# Decimal to Octal Converter

To use this decimal to octal converter, you must type a decimal value like 245 into the left field below, and then hit the Convert button. The converter will give you the octal equivalent of the given decimal number.

swap conversion: Octal To Decimal Converter
Decimal to octal conversion result in base numbers

## Decimal System

The decimal numeral system is the most commonly used and the standard system in daily life. It uses the number 10 as its base (radix). Therefore, it has 10 symbols: The numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

As one of the oldest known numeral systems, the decimal numeral system has been used by many ancient civilizations. The difficulty of representing very large numbers in the decimal system was overcome by the Hindu–Arabic numeral system. The Hindu-Arabic numeral system gives positions to the digits in a number and this method works by using powers of the base 10; digits are raised to the nth power, in accordance with their position.

For instance, take the number 2345.67 in the decimal system:

• The digit 5 is in the position of ones (100, which equals 1),
• 4 is in the position of tens (101)
• 3 is in the position of hundreds (102)
• 2 is in the position of thousands (103)
• Meanwhile, the digit 6 after the decimal point is in the tenths (1/10, which is 10-1) and 7 is in the hundredths (1/100, which is 10-2) position
• Thus, the number 2345.67 can also be represented as follows: (2 * 103) + (3 * 102) + (4 * 101) + (5 * 100) + (6 * 10-1) + (7 * 10-2)

## The Octal System

The octal number system (or shortly oct) uses the number 8 as its base (radix). As a base-8 numeral system, it uses eight symbols: The numbers from 0 to 7, namely 0, 1, 2, 3, 4, 5, 6 and 7. Although it was used by some native American tribes until the 20th century, the octal system has become popular in the early ages of computing as a language of computer programming. This is because the octal system shortens binary by simplifying long and complex chains of binary displays used by computers.

The octal system is mainly used for counting binary in groups of three: Each octal digit represents three binary digits. Since 8 is 2 to the third power (23), the octal system became a perfect abbreviation of binary for machines that employ word sizes divisible by three - which were 6-bit, 12-bit, 24-bit or 36-bit. Nowadays, most modern systems use hexadecimal rather than octal. However, octal numbers are an important part of basic knowledge in electronics.

### How to Calculate Decimal to Octal

Decimal to octal conversion can be achieved by applying the repeated division and remainder algorithm. Simply put, the decimal number is repeatedly divided by the radix 8. In between these divisions, the remainders give the octal equivalent in reverse order.

Here is how to convert decimal to octal step by step:

• Step 1: If the given decimal number is less than 8, the octal equivalent is the same. If the given number is greater than 7, divide the number by 8.
• Step 2: Write down the remainder.
• Step 3: Divide the part before the decimal point of your quotient by 8 again.
• Step 4: Write down the remainder.
• Step 5: Continue this process of dividing by 8 and noting the remainders until the last decimal digit you are left with is less than 8.
• Step 6: When the last decimal digit is less than 8, the quotient will be less than 0 and the remainder will be the digit itself.
• Step 7: The last remainder you get will be the most significant digit of your octal value while the first remainder from Step 3 is the least significant digit. Therefore, when you write the remainders in reverse order - starting at the bottom with the most significant digit and going to the top- you will reach the octal value of the given decimal number.

Now, let's apply these steps to, for example, the decimal number (501)10

```Step 1: As 501 is greater than 7, divide by 8.
501 ÷ 8 = 62.625
Step 2: To calculate the remainder, you need to multiply the part after the decimal point by 8.
0.625 * 8 = 5
So the first remainder (and the least significant digit in the octal) is 5.
Step 3: Divide 62 (the part of the quotient that is before the decimal point) by 8.
62 ÷ 8 = 7.75
Step 4: Calculate the remainder.
0.75 * 8 = 6
Step 5: Divide the integer part of the last quotient by 8.
7 ÷ 8 = 0.875
Step 6: Calculate the remainder.
0.875 * 8 = 7
(Note that when you reached a number less than the radix 8 in Step 3, the remainder 7 was already obvious. This is because if a decimal number is less than 8, the octal equivalent has the same value.)
Step 7: The remainders written from below to top give you the octal number (765)8
Therefore, (765)8 equals (501)10
```

#### Decimal to Octal Conversion Examples

Example 1: (1465)10 = (2671)8

```1465 ÷ 8 = 183.125
0.125 * 8 = 1 (Remainder: 1)
183 ÷ 8 = 22.875
0.875 * 8 = 7 (Remainder 7)
22 ÷ 8 = 2.75
0.75 * 8 = 6 (Remainder 6)
2 ÷ 8 = 0.25
0.25 *8 = 2 (Remainder 2)
Read the remainder from the most significant to the least - from bottom to top: 2671.
This is the octal equivalent of (1465)10
```

Example 2: (8)10 = (10)8

```8 ÷ 8 = 1
Remainder 0
1 ÷ 8 = 0.125
0.125 * 8 = 1 (Remainder 1)
Read the remainder from the most significant to the least - from bottom to top: 10.
```

Example 3: (10)10 = (12)8

```10 ÷ 8 = 1.25
0.25 * 8 = 2 (Remainder 2)
1 ÷ 8 = 0.125 (Remainder 1)
Read the remainder from the most significant to the least - from bottom to top: 12.
```

Example 4: (1234)10 = (2322)8

```1234 ÷ 8 = 154.25 (Remainder 2)
154 ÷ 8 = 19.25 (Remainder 2)
19 ÷ 8 = 2.375 (Remainder 3)
2 ÷ 8 = 0.25 (Remainder 2)
The octal number is 2322.
```
##### Decimal to Octal Conversion Chart Table
DecimalOctal
11
22
33
44
55
66
77
810
911
1012
1113
1214
1315
1416
1517
1620
1721
1822
1923
2024
2125
2226
2327
2430
2531
2632
2733
2834
2935
3036
3137
3240
3341
3442
3543
3644
3745
3846
3947
4050
4151
4252
4353
4454
4555
4656
4757
4860
4961
5062
5163
5264
5365
5466
5567
5670
5771
5872
5973
6074
6175
6276
6377
64100
DecimalOctal
65101
66102
67103
68104
69105
70106
71107
72110
73111
74112
75113
76114
77115
78116
79117
80120
81121
82122
83123
84124
85125
86126
87127
88130
89131
90132
91133
92134
93135
94136
95137
96140
97141
98142
99143
100144
101145
102146
103147
104150
105151
106152
107153
108154
109155
110156
111157
112160
113161
114162
115163
116164
117165
118166
119167
120170
121171
122172
123173
124174
125175
126176
127177
128200
DecimalOctal
129201
130202
131203
132204
133205
134206
135207
136210
137211
138212
139213
140214
141215
142216
143217
144220
145221
146222
147223
148224
149225
150226
151227
152230
153231
154232
155233
156234
157235
158236
159237
160240
161241
162242
163243
164244
165245
166246
167247
168250
169251
170252
171253
172254
173255
174256
175257
176260
177261
178262
179263
180264
181265
182266
183267
184270
185271
186272
187273
188274
189275
190276
191277
192300
DecimalOctal
193301
194302
195303
196304
197305
198306
199307
200310
201311
202312
203313
204314
205315
206316
207317
208320
209321
210322
211323
212324
213325
214326
215327
216330
217331
218332
219333
220334
221335
222336
223337
224340
225341
226342
227343
228344
229345
230346
231347
232350
233351
234352
235353
236354
237355
238356
239357
240360
241361
242362
243363
244364
245365
246366
247367
248370
249371
250372
251373
252374
253375
254376
255377

Wyatt 2024-03-22 13:53:46

More than 255 for the translation on the chart

Akshay Raut 2022-08-05 16:04:18

it is very helpful for me. Thanks for making such great software.

Simran Saxena 2022-06-29 07:06:43

Awesome explanation

Mofor Augustine 2022-06-19 05:38:40

I would really love to learn

Abubakar Ibrahim usman 2022-03-15 21:23:32

I really appreciate, I achieved a lot from you thank you .

Very good and very help full

Vasl 2022-02-04 18:36:14

Awesome Explanation. Thank you!

Guest 2021-09-02 15:56:30

Very good for check

Guest 2021-07-07 13:23:04

Absolutely wonderful explanation. Loved it!!

Paris 2021-06-05 09:19:37

Thanks the process is very simple

Abdullrhman Elhelw 2021-03-05 12:09:30

this site is Amazing thanks for your help

Varney S. Butler 2020-11-26 06:36:45

This step is very easy to understand, thanks for putting together the materials.

Guest 2020-10-04 17:01:36

This was really helpful, best explanation i have found.

Alisha 2020-09-02 05:20:43

Tahura 2020-07-29 03:59:41

Awesome it help me so much thanks

Mithesh Ballae Ganesh 2020-07-26 09:29:37

VERY GOOD , I USE TO CHEAT ALL TESTS