🔢 Hex to Decimal Converter with Positional Breakdown

What is the Hex to Decimal Converter?

Hexadecimal, or base 16, is the number system programmers use to write byte values compactly. It has sixteen digits: 0 to 9 keep their usual values, then A stands for 10, B for 11, C for 12, D for 13, E for 14 and F for 15. Decimal, the base 10 system everyone learns first, only has ten digits, so converting hex to decimal means translating those extra letter-digits and the base 16 place values into the base 10 form your calculator and everyday life use.

The method is positional expansion. Number the hex digits from right to left starting at zero. The rightmost digit sits in the 16^0 place (which equals 1), the next sits in the 16^1 place (16), then 16^2 (256), 16^3 (4096) and so on. To convert hex to decimal you multiply each digit's value by the place value above it and sum every product. For the hex value 1A, the A is worth 10 in the ones place (10x1 = 10) and the 1 is worth 1 in the sixteens place (1x16 = 16), so 16 + 10 = 26. That is exactly what parseInt('1A', 16) returns, and it is the calculation this tool performs and then lays out row by row.

Hex values are not always whole numbers, and they are not always positive. A hex fraction like 1F.4 works the same way but the digits after the point use negative powers of 16: the first fractional digit is worth 16^-1 (one sixteenth), the second is worth 16^-2, and so on, so 1F.4 equals 31 plus 4/16, or 31.25. Negative values are usually written with a leading minus sign for plain hex, but inside computer hardware a fixed-width value such as a byte or 32-bit word more often uses two's complement, where the top bit marks the number as negative and the remaining bits are reinterpreted. In an 8-bit signed byte, 0xFF is not 255, it is -1, while the same bit pattern read as an unsigned byte is 255. Whether a given hex value should be read as signed or unsigned depends entirely on the context it came from, such as a CPU register width or a file format's field definition.

Under the hood every hex to decimal conversion here uses the browser's built in parseInt with a radix of 16, which is fast and exact for whole numbers up to 2^53. Because the result is a normal integer, the same value is trivially re-expressed in other bases, so the converter also reports the binary (base 2) and octal (base 8) forms. This is handy when you are reading a color code, a memory address, a permission mask or a Unicode code point and need to move between the representations without a second tool.

Hex to decimal conversion turns up far more often than most people expect. Web colors such as #FF0000 are three hex byte pairs, HTTP and assembly dumps list addresses in hex, MAC addresses and UUIDs are hex, and character encodings map code points like U+1F600 that you frequently need as a plain decimal number. Windows error codes such as 0xC0000005 and HTTP status extensions are also written in hex and are far easier to look up once converted to decimal. Being able to convert hex to decimal quickly, and to see the arithmetic behind the answer, makes all of those tasks less error prone.

A quick sanity check: the number of decimal digits a hex value can produce grows roughly 20 percent faster than the hex digit count, because 16^n grows faster than any power of 10 with the same digit count. A 2-digit hex number (00 to FF) covers 0 to 255 in decimal, a 4-digit hex number (0000 to FFFF) covers 0 to 65535, and a 6-digit hex color value covers over 16.7 million combinations. Keeping that scale in mind helps you spot an obviously wrong conversion before you even check the math.

When to use it

• Turning a hex color channel like FF or 80 into its 0 to 255 decimal value when tweaking CSS or design tokens.
• Reading memory addresses, offsets or register values from a debugger or assembly dump as ordinary decimal numbers.
• Converting a Unicode code point written in hex (for example 1F600) into the decimal code point used by some APIs.
• Checking a students homework or a textbook exercise by seeing the full 16^n positional breakdown, not just the final answer.
• Translating a Windows or system error code such as 0xC0000005 into decimal so it is easier to search in documentation.
• Decoding hex fields in network packets, MAC addresses, or file headers seen in a hex editor into plain decimal values.

How to use the Hex to Decimal Converter

1. Type or paste your hexadecimal value into the box (a leading 0x or # prefix is optional).
2. Read the decimal result at the top; it updates as you type, so no button press is needed.
3. Scan the positional breakdown and table to see how each digit contributes via its 16^n place value.
4. Copy the decimal, binary or octal output with the Copy buttons if you need it elsewhere.

Formula & method

Worked examples

Hex digit to decimal value

Common hex values and their decimal equivalents

Signed vs unsigned 8-bit byte values (two's complement)

Common mistakes to avoid

• Reading letter-digits as their alphabet position. In hex, A is 10 and F is 15, not 1 or 6. A is the eleventh symbol counting from 0, so its value is 10. Mixing up the letter with its place in the alphabet is the most frequent hex to decimal error.
• Counting positions from the left. Place values are counted from the right, starting at position 0. The rightmost digit is always the ones (16^0) place. Numbering from the left gives every digit the wrong power of 16.
• Forgetting to strip or account for the 0x prefix. Notations like 0x1A and #1A carry a prefix that marks the value as hex; it is not part of the number. This tool removes 0x and # automatically, but by hand you must convert only the digits after it.
• Treating hex like base 10 place values. Each hex place is worth 16 times the one to its right (1, 16, 256, 4096), not 10 times (1, 10, 100). Using powers of 10 instead of powers of 16 produces a wildly wrong decimal result.
• Assuming a hex byte is always positive. A value like 0xFF is 255 if it is unsigned, but -1 if it is a signed 8-bit two's complement value. Whether hex is signed depends on the format it comes from (a CPU register, a file field, a network protocol), not on the digits alone.
• Losing precision on very long hex strings. JavaScript numbers, and this converter, are exact only up to 2^53. Extremely long hex strings (beyond about 13 to 14 digits) can lose precision if treated as a plain integer; such values usually need a big-integer library instead.

Glossary

Hexadecimal

Base 16 number system using digits 0 to 9 and letters A to F, where A is 10 and F is 15.

Decimal

The everyday base 10 number system, using only the digits 0 to 9.

Positional expansion

Writing a number as the sum of each digit times its place value, the core method for hex to decimal conversion.

Place value

The weight of a digit based on its position; in hex the places are powers of 16 (1, 16, 256, 4096).

Nibble

A group of four bits, exactly one hexadecimal digit, holding a value from 0 to 15.

0x prefix

A marker (0x, or # for colors) placed before hex digits to signal the value is hexadecimal, not part of the number itself.

Byte

A group of 8 bits, represented compactly as exactly two hexadecimal digits ranging from 00 to FF.

Two's complement

The standard way computers represent negative numbers in a fixed number of bits; the top bit marks the sign, so 0xFF as a signed byte is -1, not 255.

Frequently asked questions