Hex to Decimal calculator
A bidirectional conversion interface for base-16 and base-10 systems. Designed for speed, precision, and a superior developer experience.
HEXADECIMAL
DECIMAL
What is Hexadecimal?
Hexadecimal (or "hex") is a base-16 number system that is fundamental to modern computing. It serves as a more human-readable representation of binary code.
The 16 Digits
Unlike the base-10 decimal system we use daily (0-9), hex uses 16 unique digits. It uses 0-9 for the first ten values, and then the letters A-F to represent values 10 through 15.
A Bridge to Binary
Computers think in binary (base-2). A single hex digit can represent exactly four binary digits (a nibble). For example, the hex digit F is equivalent to the binary string 1111.
Why It's Used
This compact format makes it much easier for programmers and engineers to read and write low-level data like memory addresses, color codes, and file data.
The Conversion Process
Understanding how to convert between decimal and hexadecimal is key to working with low-level data. Here’s a look at the math behind the magic.
Decimal to Hexadecimal
To convert a decimal number to hex, you repeatedly divide the decimal number by 16 and record the remainders. The hex string is the sequence of remainders read from bottom to top. For example, to convert decimal 255:
255 ÷ 16 = 15remainder15 (F)15 ÷ 16 = 0remainder15 (F)
Reading the remainders up gives you FF.
Hexadecimal to Decimal
To convert a hex number to decimal, you multiply each digit by 16 raised to the power of its position (starting from 0 on the right). For example, to convert hex 1A3:
3 × 16⁰ = 3 × 1 = 3A (10) × 16¹ = 10 × 16 = 1601 × 16² = 1 × 256 = 256
Adding these up (3 + 160 + 256) gives you decimal 419.
Key Features of System.Translate
This tool was built with developers and designers in mind, offering a fast, intuitive, and error-proof conversion experience.
Bidirectional & Live
There's no need for a "swap" button. Simply type in either field, and the other updates in real time, creating a seamless workflow.
Intelligent Formatting
The calculator automatically groups hex digits into pairs and adds commas to decimal numbers, improving readability for large values.
Live Color Preview
For designers and web developers, entering a 6-digit hex code instantly generates a color swatch, allowing you to validate your color values on the fly.
Frequently Asked Questions
Get quick answers to common questions about hexadecimal, decimal, and our converter.
What are some common uses for hexadecimal numbers?
Hexadecimal is used in many areas of computing, including:
- Web Design (CSS): Color codes like
#FFA800define colors using hex values for Red, Green, and Blue. - Computer Memory: Memory addresses and error codes are often displayed in hex because it's more compact than binary.
- File Editing: Hex editors allow developers to view and edit the raw binary data of a file in a more readable format.
- Networking: MAC addresses, which uniquely identify devices, are represented as a sequence of hexadecimal numbers.
Can I convert negative numbers?
This calculator is designed for converting unsigned (non-negative) integers. Representing negative numbers requires a specific system, most commonly "two's complement," which depends on a fixed number of bits (e.g., 8-bit, 16-bit, 32-bit). For that functionality, please check out our dedicated Two's Complement Calculator.
What is the largest number I can convert?
The calculator is limited by JavaScript's maximum safe integer value, which is 9,007,199,254,740,991. Any decimal number larger than this may lose precision. In hexadecimal, this corresponds to 1FFFFFFFFFFFFF. This range is sufficient for the vast majority of practical conversion needs.
