Hexadecimal Calculator

A hexadecimal calculator performs arithmetic using base-16 numbers and converts values between hexadecimal, decimal, binary, and octal. Hexadecimal is widely used in programming, computer science, digital electronics, networking, memory addressing, color values, debugging, and low-level data work.

Unlike the decimal system, which uses ten symbols from 0 through 9, hexadecimal uses sixteen symbols. The first ten are the familiar digits 0 through 9. The remaining six values are represented by the letters A, B, C, D, E, and F, which correspond to decimal values 10 through 15.

This calculator lets you enter two hexadecimal integers and perform addition, subtraction, multiplication, division, modulo, AND, OR, or XOR operations. It also includes a separate base converter so you can translate values between the four most common positional number systems used in computing.

What Is the Hexadecimal Number System?

Hexadecimal is a base-16 positional number system. Each position represents a power of 16. From right to left, the positions have values of 16⁰, 16¹, 16², 16³, and so on.

For example, the hexadecimal value 2F contains a 2 in the sixteens position and F in the ones position. Since F represents decimal 15, the decimal value is:

The hexadecimal value 100 is equal to decimal 256 because the leftmost 1 occupies the 16² position. This is similar to how decimal 100 represents one hundred because the leftmost 1 occupies the 10² position.

Why Hexadecimal Uses A Through F

A base-16 number system needs sixteen unique digits. Decimal already provides ten symbols, 0 through 9, so hexadecimal uses six additional symbols for values ten through fifteen.

A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15. After F, the next hexadecimal number is 10, which represents decimal 16.

That pattern is important when doing arithmetic. For example, hexadecimal F plus 1 equals hexadecimal 10, just as decimal 9 plus 1 becomes decimal 10.

Hexadecimal Addition

Hexadecimal addition works like decimal addition, but carrying happens at 16 instead of 10. Add the rightmost digits first. If the sum is 16 or greater, write the remainder and carry one into the next hexadecimal position.

For a simple example, hexadecimal A plus 5 equals F because decimal 10 plus 5 equals 15. Hexadecimal F plus 1 equals 10 because decimal 15 plus 1 equals 16.

The calculator handles carries automatically, which is especially helpful when adding long hexadecimal values such as memory addresses or encoded identifiers.

Hexadecimal Subtraction

Hex subtraction follows the same positional idea as decimal subtraction. When the top digit is smaller than the bottom digit, borrow one from the next column. In hexadecimal, borrowing one adds decimal 16 to the current position.

For example, hexadecimal 100 minus 1 equals FF. In decimal, this is 256 minus 1, which equals 255. Decimal 255 is hexadecimal FF.

This relationship is common in computing because values such as FF, FFFF, and FFFFFFFF represent sequences of bits set to 1.

Hexadecimal Multiplication

Hexadecimal multiplication can be done using the same long multiplication process taught for decimal numbers, but each digit represents a base-16 value.

For example, hexadecimal A multiplied by hexadecimal 10 equals A0. Hexadecimal 10 represents decimal 16, and decimal 10 times 16 equals 160. Decimal 160 converts back to hexadecimal A0.

For larger values, converting each operand into its numerical value and letting the calculator perform the multiplication is much faster and less error-prone than working through every hexadecimal digit manually.

Hexadecimal Division

Hexadecimal division divides one base-16 integer by another. This calculator returns the integer quotient for the main result. If you need the remainder, use the modulo operation.

For example, hexadecimal 100 divided by hexadecimal 10 equals hexadecimal 10. In decimal, that is 256 divided by 16, which equals 16.

Division by zero is undefined, so the calculator blocks that input and displays a validation message instead of returning an invalid result.

What Is Hexadecimal Modulo?

Modulo returns the remainder after integer division. For example, if one value does not divide evenly by another, modulo tells you what is left over.

In programming, modulo is often used for wrapping values, indexing, grouping, checking divisibility, and extracting parts of numerical data. The arithmetic itself is the same regardless of whether the numbers are displayed in decimal or hexadecimal.

Hexadecimal and Binary

Hexadecimal is especially convenient in computing because one hexadecimal digit corresponds exactly to four binary bits. This makes long binary numbers much shorter and easier for humans to read.

For example, binary 1111 is hexadecimal F. Binary 1010 is hexadecimal A. The eight-bit binary value 11111111 can be split into two groups of four bits: 1111 1111. Each group becomes F, so the hexadecimal value is FF.

Because of this direct four-bit relationship, hexadecimal appears frequently when displaying bytes, machine code, memory addresses, Unicode values, packet data, and debugging output.

How to Convert Hexadecimal to Decimal

To convert hexadecimal to decimal manually, multiply each hexadecimal digit by the appropriate power of 16 and add the results.

Consider hexadecimal 3A7. The rightmost 7 represents seven ones. A represents decimal 10 in the sixteens position, and 3 is in the 256s position.

The base converter performs this calculation automatically and shows the same integer in decimal, binary, octal, and hexadecimal.

How to Convert Decimal to Hexadecimal

One manual method is repeated division by 16. Divide the decimal number by 16, record the remainder, and continue dividing the quotient by 16 until the quotient reaches zero. Read the remainders from last to first.

Remainders 10 through 15 are written as A through F. For example, decimal 255 divided by 16 gives a quotient of 15 with a remainder of 15. Both values are F in hexadecimal, producing FF.

The converter on this page avoids the manual steps and can work directly from decimal input.

How to Convert Hexadecimal to Binary

Convert each hexadecimal digit into four binary bits. For example, hexadecimal C becomes 1100 and hexadecimal 5 becomes 0101. Therefore, hexadecimal C5 becomes binary 11000101.

Leading zeros may be omitted when writing the final numerical value, but keeping four bits per hex digit can make the relationship easier to see.

This direct mapping is one of the main reasons hexadecimal is so useful to programmers and engineers who work with binary data.

How to Convert Binary to Hexadecimal

Starting from the right side of a binary number, divide the bits into groups of four. If the leftmost group contains fewer than four bits, pad it with leading zeros. Convert each four-bit group into the matching hexadecimal digit.

Binary 10110110 can be grouped as 1011 0110. Binary 1011 is B, and 0110 is 6, so the hexadecimal representation is B6.

Hexadecimal and Octal

Octal uses base 8 and digits 0 through 7. Although octal was historically common in computing, hexadecimal is usually more compact for representing modern binary values because one hexadecimal digit maps cleanly to four bits.

Conversion between hex and octal is often easiest by using binary as an intermediate representation or by converting the numerical value directly.

The built-in converter displays all four representations at once, making it easy to compare them.

Bitwise AND in Hexadecimal

Bitwise AND compares corresponding binary bits. A result bit is 1 only when both input bits are 1. Otherwise, the result bit is 0.

For example, hexadecimal FF is binary 11111111 and hexadecimal 0F is binary 00001111. Applying AND gives binary 00001111, which is hexadecimal F.

AND operations are commonly used with bit masks to keep selected bits and clear others.

Bitwise OR in Hexadecimal

Bitwise OR produces a 1 when either corresponding input bit is 1. It is often used when setting flags or combining bit fields.

For example, hexadecimal F0 OR hexadecimal 0F equals FF because the upper four bits come from F0 and the lower four bits come from 0F.

Bitwise XOR in Hexadecimal

XOR means exclusive OR. The result bit is 1 when the two input bits are different and 0 when they are the same.

XOR is used in many programming tasks, checksums, simple data transformations, graphics operations, parity calculations, and low-level algorithms.

Because hexadecimal compresses four binary bits into one digit, hexadecimal notation makes long bitwise values easier to read than raw binary.

What Does the 0x Prefix Mean?

Many programming languages write hexadecimal numbers with a 0x prefix. For example, decimal 255 may be written as 0xFF.

The prefix is not part of the numerical value. It simply tells the reader or programming language that the following digits should be interpreted as hexadecimal.

This calculator accepts hexadecimal input with or without the 0x prefix, so both FF and 0xFF are valid.

Where Hexadecimal Is Used

Hexadecimal appears throughout software development and computer engineering. Memory addresses are often shown in hex because the notation is shorter than binary and maps naturally to groups of bits.

Web developers frequently see hexadecimal in CSS color values. A color such as #FF0000 represents red, where each pair of hex digits controls one RGB color channel.

Hex values also appear in Unicode code points, file formats, network packets, error codes, embedded systems, hardware registers, cryptographic output, MAC addresses, debugging tools, and reverse engineering.

Although each use has its own format and conventions, the underlying base-16 number system remains the same.

Hexadecimal in Web Colors

Six-digit CSS hexadecimal colors contain three two-digit components: red, green, and blue. Each component ranges from hexadecimal 00 to FF, equivalent to decimal 0 through 255.

For example, #FF0000 means maximum red with no green and no blue. #00FF00 means maximum green, and #0000FF means maximum blue. #FFFFFF represents white because all three channels are at 255.

A general hexadecimal calculator can help convert individual channel values, although color design also involves visual and perceptual considerations beyond numerical conversion.

How to Use the Hexadecimal Calculator

Enter the first hexadecimal number in Value A. Choose the arithmetic or bitwise operation you want to perform, then enter the second hexadecimal number in Value B.

Select Calculate Hex Result. The main result is shown in hexadecimal, and the same resulting integer is also displayed in decimal, binary, and octal.

If you only need to convert a number rather than perform arithmetic, use the separate Number Base Converter. Choose the input base, enter your number, and select Convert Number.

Inputs are validated according to their selected base. A binary value may contain only 0 and 1, an octal value may contain only digits 0 through 7, decimal uses 0 through 9, and hexadecimal accepts 0 through 9 plus A through F.

Common Hexadecimal Mistakes

One common mistake is reading hexadecimal digits as ordinary decimal digits. Hexadecimal 10 does not mean decimal ten. It represents decimal sixteen.

Another mistake is treating A through F as letters rather than numeric digits. In base 16, these characters have exact numeric values from 10 through 15.

Users may also accidentally include characters that are not valid in hexadecimal. For example, G is not a hexadecimal digit. Valid hex digits stop at F.

Finally, bitwise calculations are operations on integer bit patterns. They are different from ordinary arithmetic even when the same inputs are displayed in hexadecimal.

Why Programmers Prefer Hex Over Long Binary Strings

Binary is the fundamental representation used by digital systems, but long sequences of 0s and 1s are difficult for people to scan and compare. Hexadecimal dramatically shortens those values without losing the direct relationship to individual bits.

A 32-bit binary number can require 32 characters, while the equivalent hexadecimal value requires only eight hexadecimal digits. Each hex digit maps to one group of four bits, making conversion predictable and compact.

That balance between compactness and binary alignment is why hexadecimal remains an important notation in modern programming, electronics, networking, operating systems, and digital design.