Hex Calculator
A hex calculator performs basic arithmetic operations like addition, subtraction, multiplication, and division on hexadecimal numbers. Hexadecimal is a base 16 numeral system that uses sixteen distinct symbols: numbers 0 through 9 to represent values zero to nine, and letters A through F to represent values ten to fifteen. This tool allows programmers, students, and engineers to compute math problems directly in base 16 or convert hex values into decimal, binary, and octal systems instantly.
Maximum value: FFFFFFFF₁₆ (4,294,967,295₁₀)
Enter hex numbers (0-9, A-F)
= 2575 in decimal
= 2860 in decimal
Hexadecimal Result
153B₁₆
Decimal Result
5,435₁₀
Additional Number Formats
Step-by-Step Solution
Convert hexadecimal inputs to decimal
A0F₁₆ = 2575₁₀, B2C₁₆ = 2860₁₀
Perform addition
2575 + 2860 = 5435
Convert result back to hexadecimal
5435₁₀ = 153B₁₆
Number Converter
Decimal Result
41202₁₀
All Number Formats
Created by Ethan Park
Last updated: September 5, 2026
How to Do Hexadecimal Math
Hexadecimal calculations follow the same arithmetic principles as standard decimal math. The main difference is that base 16 regrouping occurs in sets of 16 rather than sets of 10.
When doing arithmetic by hand, you convert hex characters to their decimal equivalents, perform the operation, and convert the result back to base 16. If you are working on digital logic circuits, you can use a binary calculator to verify bitwise operations alongside your base 16 results.
Here are the primary arithmetic rules for hex calculations:
- Addition: Add two hex values together. If the sum exceeds 15, carry 1 to the next column and subtract 16 from the current position.
- Subtraction: Subtract the lower digit from the upper digit. If borrowing is needed, borrow 1 from the adjacent column, which adds 16 to the current position.
- Multiplication: Multiply digits using their decimal equivalents, convert the result back to base 16, and handle carries across higher powers of 16.
- Division: Divide using long division steps by estimating how many times the divisor fits into the dividend in base 16.
Hexadecimal Arithmetic Operations
Understanding how base 16 operations function step by step helps prevent manual calculation mistakes.
Hex Addition
Adding hexadecimal numbers requires tracking positional values based on powers of 16.
Example: Add 1A + 2F
- Add the rightmost digits: A (10) + F (15) = 25 in decimal.
- Since 25 is greater than 15, divide by 16: 25 / 16 = 1 with a remainder of 9. Write down 9 and carry 1.
- Add the next column including the carry: 1 + 1 + 2 = 4.
- Result: 49 in hex.
Hex Subtraction
Subtraction relies on borrowing 16 from the next left position whenever a top digit is smaller than the bottom digit.
Example: Subtract 32 - 1B
- Subtract the rightmost digits: 2 minus B (11) requires a borrow.
- Borrow 1 from the 3 column, reducing 3 to 2. Add 16 to 2, making it 18.
- Subtract: 18 - 11 = 7.
- Subtract the next column: 2 - 1 = 1.
- Result: 17 in hex.
You can check conversions for other systems using the octal calculator when working with low-level computer architecture.
Hexadecimal Conversion Table
Converting between base 16, base 10, base 8, and base 2 is essential for programming and memory addressing. The chart below lists the standard conversions for values 0 through 15.
| Hexadecimal (Base 16) | Decimal (Base 10) | Binary (Base 2) | Octal (Base 8) |
|---|---|---|---|
| 0 | 0 | 0000 | 0 |
| 1 | 1 | 0001 | 1 |
| 2 | 2 | 0010 | 2 |
| 3 | 3 | 0011 | 3 |
| 4 | 4 | 0100 | 4 |
| 5 | 5 | 0101 | 5 |
| 6 | 6 | 0110 | 6 |
| 7 | 7 | 0111 | 7 |
| 8 | 8 | 1000 | 10 |
| 9 | 9 | 1001 | 11 |
| A | 10 | 1010 | 12 |
| B | 11 | 1011 | 13 |
| C | 12 | 1100 | 14 |
| D | 13 | 1101 | 15 |
| E | 14 | 1110 | 16 |
| F | 15 | 1111 | 17 |
Converting Hex to Decimal and Binary
Base 16 is widely used in computing because each hex digit maps directly to four binary bits, known as a nibble.
To convert hex to decimal, multiply each digit by 16 raised to the power of its position index, starting from 0 on the far right:
Decimal Value = (Digit_n * 16^n) + ... + (Digit_1 * 16^1) + (Digit_0 * 16^0)
To convert hex to binary, replace each hexadecimal character with its corresponding 4-bit binary group from the table above. If your calculations involve signed integers or twos complement values, run your results through a modulo calculator to determine remainder limits in bitwise structures.
Frequently Asked Questions
What does hex stand for?
Hex stands for hexadecimal, which is the base 16 numbering system used in computer science to represent binary data in a readable format.
Why do we use letters A through F in hex?
Base 10 only has ten unique numeric digits (0 to 9). Hexadecimal requires sixteen distinct symbols, so the letters A, B, C, D, E, and F represent the single-digit quantities 10, 11, 12, 13, 14, and 15.
What is 10 in hexadecimal?
The hex number 10 represents the decimal value 16. It consists of one group of 16 and zero groups of 1.
How do you convert hex to binary quickly?
Translate every single hex character into its 4-digit binary equivalent. For instance, the hex value 4A converts to 0100 (4) and 1010 (A), yielding 01001010 in binary.
Is hexadecimal case sensitive?
No, hexadecimal is not case sensitive. The lowercase letters a, b, c, d, e, and f mean the exact same thing as uppercase letters A, B, C, D, E, and F.