Hex to Decimal Explained: Simple Guide With 12 Examples

Hex to decimal sounds technical, but it is one small rule used again and again: every hex digit is worth 16 times the digit to its right. This guide starts with what hexadecimal is, covers why programmers like it, and then walks through twelve conversions you can check yourself.

What hexadecimal is, before hex to decimal

Our everyday numbers are base 10: ten digits, 0 to 9, and each place is worth ten times the one on its right. Hexadecimal is base 16. It needs sixteen digits, so after 9 it borrows the letters A to F. A is ten, B is eleven, and so on up to F, which is fifteen.

Case does not matter. ff, Ff and FF are the same number. You will often see a 0x in front, as in 0xFF, or a # in front for colours. Those marks only say this is hex. They carry no value. None of those marks change a hex to decimal result.

Why it matters and where hex came from

Computers work in binary, which is long and hard to read. Hex is a shortcut. Four bits make exactly one hex digit, so a byte of eight bits is always two hex characters. The binary string 11111111 becomes FF, and nothing is lost.

A little history helps. Early machines had word sizes such as 12, 18 or 36 bits, which split neatly into groups of three bits, so octal was popular. Once 8 bit bytes became the norm in the 1960s, with machines like the IBM System/360, groups of four bits fit better and hex took over as the human friendly view of binary.

How the conversion works, step by step

1. Turn each digit into a numberDigits 0 to 9 keep their value. A is 10, B is 11, C is 12, D is 13, E is 14, F is 15.
2. Give each place a weightFrom the right, the weights are 16⁰ = 1, 16¹ = 16, 16² = 256, 16³ = 4096 and so on.
3. Multiply digit by weightThe digit A in the 16s place contributes 10 × 16 = 160.
4. Add everything upThe total is the decimal value. Check it by counting the digits: the answer should have the right order of magnitude.

Twelve worked examples

Work the first ones by hand, then use the rest as a check. The second column shows the sum.

The last row is the longest. Eight digits, so the leftmost weight is 16⁷, which is 268,435,456.

Shortcuts that make it faster

The slow part is multiplying by 16. Learn the sixteen multiples once and every two digit value takes a single addition. The left digit picks the row, the right digit is just added.

Try 9C. The left digit 9 gives 144, the right digit C is 12, and the sum is 156. Try E3: 224 plus 3 is 227. After a day of practice you will do these in your head. Each hex to decimal step here is one lookup and one addition.

For longer values, work in pairs from the right. Each pair is a byte, and each byte is worth 256 times the byte to its right. So 1A3F is the pair 1A, which is 26, times 256 plus the pair 3F, which is 63. That is 6,656 + 63 = 6,719, the same answer as before, with fewer steps.

Going back: decimal to hex

Divide by 16 and collect the remainders from the bottom up. For 500: 500 ÷ 16 = 31 remainder 4. Then 31 ÷ 16 = 1 remainder 15, which is F. Then 1 ÷ 16 = 0 remainder 1. Read upward: 1, F, 4. So 500 is 1F4, which matches the table.

Colour codes

Colour codes are three hex pairs: red, green and blue, each from 00 to FF, which is 0 to 255 in decimal. CSS also allows a short three digit form where each digit doubles, and four and eight digit forms that add transparency. The MDN reference for hex colours lists all four.

The converter shows a swatch only for exactly 3 or 6 digits, so it never invents a colour you did not type. It also works out brightness with the luminance formula 0.299 × R + 0.587 × G + 0.114 × B. For #FF8000 that is 0.299 × 255 + 0.587 × 128, about 151 out of 255. To pick colours visually, a colour picker pairs well with this.

Where it shows up in real work

You rarely convert for fun. Hex shows up because something else prints it, and you need the decimal to make sense of it.

The ASCII gap is worth remembering. Small letters sit exactly 32 above capitals, which is a single bit, hex 20. Flip that bit and you change the case. Knowing the decimal and hex side by side makes patterns like this visible.

How much space does a value need?

Every two hex digits fill one byte. A value that needs 9 bits, like 1F4, must be stored in 2 bytes even though the second byte is mostly empty.

Glossary of terms

Base (radix)

The count of distinct digits a system uses. Decimal is base 10, binary base 2, octal base 8, hex base 16.

Digit

A single symbol in a number. Hex digits run from 0 to F.

Bit

One binary digit, 0 or 1.

Nibble

Four bits, which is exactly one hex digit.

Byte

Eight bits, which is exactly two hex digits and holds 0 to 255.

Prefix 0x

A marker used in many programming languages to say the number that follows is hexadecimal.

Place value

The weight of a position in a number. In hex it grows by a factor of 16 per place.

Four mistakes to avoid

• Reading 10 in hex as ten. It is sixteen, since 1 × 16 + 0.
• Counting positions from the left. The smallest weight is on the right.
• Treating the 0x or # as part of the number.
• Forgetting that a value like 1F4 has three digits, so its top weight is 16², not 16³.

If you work with bits directly, the binary to decimal converter shows the same idea in base 2.

Frequently asked questions

• Binary to Decimal Converter
• Octal Converter Online Free
• Color Picker

Sources: MDN Web Docs: hex color