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Octal to Decimal Converter
Convert any octal number to decimal instantly — with the full step-by-step working shown. Free, fast, no sign-up.
Only octal digits allowed (0-7) — spaces, commas and dashes are ignored.
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Also equals
- Binary
- Decimal
- Octal
- Hex
Step-by-step calculation
| Digit | Position | Value (8n) | Contribution |
|---|---|---|---|
| Total | |||
How to convert octal to decimal
- Write down the octal number and number each digit's position from right to left, starting at 0.
- Multiply each digit (0-7) by 8 raised to the power of its position.
- Add all the results together — that's your decimal number.
Example: 175₈ = (1 × 8²) + (7 × 8¹) + (5 × 8⁰) = 64 + 56 + 5 = 125.
Background reading: the octal number system on Wikipedia.
Conversion table
Octal 0–17 (decimal 0–15) with the positional calculation, plus larger examples.
| Octal | Decimal | Calculation |
|---|---|---|
| 0 | 0 | 0₈ = 0×1 = 0 |
| 1 | 1 | 1₈ = 1×1 = 1 |
| 2 | 2 | 2₈ = 2×1 = 2 |
| 3 | 3 | 3₈ = 3×1 = 3 |
| 4 | 4 | 4₈ = 4×1 = 4 |
| 5 | 5 | 5₈ = 5×1 = 5 |
| 6 | 6 | 6₈ = 6×1 = 6 |
| 7 | 7 | 7₈ = 7×1 = 7 |
| 10 | 8 | 10₈ = 1×8+0×1 = 8 |
| 11 | 9 | 11₈ = 1×8+1×1 = 9 |
| 12 | 10 | 12₈ = 1×8+2×1 = 10 |
| 13 | 11 | 13₈ = 1×8+3×1 = 11 |
| 14 | 12 | 14₈ = 1×8+4×1 = 12 |
| 15 | 13 | 15₈ = 1×8+5×1 = 13 |
| 16 | 14 | 16₈ = 1×8+6×1 = 14 |
| 17 | 15 | 17₈ = 1×8+7×1 = 15 |
| 100 | 64 | 100₈ = 1×64 = 64 |
| 777 | 511 | 777₈ = 7×64 + 7×8 + 7 = 511 |
Powers of 8
| Power | Value |
|---|---|
| 80 | 1 |
| 81 | 8 |
| 82 | 64 |
| 83 | 512 |
| 84 | 4096 |
| 85 | 32768 |
Octal to decimal in code
Python
int("17", 8) # → 15JavaScript
parseInt("17", 8); // → 15C
#include <stdio.h>
#include <stdlib.h>
int main(void) {
long v = strtol("17", NULL, 8);
printf("%ld\n", v); /* → 15 */
return 0;
}Common values
17₈ = 1510₈ = 8100₈ = 64777₈ = 5110₈ = 020₈ = 16
Key takeaways
- Each octal digit is worth 8× the digit to its right.
- Digits allowed: 0–7 only; 8 and 9 never appear in octal.
- 17₈ = 15, 100₈ = 64, 777₈ = 511.
- Octal maps 1 digit ↔ 3 bits, which is why Unix permissions use it.
Frequently asked questions
How do I convert octal to decimal?
Multiply each octal digit by 8 raised to its position power (from 0 at the right) and sum the results. Or just use the converter above — it shows every step.
What is 17 in decimal?
17₈ = 15 in decimal.
Can this converter handle large octal numbers?
Yes — it supports octal numbers of any length with full precision.
What is 10 in octal in decimal?
10₈ = 8 in decimal.
What is 777 in decimal?
777₈ = 7×64 + 7×8 + 7 = 511.
Why is octal used?
Each octal digit maps to exactly three binary bits, so it was a compact shorthand for binary on early computers.
Do leading zeros matter in octal?
In some programming languages a leading 0 marks a number as octal (for example 017 = 15). The converter treats the input as octal regardless.
Need the reverse? Try our decimal to octal converter.