Hexadecimal to Decimal Converter

Convert hex values to decimal numbers instantly with detailed calculations

Enter Hexadecimal Value Invalid hexadecimal value

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How Hexadecimal to Decimal Conversion Works

Hexadecimal is a base-16 number system that uses 16 distinct symbols: 0-9 represent values zero to nine, and A-F represent values ten to fifteen. Converting hex to decimal involves multiplying each digit by powers of 16 and summing the results.

Conversion Formula

For a hexadecimal number with digits d_n-1…d₂d₁d₀:

Decimal = d_n-1 × 16^n-1 + … + d₂ × 16² + d₁ × 16¹ + d₀ × 16⁰

Step-by-Step Conversion Examples

Example 1: Convert 2F to Decimal

2F₁₆ = (2 × 16¹) + (F × 16⁰)
= (2 × 16) + (15 × 1)
= 32 + 15
= 47₁₀

Example 2: Convert 1A3 to Decimal

1A3₁₆ = (1 × 16²) + (A × 16¹) + (3 × 16⁰)
= (1 × 256) + (10 × 16) + (3 × 1)
= 256 + 160 + 3
= 419₁₀

Example 3: Convert CAFE to Decimal

CAFE₁₆ = (C × 16³) + (A × 16²) + (F × 16¹) + (E × 16⁰)
= (12 × 4096) + (10 × 256) + (15 × 16) + (14 × 1)
= 49152 + 2560 + 240 + 14
= 51966₁₀

Hexadecimal to Decimal Conversion Chart

Quick reference table for common hexadecimal values and their decimal equivalents:

Hex	Decimal	Hex	Decimal	Hex	Decimal	Hex	Decimal
0	0	10	16	40	64	A0	160
1	1	11	17	50	80	B0	176
2	2	12	18	60	96	C0	192
3	3	13	19	70	112	D0	208
4	4	14	20	80	128	E0	224
5	5	15	21	90	144	F0	240
6	6	1A	26	100	256	FF	255
7	7	1F	31	200	512	FFF	4095
8	8	20	32	300	768	FFFF	65535
9	9	2F	47	400	1024	FFFFF	1048575
A	10	30	48	500	1280	FFFFFF	16777215
B	11	3C	60	600	1536	FFFFFFF	268435455
C	12	3E	62	700	1792	FFFFFFFF	4294967295
D	13	3F	63	800	2048	–	–
E	14	40	64	900	2304	–	–
F	15	–	–	A00	2560	–	–

Popular Hexadecimal Conversions

Here are some frequently converted hex values in programming and computer science:

Color Codes

FFFFFF = 16,777,215 (White)
000000 = 0 (Black)
FF0000 = 16,711,680 (Red)
00FF00 = 65,280 (Green)
0000FF = 255 (Blue)

Memory Addresses

1000 = 4,096
2000 = 8,192
4000 = 16,384
8000 = 32,768
10000 = 65,536

Binary Multiples

FF = 255 (1 byte max)
FFFF = 65,535 (2 bytes)
FFFFFF = 16,777,215 (3 bytes)
FFFFFFFF = 4,294,967,295 (4 bytes)

Powers of 16

10 = 16 (16¹)
100 = 256 (16²)
1000 = 4,096 (16³)
10000 = 65,536 (16⁴)

About Hexadecimal System

The hexadecimal number system is a base-16 positional numeral system that uses sixteen distinct symbols. Unlike the decimal system which uses ten digits (0-9), hexadecimal extends the digit range by including letters A through F to represent values from 10 to 15.

Hexadecimal Digit Values

0=0, 1=1, 2=2, 3=3, 4=4, 5=5, 6=6, 7=7, 8=8, 9=9, A=10, B=11, C=12, D=13, E=14, F=15

Why Use Hexadecimal?

Hexadecimal notation provides a more compact and human-readable representation of binary data. Each hex digit represents exactly four binary digits (bits), making it particularly useful in computer programming, memory addressing, and color coding in web design.

Programming Applications

Memory addresses, machine code representation, debugging output, bitwise operations, and low-level system programming all commonly use hexadecimal notation.

Web Design Usage

HTML and CSS color codes use hexadecimal format (#RRGGBB) where each pair of digits represents red, green, and blue intensity values from 00 to FF.

About Decimal System

The decimal system, also known as base-10 or denary, is the standard number system used in everyday life. It employs ten digits (0-9) and each position represents a power of 10. This system originated from counting on ten fingers and has been used by numerous ancient civilizations.

Decimal Position Values

In the decimal system, each digit position represents a power of 10. The rightmost digit is the ones place (10⁰), the next is tens (10¹), then hundreds (10²), and so on. For example, the number 5,432 represents:

5,432 = (5 × 10³) + (4 × 10²) + (3 × 10¹) + (2 × 10⁰)
= 5,000 + 400 + 30 + 2

Related Number System Conversions

Hexadecimal is one of several number systems used in computing. Here are other common conversions:

Hex to Binary

Convert hexadecimal directly to binary representation. Each hex digit converts to exactly 4 binary digits.

Hex to Octal

Transform hexadecimal values into base-8 octal notation, another compact way to represent binary data.

Decimal to Hex

Reverse conversion from base-10 decimal numbers back to hexadecimal format.

Binary to Decimal

Convert binary (base-2) numbers to decimal format for easier human comprehension.

Frequently Asked Questions

What is hexadecimal used for?

Hexadecimal is widely used in computer science and programming for representing memory addresses, color codes in web design, MAC addresses, IPv6 addresses, assembly language programming, and debugging. Its compact notation makes binary data more readable while maintaining a direct relationship with binary values.

How do you convert hex to decimal manually?

To convert manually, multiply each hex digit by 16 raised to the power of its position (starting from 0 on the right), then sum all values. Remember that A=10, B=11, C=12, D=13, E=14, and F=15. For example, 2A = (2×16¹) + (10×16⁰) = 32 + 10 = 42.

What is the largest hex value I can convert?

This converter supports up to 16 hexadecimal digits, with a maximum value of 7FFFFFFFFFFFFFFF. This equals 9,223,372,036,854,775,807 in decimal, which is the largest signed 64-bit integer value.

Can hexadecimal have decimal points?

Yes, hexadecimal can represent fractional values using a decimal point (or hexadecimal point). Digits after the point represent negative powers of 16. For example, 0.8 in hex equals 0.5 in decimal because 8×16^-1 = 8÷16 = 0.5.

Why is FF equal to 255?

FF represents the maximum value for a single byte (8 bits). F=15, so FF = (15×16¹) + (15×16⁰) = 240 + 15 = 255. This is why FF appears frequently in programming and represents the maximum intensity in RGB color codes.

What’s the difference between hex and decimal?

Hexadecimal is base-16 using digits 0-9 and A-F, while decimal is base-10 using only 0-9. Hex is more compact for representing binary data, with each hex digit representing exactly 4 bits. Decimal is more intuitive for humans but less efficient for computer-related values.

How does hexadecimal relate to binary?

Hexadecimal has a direct relationship with binary. Each hex digit represents exactly four binary digits (bits). For example, F in hex equals 1111 in binary. This makes hex a convenient shorthand for writing and reading binary values.

Are hexadecimal letters case-sensitive?

No, hexadecimal letters are not case-sensitive. You can write A-F in either uppercase or lowercase (a-f), and they represent the same values. Most programming languages and systems accept both formats interchangeably.