A hexadecimal calculator performs arithmetic and bitwise operations on numbers written in base 16, the counting system that uses the digits 0 through 9 and the letters A through F. The calculator below takes two hex values, applies the operation you pick, and shows the answer in hexadecimal, decimal, binary, and octal at the same time, all inside your browser.
What Hexadecimal Is
Hexadecimal is a base 16 number system. Everyday counting uses base 10, which has ten digits, 0 through 9. Hexadecimal has sixteen, so after 9 it continues with the letters A, B, C, D, E, and F to stand for the values ten through fifteen. Each position in a hex number is worth sixteen times the position to its right, just as each position in a decimal number is worth ten times the one to its right. The value 1A, for example, means one sixteen plus ten, which is 26 in decimal.
How to Use This Calculator
- Type your first number into the first field using hex digits, the characters 0 through 9 and A through F.
- Choose an operation from the menu: add, subtract, multiply, divide, AND, OR, or XOR.
- Type your second number into the second field.
- Read the result. The large value is the answer in hexadecimal, and the list below shows the same number in decimal, binary, and octal.
- Change any field at any time. The calculator updates as you type, with no button to press.
How Hex Math Works (and Bitwise AND, OR, XOR)
For add, subtract, multiply, and divide, the calculator reads each hex value as a number, runs the operation, and writes the result back in base 16. Division returns the whole-number quotient and ignores any remainder. The bitwise operations work differently. AND, OR, and XOR line the two numbers up by their binary bits and compare each pair of bits. AND keeps a 1 only where both numbers have a 1. OR keeps a 1 where either number has a 1. XOR keeps a 1 only where the two bits differ. Hexadecimal is the natural way to write these results because every hex digit maps to exactly four binary bits.
Hex, Decimal, and Binary for 0 to F
| 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 |
Why Programmers Use Hex
Programmers reach for hexadecimal because it sits between human reading and machine bits. Memory addresses are shown in hex because the compact two-digit-per-byte format is far easier to scan than binary and lines up with how memory is grouped. Color codes on the web use hex too: a value like #1A2B3C is three bytes, one each for red, green, and blue. Bit masks, file signatures, and the output of hash functions are all written in hex for the same reason. When you need to see or set individual bits, hex shows them in a form you can actually read.
When to Use It
Use this calculator whenever you are working with values that are written in hex and you want a fast, correct answer without converting by hand. That covers setting or checking a bit mask, working out an offset from a memory address, combining color channels, or simply confirming what a hex value equals in decimal. The instant decimal, binary, and octal readouts also make it a quick base converter, so you can move a single number between systems while you work.
Last Thoughts on Hexadecimal Math
Hexadecimal looks unfamiliar at first because of the letters, but it is just base 16, and once you see that each digit is four binary bits the system stops feeling foreign. Arithmetic in hex follows the same rules as decimal, and the bitwise operations are simply bit-by-bit comparisons. This tool handles both so you can stay in hex and still see every other base at a glance.
Run a calculation above, then explore the rest of our free online tools. If you work with bits often, the binary calculator covers the same operations in base 2, the color picker turns hex color codes into the colors they describe, and the JSON formatter tidies the data files those values often live in.
Key Takeaways:
- Hexadecimal is base 16: digits 0 through 9 then letters A through F stand for the values zero through fifteen.
- This calculator adds, subtracts, multiplies, divides, and runs bitwise AND, OR, and XOR on two hex values.
- AND, OR, and XOR compare the numbers bit by bit, which is the most common reason to use hex in code.
- Each result is shown in hex, decimal, binary, and octal at the same time, so it doubles as a base converter.
- One hex digit equals exactly four binary bits, and one byte is always two hex digits.
- Programmers use hex for memory addresses, color codes, bit masks, and hashes because it reads bits compactly.
Frequently Asked Questions (FAQs)
What is a hexadecimal calculator?
A hexadecimal calculator performs arithmetic and bitwise operations on numbers written in base 16. You enter two hex values, choose an operation, and it returns the result. This one also shows the answer in decimal, binary, and octal so you can read it in whichever base you need.
What do the letters A to F mean in hex?
Base 16 needs sixteen single-character digits, but our normal digits only go up to 9. The letters A, B, C, D, E, and F fill the gap and stand for the values ten, eleven, twelve, thirteen, fourteen, and fifteen. So F is the largest single hex digit, equal to 15 in decimal.
What do AND, OR, and XOR do?
They are bitwise operations that compare the two numbers one binary bit at a time. AND outputs a 1 only where both numbers have a 1. OR outputs a 1 where either has a 1. XOR outputs a 1 only where the two bits differ. These are the operations behind bit masks and flag handling in code.
How does hex division work here?
Division returns the whole-number quotient and discards any remainder, the same as integer division in most programming languages. If the second value is zero, the calculator shows a friendly message instead of an answer, since dividing by zero is undefined.
Why do programmers use hexadecimal?
Hex is compact and lines up neatly with binary, since one hex digit equals four bits and one byte is two hex digits. That makes it the standard way to show memory addresses, color codes, bit masks, and hash values, which would be far harder to read as long binary strings.
Is my data sent anywhere?
No. The calculator runs entirely in your browser. Your values are converted and computed on your own device and are never uploaded, logged, or stored on any server. You can use it offline once the page has loaded.
