Hex Calculator: How to Convert Hex, Decimal, and Binary (With Examples)
Hexadecimal turns up everywhere in computing: web colors, memory addresses, error codes, MAC addresses, and file data. A hex calculator lets you convert between hex, decimal, and binary instantly and add or subtract hex values without translating everything by hand.
This guide explains what hex is, how to convert by hand, how to do hex arithmetic, and how to read color codes, with examples you can check yourself.
What Is a Hex Calculator?
A hex calculator works with hexadecimal, the base-16 number system. The free hex calculator can:
- Convert a value between hexadecimal, decimal, and binary
- Add and subtract two hexadecimal values
It’s handy for programmers, students, web designers, and anyone debugging low-level data.
What Is Hexadecimal?
Decimal uses 10 digits (0 to 9). Hexadecimal uses 16 symbols: 0 to 9, then A to F for the values 10 to 15.
Hex is popular because one hex digit equals exactly four binary digits (bits). That makes it a compact, readable shorthand for binary data. For example, the 8-bit binary number 10110111 is just B7 in hex.
Hex, Decimal, and Binary Chart
| Hex | Decimal | Binary |
|---|---|---|
| 0 | 0 | 0000 |
| 1 | 1 | 0001 |
| 2 | 2 | 0010 |
| 3 | 3 | 0011 |
| 4 | 4 | 0100 |
| 5 | 5 | 0101 |
| 6 | 6 | 0110 |
| 7 | 7 | 0111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| A | 10 | 1010 |
| B | 11 | 1011 |
| C | 12 | 1100 |
| D | 13 | 1101 |
| E | 14 | 1110 |
| F | 15 | 1111 |
Place Values in Hexadecimal
Each position is a power of 16, counting from the right:
| Position | 4th | 3rd | 2nd | 1st |
|---|---|---|---|---|
| Value | 16³ = 4,096 | 16² = 256 | 16¹ = 16 | 16⁰ = 1 |
How to Convert Hex to Decimal
Formula: multiply each digit by its place value and add the results.
Example 1: Convert 1A3 to decimal.
- 1 × 256 = 256
- A (10) × 16 = 160
- 3 × 1 = 3
- Total: 419
Example 2: Convert 7E.
- 7 × 16 = 112
- E (14) × 1 = 14
- Total: 126
Example 3: Convert 3C9.
- 3 × 256 = 768
- C (12) × 16 = 192
- 9 × 1 = 9
- Total: 969
How to Convert Decimal to Hex
Method: divide by 16 repeatedly, record the remainders, then read them from last to first.
Example 4: Convert 500 to hex.
- 500 ÷ 16 = 31 remainder 4
- 31 ÷ 16 = 1 remainder 15 (F)
- 1 ÷ 16 = 0 remainder 1
- Read upward: 1F4
Check: 256 + 240 + 4 = 500.
Example 5: Convert 1,000 to hex.
- 1,000 ÷ 16 = 62 remainder 8
- 62 ÷ 16 = 3 remainder 14 (E)
- 3 ÷ 16 = 0 remainder 3
- Result: 3E8
How to Convert Hex to Binary
Swap each hex digit for its 4-bit group, using the chart above.
Example 6: B7 becomes 1011 + 0111 = 10110111, which equals 183 in decimal (11 × 16 + 7).
How to Convert Binary to Hex
Split the binary number into groups of four bits from the right, then convert each group.
Example 7: 11010110 splits into 1101 and 0110, which is D and 6, so the result is D6 (214 in decimal).
If the leftmost group has fewer than four bits, pad it with zeros on the left.
Hex Arithmetic
Adding Hex Numbers
Example 8: A9 + 5C
Method 1: via decimal. A9 = 169 and 5C = 92. 169 + 92 = 261, which is 105 in hex.
Method 2: digit by digit, carrying at 16.
- 9 + C (12) = 21 = 16 + 5, so write 5, carry 1
- A (10) + 5 + 1 = 16, so write 0, carry 1
- Carry the last 1: 105
Subtracting Hex Numbers
Example 9: F0 − 3A
- F0 = 240 and 3A = 58
- 240 − 58 = 182, which is B6 in hex
Multiplying Hex Numbers
Example 10: 1F × 4
- 1F = 31, and 31 × 4 = 124, which is 7C
Shortcut: multiplying by 10 in hex (16 in decimal) just adds a zero, so 2B × 10 = 2B0, much like multiplying by 10 in decimal.
Hex Color Codes Explained
Web colors use six hex digits in the form #RRGGBB, with two digits each for red, green, and blue. Each pair runs from 00 (0) to FF (255).
| Hex Color | Red | Green | Blue | Look |
|---|---|---|---|---|
#FF0000 |
255 | 0 | 0 | Pure red |
#FFA500 |
255 | 165 | 0 | Orange |
#228B22 |
34 | 139 | 34 | Forest green |
#1E90FF |
30 | 144 | 255 | Bright blue |
#808080 |
128 | 128 | 128 | Mid gray |
#000000 |
0 | 0 | 0 | Black |
#FFFFFF |
255 | 255 | 255 | White |
Example 11: Decode #1E90FF.
- 1E = 1 × 16 + 14 = 30 (red)
- 90 = 9 × 16 + 0 = 144 (green)
- FF = 255 (blue)
So #1E90FF is rgb(30, 144, 255).
Reverse example: rgb(34, 139, 34) becomes 22, 8B, 22, giving #228B22. (139 ÷ 16 = 8 remainder 11, and 11 is B.)
When all three pairs match, such as #808080, you get a shade of gray.
Common Hex Values to Know
| Hex | Decimal | Why It Matters |
|---|---|---|
| FF | 255 | Largest value of one byte |
| 100 | 256 | Number of values in one byte |
| 400 | 1,024 | One kibibyte |
| 7FFF | 32,767 | Largest signed 16-bit value |
| FFFF | 65,535 | Largest unsigned 16-bit value |
| FFFFFFFF | 4,294,967,295 | Largest unsigned 32-bit value |
Two hex digits equal one byte, and a 32-bit value takes eight hex digits.
Where Hex Is Used
- Web design: Color codes like
#228B22 - Programming and debugging: Memory addresses, error codes, and bit masks
- Networking: MAC addresses (12 hex digits) and IPv6 addresses (eight groups of four hex digits)
- Character encoding: ASCII and Unicode code points. For example,
41is “A” (65),61is “a” (97),30is the digit “0” (48), and20is a space (32) - File inspection: Hex editors show raw file bytes in hex
Hex Notation: Prefixes and Suffixes
Hex values are written in different ways depending on the context:
- 0x2F: C, C++, Java, JavaScript, Python
- #FF5733: CSS and HTML colors
- 2Fh: Assembly and some documentation
- $2F: Some assembly languages and older systems
- \x2F: Escape sequences inside strings
The math is the same in all of them. Only the notation changes.
Hex and Negative Numbers
Computers usually store negative integers in two’s complement form. In an 8-bit signed value, FF means −1 and 80 means −128. The same hex digits can mean different numbers depending on whether the value is signed or unsigned, so always check which one your system uses.
Common Mistakes to Avoid
- Forgetting that A to F stand for 10 to 15
- Reading hex digits as decimal (
10in hex is 16, not 10) - Mixing up place values, which are powers of 16
- Dropping the leading zeros of binary groups when converting
- Ignoring whether a value is signed or unsigned
- Confusing the letter O with the digit 0 when typing hex
FAQ: Hex Calculator
How do you convert hex to decimal?
Multiply each digit by 16 raised to its position, then add the results. For example, 2F = 2 × 16 + 15 = 47.
How do you convert decimal to hex?
Divide by 16 repeatedly, note the remainders, and read them in reverse order.
What is FF in decimal?
255.
Why do programmers use hex instead of binary?
Hex is much shorter and each digit maps to exactly four bits, so it’s easy to read and convert.
What is the hex value of 255?
FF.
Is hex case-sensitive?
No. ff and FF are the same value, though some style guides prefer uppercase.
How do I read a hex color code?
Split it into three pairs for red, green, and blue, then convert each pair to decimal (0 to 255).
Is the hex calculator free?
Yes. The free hex calculator needs no sign-up.
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Final Thoughts
Hexadecimal looks odd at first, but it follows simple rules: 16 symbols, place values that are powers of 16, and a clean link to binary. Once you see that each hex digit is four bits, conversions get much easier. Use the free hex calculator to check your work, and double-check any critical results in programming or engineering projects.
This article is for educational purposes. Verify results independently for programming or engineering work where precision is critical.
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