Octal Converter

Convert between octal, decimal, binary, and hexadecimal number systems with step-by-step explanation.

Tested tool guide Tested browser tools Checked August 16, 2026

What Octal Converter does, with a checked example

Octal Converter centers base 8 while showing the same integer in decimal, binary, and hexadecimal. After the source base is identified, it evaluates each digit by that base's place values and gives a step-by-step equivalence rather than treating the characters as an ordinary decimal number. The important constraint is that an octal numeral can contain only digits 0 through 7. A value such as 128 is valid decimal, but it is not valid octal because 8 cannot occupy an octal position.

Worked example

A concrete input and expected output from the current implementation.

Input

Expected output

Octal: 157; Decimal: 111; Binary: 1101111; Hexadecimal: 6F

With octal selected as the source, 157 equals 1 x 8^2 + 5 x 8^1 + 7 x 8^0, or 64 + 40 + 7 = 111. Binary 1101111 and hexadecimal 6F also represent decimal 111.

How the result is produced

Octal place values

For an octal source, positions are powers of eight. Reading from the right, their weights are 8^0, 8^1, 8^2, and so on. Each octal digit is multiplied by its position's weight, and those products are added. This expansion supplies the decimal value used to verify that every displayed representation denotes the same integer.

Binary and hexadecimal grouping

One octal digit corresponds to exactly three binary bits because eight equals 2^3. Thus octal 157 maps by digit to binary groups 001, 101, and 111, with the initial padding zeros omitted from the final numeral. Hexadecimal groups binary digits in fours instead, producing 0110 1111, or 6F, for the same value.

Good uses

Translate an octal Unix permission value such as 755 into binary bits or a decimal integer.
Check an octal address or data word from older computer documentation against its hexadecimal equivalent.
Verify base-8 place-value exercises by comparing the expanded arithmetic with the converted result.

Limits and checks

An octal input cannot contain 8 or 9. If either appears, the value must be corrected or interpreted under another source base.
The same characters represent different quantities under different bases. For example, 100 is 64 in octal but 100 when interpreted as decimal.
Do not assume programming prefixes are part of the numeral. The notation 0o157 identifies octal in some languages, while the bare octal digit string is 157.

Common questions

Can it convert decimal, binary, or hexadecimal back to octal?

Yes. Set the appropriate source representation and convert the entered numeral to octal. The digits are interpreted under the selected source base before the equivalent base-8 numeral is reported. For example, decimal 64 corresponds to octal 100. Hexadecimal letters A through F are meaningful only when hexadecimal is selected as the source.

Why does octal 10 become decimal 8 instead of decimal 10?

Octal 10 has one unit in the eights position and zero units in the ones position, so its value is 1 x 8 + 0 = 8. It does not mean decimal ten. Each written base uses the symbol 10 for that base itself: binary 10 is 2, octal 10 is 8, and hexadecimal 10 is 16.

References and verification

The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.