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Convert Octal to Decimal

Need to turn an octal decimal number into a standard base-10 value? Our free octal to decimal converter makes it simple. Just enter your base-8 value below to instantly convert base 8 to base 10.

Octal to decimal calculator

Allowed digits: 0 to 7
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Output base: 10
Enter a value above to see the result
Conversion Octal (Base 8) → Decimal (Base 10)

Quick Reference

Octal to Decimal Conversion Chart

Skip the manual math. Here are some of the most common conversions you might need, showing exactly how base 8 translates to base 10.

Common octal to decimal conversions from 0 to 777
Octal Calculation Decimal
0 0 0
1 1 1
7 7 7
10 1×8¹ + 0×8⁰ 8
11 1×8¹ + 1×8⁰ 9
12 1×8¹ + 2×8⁰ 10
17 1×8¹ + 7×8⁰ 15
20 2×8¹ + 0×8⁰ 16
25 2×8¹ + 5×8⁰ 21
77 7×8¹ + 7×8⁰ 63
100 1×8² 64
123 1×8² + 2×8¹ + 3×8⁰ 83
200 2×8² 128
377 3×64 + 7×8 + 7 255
777 7×64 + 7×8 + 7 511

Step-by-Step

How to Convert Base 8 to Base 10

Wondering how to change octal to decimal by hand? The math is actually pretty straightforward once you understand positional values.

The Method

An octal system uses eight digits (0-7), while our standard decimal system uses ten (0-9). To manually calculate an octal number to decimal, you multiply each digit by its corresponding power of 8.

Decimal = Σ(octal digit × 8^position)

Starting from the rightmost digit, each position represents an increasing power of 8 (8⁰, 8¹, 8², 8³, and so on).

Converting from Base 8 to Base 10 Manually

1

Write the octal number

Start with the octal value you want to convert. For this example, let's use 123.

2

Assign powers of 8

Reading right to left, assign the positional multipliers: 8⁰ (1), 8¹ (8), and 8² (64).

3

Multiply and add

Multiply the digits by their positions: (1×64) + (2×8) + (3×1) = 83. Your final result is 83 in decimal.

System Differences

Understanding the Octal to Decimal Transition

Converting from base 8 to base 10 bridges the gap between digital computing and human-readable numbers. While computers love binary and its easy translation to octal, humans think in tens.

So, how do you convert base 8 to base 10 effectively? The easiest route is using a dedicated calculator octal to decimal tool. When working with larger values, doing it by hand leaves too much room for simple arithmetic errors.

If you are doing it manually, always remember that every position in an octal decimal number is worth exactly eight times more than the position to its right.

Worked Examples

Sample Octal to Decimal Calculations

Let's look at how to convert from octal to decimal using real-world examples.

10 in octal to decimal

Multiply 1 by 8, and add 0. 10 in octal is 8 in decimal.

17 in octal to decimal

Multiply 1 by 8, and add 7. 17 in octal is 15 in decimal.

25 in octal to decimal

Take 2 times 8 (16) and add 5. You get 21.

77 in octal to decimal

Take 7 times 8 (56) and add 7. The result is 63.

100 in octal to decimal

Here you just need 1 times 64. 100 in octal is 64 in decimal.

123 in octal to decimal

(1×64) + (2×8) + (3×1) = 83.

377 in octal to decimal

(3×64) + (7×8) + 7 = 192 + 56 + 7. The answer is 255.

777 in octal to decimal

(7×64) + (7×8) + 7 = 448 + 56 + 7. The final result is 511.

FAQ

Frequently Asked Questions

Everything you need to know about navigating the octal to decimal conversion calculator.