Whether you're a programmer debugging code, a student learning number systems, or a professional working with memory addresses and color codes, understanding hexadecimal to decimal conversion is a fundamental skill. Our hex to decimal converter simplifies this process, transforming complex hexadecimal values into familiar decimal numbers instantly. This tool eliminates manual calculation errors and saves valuable time when working with computer systems, web development, or digital design projects.

How to Convert Hex to Decimal

Converting hexadecimal numbers to decimal requires understanding positional notation. Each digit in a hexadecimal number represents a value multiplied by a power of 16, starting from the rightmost position. The process involves three main steps that anyone can master with practice.

First, identify each hexadecimal digit and its position from right to left. The rightmost digit occupies position 0, the next digit position 1, and so on. Second, convert each hexadecimal digit to its decimal equivalent. Remember that digits 0-9 represent their numeric values, while letters A through F represent decimal values 10 through 15 respectively. Third, multiply each digit's decimal value by 16 raised to its position power, then sum all the results together.

For instance, when converting the hexadecimal number 2B3, you would calculate: (2 × 16²) + (11 × 16¹) + (3 × 16⁰) = (2 × 256) + (11 × 16) + (3 × 1) = 512 + 176 + 3 = 691. This systematic approach ensures accurate conversions every time, whether you're working with simple two-digit hex values or complex multi-digit hexadecimal numbers.

Hex to Decimal Formula

The mathematical formula for converting hexadecimal to decimal follows a straightforward pattern based on positional notation. The general formula can be expressed as:

In this formula, d represents each hexadecimal digit, and n represents the position of that digit counting from right to left, starting at zero. The subscript indicates the position, with d₀ being the rightmost digit and dₙ being the leftmost digit. Each term multiplies the digit's decimal value by 16 raised to its positional power.

To apply this formula practically, work from right to left. For a hexadecimal number like A7F, you calculate: F (15) × 16⁰ + 7 × 16¹ + A (10) × 16² = 15 × 1 + 7 × 16 + 10 × 256 = 15 + 112 + 2560 = 2687. This formula works for any hexadecimal number, regardless of length, making it the universal method for hex-to-decimal conversion.

How to Convert Fractional Hexadecimal Numbers to Decimal

Converting fractional hexadecimal numbers requires extending the conversion process to handle digits after the hexadecimal point. The principle remains similar to integer conversion, but negative powers of 16 are used for fractional parts. This technique is essential when working with precise hexadecimal representations that include decimal components.

For the integer part, use the standard conversion method with positive powers of 16. For the fractional part, use negative powers starting from -1 for the first digit after the point, -2 for the second, and so on. Each fractional digit is multiplied by 16 raised to its negative positional power, then all fractional contributions are added together.

Consider the hexadecimal number 3A.5B. The integer part 3A converts to 58 in decimal. For the fractional part .5B, calculate: (5 × 16⁻¹) + (11 × 16⁻²) = (5 × 0.0625) + (11 × 0.00390625) = 0.3125 + 0.04296875 = 0.35546875. Combining both parts gives 58.35546875 as the final decimal result. This method ensures precise conversion of any fractional hexadecimal value.

When working with fractional hex numbers, remember that each position after the point represents increasingly smaller values. The first position after the point represents sixteenths (1/16), the second represents 256ths (1/256), the third represents 4096ths (1/4096), and so on. This pattern continues infinitely, allowing representation of any decimal fraction in hexadecimal notation.

Hex to Decimal Conversion Table

A conversion table provides quick reference for common hexadecimal values and their decimal equivalents. This reference tool is invaluable for rapid conversions and helps build familiarity with hexadecimal notation patterns.

This table covers all sixteen hexadecimal digits from 0 to F. For multi-digit hexadecimal numbers, combine the values using the positional formula. Common two-digit combinations include FF (255), 10 (16), 1A (26), and 64 (100). Memorizing these basic conversions accelerates your ability to work with hexadecimal values in practical applications.