | ? | ? |

Step 3) We now divide the remainder by the next (lower) power of 8.

So we have 434 ÷ 64 = 6 r. 50

The quotient us what number goes with the place value of 64, which is 6.

8^{3} |
8^{2} |
8^{1} |
8^{0} |
---|---|---|---|

512 | 64 | 8 | 1 |

1 | 6 | ? | ? |

Step 4) We now divide the remainder by the next (lower) power of 8.

So we have 50 ÷ 8 = 6 r. 2

The quotient us what number goes with the place value of 8, which is 6.

8^{3} |
8^{2} |
8^{1} |
8^{0} |
---|---|---|---|

512 | 64 | 8 | 1 |

1 | 6 | 6 | ? |

Step 5) We now divide the remainder by the next (lower) power of 8.

So we have 2 ÷ 1 = 2

The quotient us what number goes with the place value of 1s, which is 2.

8^{3} |
8^{2} |
8^{1} |
8^{0} |
---|---|---|---|

512 | 64 | 8 | 1 |

1 | 6 | 6 | 2 |

Step 6) Put your place value parts together.

Our number 946 = 512x1 + 64x6 + 8x6 + 1x2.

So our octal answer is 1662.

This quick conversion table converts octal numbers up to the value of (20)_{8} into decimal.

Octal | Decimal |
---|---|

00 | 0 |

01 | 1 |

02 | 2 |

03 | 3 |

04 | 4 |

05 | 5 |

06 | 6 |

07 | 7 |

10 | 8 |

11 | 9 |

12 | 10 |

13 | 11 |

14 | 12 |

15 | 13 |

16 | 14 |

17 | 15 |

20 | 16 |

Take a look at some more of our resources similar to our mm to inches conversion calculator.

Our number system converters will convert numbers from binary, octal or hexadecimal into decimal (or from decimal to binary, octal or hex).

The calculators also show you detailed working out so you can see how to do it yourself!

Here are some of our specific online calculators for converting between two units of measure.

Our prime number calculator will help you to find all the factors of any given number and tell you whether or not the number you are looking at is prime or not.

The calculator will also show you your number as a product of primes.

If you want to learn more about octal numbers, take a look at this article in the kiddle encyclopedia!

The article talks about the history of octal numbers, octal arithmetic and has some other facts too!

Using the link below will open the kiddle webpage in a new browser window.

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How to Print or Save these sheets

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