Octal to Decimal Converter

To use this octal (base-8) to decimal (base-10) conversion tool, you must type an octal value like 345 into the left field below and hit the Convert button. The converter will give you the decimal equivalent of the given octal.

swap conversion: Decimal To Octal Converter

Octal to decimal conversion result in base numbers

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.

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:


How to Calculate Octal to Decimal

An octal number can be converted to a decimal number by following simple rules. Here are two ways to convert octal to decimal step by step. The first is a more conventional method whereas the second one applies the repeated division and remainder algorithm technique in reverse.

Method 1:

Now, let’s apply these steps to, for example, the octal number (765)8

Step 1: This octal number has 3 digits.
Step 2: n is 3. 
Step 3: 5 is in position 1, so n-1 will be equal to 0. This will lead to 80
6 is in position 2, so n-1 will be 1. This will lead to 81;
7 is in position 3, so n-1 will be 2. This will lead to 82.
Step 4: (5 * 80) + (6 * 81) + (7 * 82)
Step 5: 5 + 48 + 448 = 501
Step 6: (501)10 equals (765)8

Method 2:

Let’s apply these steps to the same octal number above, (765)8

Step 1: Write down 0.
Step 2: Remove 7 (the leftmost digit) and add it to 0, which is 0 + 7 = 7. 
Step 3: Multiply the result by 8, which is 7 * 8 = 56.
Step 4: In the octal number (765)8, the leftmost digit is now 6. Add 6 to 56 and multiply the result by 8, which follows as: (6 + 56) * 8 = 496.
Step 5: In the octal number (765)8, we are only left with the digit 5. Therefore; 496 + 5 = 501.
Step 6: (501)10 equals (765)8

Example 1: (345)8 = (229)10

Method 1: 
(5 * 80) + (4 * 81) + (3 * 82) = 5 + 32 + 192 = 229

Method 2: 
0 + 3 = 3
3 * 8 = 24
24 + 4 = 28
28 * 8 = 224
224 + 5 = 229 

Example 2: (2675)8 = (1469)10

Method 1: 
(5 * 80) + (7 * 81) + (6 * 82) + (2 * 83) = 5 + 56 + 384 + 1024 = 1469

Method 2: 
0 + 2 = 2
2 * 8 = 16
16 + 6 = 22
22 * 8 = 176
176 + 7 = 183
183 * 8 = 1464
1464 + 5 = 1469

Related converters:
Decimal To Octal Converter

Octal Decimal Conversion Chart Table

OctalDecimal
11
22
33
44
55
66
77
108
119
1210
1311
1412
1513
1614
1715
2016
2117
2218
2319
2420
2521
2622
2723
3024
3125
3226
3327
3428
3529
3630
3731
4032
4133
4234
4335
4436
4537
4638
4739
5040
5141
5242
5343
5444
5545
5646
5747
6048
6149
6250
6351
6452
6553
6654
6755
7056
7157
7258
7359
7460
7561
7662
7763
10064
OctalDecimal
10165
10266
10367
10468
10569
10670
10771
11072
11173
11274
11375
11476
11577
11678
11779
12080
12181
12282
12383
12484
12585
12686
12787
13088
13189
13290
13391
13492
13593
13694
13795
14096
14197
14298
14399
144100
145101
146102
147103
150104
151105
152106
153107
154108
155109
156110
157111
160112
161113
162114
163115
164116
165117
166118
167119
170120
171121
172122
173123
174124
175125
176126
177127
200128
OctalDecimal
201129
202130
203131
204132
205133
206134
207135
210136
211137
212138
213139
214140
215141
216142
217143
220144
221145
222146
223147
224148
225149
226150
227151
230152
231153
232154
233155
234156
235157
236158
237159
240160
241161
242162
243163
244164
245165
246166
247167
250168
251169
252170
253171
254172
255173
256174
257175
260176
261177
262178
263179
264180
265181
266182
267183
270184
271185
272186
273187
274188
275189
276190
277191
300192
OctalDecimal
301193
302194
303195
304196
305197
306198
307199
310200
311201
312202
313203
314204
315205
316206
317207
320208
321209
322210
323211
324212
325213
326214
327215
330216
331217
332218
333219
334220
335221
336222
337223
340224
341225
342226
343227
344228
345229
346230
347231
350232
351233
352234
353235
354236
355237
356238
357239
360240
361241
362242
363243
364244
365245
366246
367247
370248
371249
372250
373251
374252
375253
376254
377255

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