Decimal ↔ Hexadecimal Converter

Convert between decimal and hexadecimal numbers instantly

Decimal Number

Enter decimal (base-10) number (0-65535)

Hexadecimal Number

Enter hexadecimal (base-16) number

Conversion Result

255₁₀ = FF₁₆

Binary: 11111111₂ • Bits: 8

📚 Decimal ↔ Hexadecimal Conversion Details

Decimal to Hex Formula

// Divide by 16, track remainders
255 ÷ 16 = 15 remainder 15
15 ÷ 16 = 0 remainder 15
Result: FF (15=F, 15=F)

Repeatedly divide by 16 and use remainders (0-15 → 0-9,A-F)

Hex to Decimal Formula

// Multiply digits by 16^n
FF = F×16¹ + F×16⁰
= 15×16 + 15×1
= 240 + 15 = 255

Multiply each digit by 16^n where n is digit position from right

Bidirectional Conversion

This converter works both ways simultaneously:

Type decimal → hex updates automatically
Type hex → decimal updates automatically
Real-time conversion as you type

Common Uses

Computer programming
Color codes (RGB/HEX)
Memory addresses
Digital electronics

🔢 How This Converter Works

This is a bidirectional converter for number systems:

Decimal → Hexadecimal: Divide decimal by 16 repeatedly, convert remainders to hex digits
Hexadecimal → Decimal: Multiply each hex digit by appropriate power of 16
Real-time: Updates happen as you type in either field
Validation: Hex input accepts only 0-9 and A-F characters

// Conversion Algorithms

// Decimal to Hexadecimal
function decimalToHex(decimal) {
return decimal.toString(16).toUpperCase();
}

// Hexadecimal to Decimal
function hexToDecimal(hex) {
return parseInt(hex, 16);
}

📊 Common Conversion Table

Decimal	Hexadecimal	Binary
0	0	0000
1	1	0001
10	A	1010
15	F	1111
16	10	00010000
255	FF	11111111
256	100	000100000000
4096	1000	0001000000000000

🎨 Hexadecimal Color Codes

Hexadecimal is commonly used for color codes in web design:

#FF0000
Red: 255,0,0

#00FF00
Green: 0,255,0

#0000FF
Blue: 0,0,255

#FFFF00
Yellow: 255,255,0

#FFFFFF
White: 255,255,255

#000000
Black: 0,0,0

❓ Frequently Asked Questions

Q: What is hexadecimal numbering system?

A: Hexadecimal is a base-16 number system using digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15).

Q: Why is hexadecimal used in computing?

A: Hexadecimal is convenient because one hex digit represents exactly 4 binary bits (nibble), making it easier to read and write binary data.

Q: What is the largest decimal number this converter handles?

A: This converter handles numbers up to 65,535 (FFFF in hex) for optimal performance, but can handle larger numbers as well.

Q: How do I convert hex to decimal manually?

A: Multiply each hex digit by 16 raised to its position power (starting from 0 on the right), then sum all results.