Computer Science · Digital & Computing
Hexadecimal ↔ Decimal Converter
Convert hexadecimal (base-16) to decimal (base-10) and back in both directions.
Calculator
Formula
Hex to decimal: each hex digit h_i (0–F) is multiplied by 16 raised to its position i from the right. Decimal to hex: repeatedly divide by 16 and collect remainders (0–9, A–F).
Source: Knuth, D. E. — The Art of Computer Programming, Vol. 2. Addison-Wesley, 1997.
How it works
Hexadecimal uses 16 symbols: 0–9 and A–F (where A=10, B=11, C=12, D=13, E=14, F=15). Each hex digit represents exactly 4 binary bits, making hex a compact representation of binary data widely used in programming, memory addresses, and color codes.
Hex to decimal: multiply each digit by 16 raised to its position from the right and sum. Decimal to hex: repeatedly divide by 16, collecting remainders as hex digits read bottom-to-top.
Worked example
Hex → Decimal: Convert 1F4.
1×16² + F×16¹ + 4×16⁰ = 256 + 240 + 4 = 500
Decimal → Hex: Convert 500.
500÷16=31 r4, 31÷16=1 r15(F), 1÷16=0 r1 → read upward: 1F4
Limitations & notes
Handles non-negative integers only. Numbers above 53 bits may lose precision. Input letters must be A–F (case-insensitive). Does not support hex fractions or negative numbers.
Frequently asked questions
What are the hex digits A–F?
A=10, B=11, C=12, D=13, E=14, F=15. These extend the decimal digits 0–9 to give 16 unique symbols for base-16.
Why is hexadecimal used in computing?
Each hex digit maps exactly to 4 binary bits, so 2 hex digits represent a byte. This makes hex much more compact and readable than binary for memory addresses, color codes, and machine code.
How do I convert hex FF to decimal?
F×16 + F×1 = 15×16 + 15 = 240 + 15 = 255. This is why #FF in RGB color codes means maximum intensity (255).
Is hex conversion lossless?
Yes, for non-negative integers within JavaScript's 53-bit safe integer range. Every integer maps exactly to one hex representation.
How does hex relate to binary?
Every hex digit = exactly 4 binary bits. Hex 1F4 = binary 0001 1111 0100. This direct mapping makes hex a shorthand for binary in all computing contexts.
Last updated: 2025-01-15 · Formula verified against primary sources.