Math & Algebra Tool

Base Converter

Convert numbers between Binary, Decimal, Hexadecimal, and more.

Σ The Formula

Convert between binary, octal, decimal, hexadecimal

Real World Examples

Decimal to Binary
42₁₀ = 101010₂
Hex to Decimal
FF₁₆ = 255₁₀
Binary to Octal
101101₂ = 55₈
Computer Color
White = #FFFFFF (Hex) = (255,255,255) (RGB)

# About This Calculator

A Base Converter translates numbers between different counting systems. We use Base 10 (Decimal) in everyday life, relying on ten digits (0-9). Computers, however, operate on Base 2 (Binary), using only 0 and 1.

Programmers often use Base 16 (Hexadecimal) because it's a compact way to represent binary data (one hex digit = 4 binary bits). Base 8 (Octal) is also used in Unix file permissions.

Understanding bases is creating for computer science, networking (IP addresses), and web design (color codes). Converting manually involves repeated division (to change base) or expansion (to decimal).

This tool supports instant conversion between Binary (2), Octal (8), Decimal (10), and Hexadecimal (16), along with any custom base up to 36.

How To Use

  1. Enter the number in the input field.
  2. Select the base you are converting FROM.
  3. Select the base you are converting TO.
  4. The result appears instantly.

Frequently Asked Questions

Why do computers use binary?+

Because computer hardware is made of transistors that act like switches, having two states: ON (1) and OFF (0). It's the most reliable way to store data physically.

What is Hexadecimal used for?+

It creates human-readable codes for binary data. For example, the binary color '1111 1111' is just 'FF' in hex. It saves space and reduces reading errors.

How do I convert Decimal to Binary manually?+

Repeatedly divide the number by 2 and write down the remainders. Read the remainders from bottom to top. For 5: 5/2=2 R1, 2/2=1 R0, 1/2=0 R1 → 101.

What is the highest base possible here?+

Base 36 (using digits 0-9 and letters A-Z). You can theoretically go higher with more symbols, but 36 is standard for alphanumeric systems.

label={({ name, percent }: { name: string, percent: number }) => `${name} ${(percent * 100).toFixed(0)}%`}?+

No! '10' in Binary means 2 (1 two and 0 ones). '10' in Decimal means ten. The value depends on the base.

Is Base Converter free to use?+

Yes, Base Converter on Matheric is completely free to use. We believe in accessible education and utility for everyone.

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