Number Base Converter — binary, octal, decimal, hex & custom

This number base converter takes a value in one numeral system and instantly shows you its equivalent in binary, octal, decimal, and hexadecimal all at once — plus any custom base from 2 to 36 you want to check. Type 255 in decimal and immediately see 11111111 in binary, 377 in octal, and FF in hex, with no manual long division and no separate lookup for each base.

We built this free tool at Arb Digital for developers, students, and anyone who works with color codes, memory addresses, or networking configuration and needs a fast, reliable way to move between number systems without opening a spreadsheet or writing a script.

What This Number Base Converter Does

You type a value and tell the tool what base that value is currently written in — decimal by default, but you can switch the dropdown to binary, octal, hexadecimal, or any custom base from 2 to 36 using the base field next to it. The converter parses your input according to the digits that base allows (binary only accepts 0 and 1, octal accepts 0–7, hexadecimal accepts 0–9 and A–F, and so on), rejects anything invalid with a clear message, and then displays the equivalent value in all four common bases simultaneously in the result grid, plus your chosen custom base in the tip line below.

This "show everything at once" approach saves the extra step of converting one base at a time. If you're debugging a bit mask, you might need the binary and hex forms side by side; if you're a student learning place value, seeing decimal, binary, octal, and hex together on one screen makes the relationships between them click much faster than converting one pair at a time.

How to Use It

1. Choose your input base. Use the "From base" dropdown for the four most common bases, or set the "Custom base" field to any value from 2 to 36 and pick the matching option (or type it directly if it isn't in the list).
2. Type the value exactly as it's written in that base — for hexadecimal you can use upper or lowercase letters (both FF and ff work).
3. Click Convert. All four standard bases update immediately, along with your custom base if it's different from the four presets.
4. Check for a validation error. If you type a digit that isn't legal in the base you selected (like a "9" while converting from binary), the tool flags it instead of silently producing a wrong answer.

How Base Conversion Actually Works

Every number system, or "radix," represents quantities using place value — each digit position is worth a power of the base. In decimal (base 10), the digits in "255" represent 2×10² + 5×10¹ + 5×10⁰, which is 200 + 50 + 5 = 255. Binary (base 2) works identically but with powers of 2 instead of 10, so "11111111" means 1×2⁷ + 1×2⁶ + 1×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 1×2⁰, which adds up to 255. Octal (base 8) and hexadecimal (base 16) follow the same pattern with powers of 8 and 16. Because 8 and 16 are both powers of 2 (2³ and 2⁴), octal and hex convert to and from binary especially cleanly — each octal digit maps to exactly 3 binary bits, and each hex digit maps to exactly 4 binary bits, which is precisely why hexadecimal is the preferred shorthand for binary data in computing. For a deeper technical reference on positional numeral systems, see Khan Academy's explanation of positional numeral systems.

This converter works internally by first converting your input into a plain decimal integer (multiplying each digit by the appropriate power of the source base and summing), then converting that decimal value out to each target base by repeated division: dividing by the target base and reading the remainders from last to first gives you the digits of the number in that base, from most significant to least significant.

Where Each Base Shows Up in the Real World

These aren't abstract math exercises — each base has a specific home in technology and everyday life:

• Binary (base 2) — the native language of every digital computer. Transistors are either on or off, so every piece of data a computer stores or processes is ultimately a sequence of 1s and 0s. CPU instructions, boolean logic, and low-level networking flags are all expressed in binary.
• Octal (base 8) — best known today for Unix and Linux file permissions, where a permission set like "755" (read/write/execute for the owner, read/execute for group and others) is a compact octal representation of nine binary permission bits. Octal was more common in older computing eras built around 12-bit and 36-bit word sizes.
• Decimal (base 10) — the everyday counting system nearly every human culture uses, almost certainly because we have ten fingers. It's the base you use for money, measurements, and ordinary arithmetic.
• Hexadecimal (base 16) — the standard shorthand in programming and web design for representing binary data compactly. CSS color codes like #FF8800, memory addresses, MAC addresses, and hash digests (like MD5 or SHA checksums) are all written in hex because two hex digits neatly represent one full byte (8 bits).
• Base 36 — used in URL shorteners, license plate schemes, and some database ID encodings because it packs the most information into the fewest characters using only the 10 digits and 26 letters of the Latin alphabet.
• Base 60 (sexagesimal) — not covered by this tool's custom range, but worth mentioning: it's why we have 60 seconds in a minute and 60 minutes in an hour, a legacy of ancient Babylonian mathematics.

Reading and Writing Numbers in Any Base

Once you understand place value, reading a number in any base becomes mechanical. Take hexadecimal FF: the "F" in the ones place is worth 15, and the "F" in the sixteens place is worth 15×16 = 240, so FF = 240 + 15 = 255. Or take binary 11111111 again: it's simply the sum of the first eight powers of two (1+2+4+8+16+32+64+128), which totals 255 — no coincidence, since 255 is one less than 256 (2 to the 8th power), the classic "all bits set" value for an 8-bit byte. Recognizing these patterns — powers of two, powers of sixteen, all-bits-set values — makes mental base conversion much faster once you've done it a few times, even without a calculator.

A Worked Example Across All Four Bases

Consider the decimal number 500. Converting it to binary by repeated division by 2 gives 111110100 — you can verify this by dividing 500 by 2 repeatedly and reading the remainders from bottom to top (500÷2=250 r0, 250÷2=125 r0, 125÷2=62 r1, and so on down to 1). In octal, the same repeated-division process using 8 instead of 2 gives 764. In hexadecimal, dividing by 16 repeatedly gives 1F4. You can sanity-check the hex answer quickly: 1×16² + F×16¹ + 4×16⁰ = 256 + 240 + 4 = 500, which confirms the conversion is correct. Working through an example like this by hand once or twice is the fastest way to internalize why the algorithm behind this converter works, even though the tool will always do the heavy lifting for you afterward.

This same worked-example approach is useful for spotting your own conversion mistakes. If you ever get a hex or octal result that looks obviously wrong, multiply each digit by its place value and add them up in decimal — if the sum doesn't match the number you started with, you'll immediately know where in the process the error happened, whether it was a misread digit or an arithmetic slip in the division steps.

Common Mistakes to Avoid

• Using digits that don't belong to the base — binary can only contain 0 and 1; typing "2" or "9" while converting from binary is invalid, even though those are perfectly normal decimal digits.
• Forgetting that hex letters stop at F — hexadecimal only uses 0–9 and A–F (16 symbols total); "G" is never valid in base 16.
• Mixing up octal and decimal — a number like "377" looks like a normal decimal number but converts very differently depending on whether you tell the tool it's octal or decimal, so always double-check your "from base" selection.
• Assuming leading zeros change the value — "00FF" and "FF" represent the exact same value in hexadecimal; leading zeros are just padding.
• Confusing base 36 with base-62 encodings — some URL shorteners use mixed-case base 62 (0–9, a–z, A–Z) rather than the case-insensitive base 36 this tool supports, so results won't always match a base-62 shortener directly.

Related Free Tools From Arb Digital

Pair this with our Text to Binary converter to see how letters map to binary and back, or the ASCII Table for a quick lookup of character codes across decimal, hex, and binary. If you work with dates and timestamps, try the Unix Timestamp Converter and the Date Format Converter, or check out the Roman Numeral Converter for a completely different kind of numeral system. Browse the full free online tools hub for more.

Frequently Asked Questions

This tool runs entirely in your browser — no data is sent to any server, and no external libraries are used.