Skip to content
Math

Number Base Converter

Last updated: July 11, 2026

Convert numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36 with our free online base converter.

How to Use This Calculator

  1. Enter a number in the input field.
  2. Select its source base (binary, octal, decimal, or hexadecimal).
  3. Click Convert to see the equivalent in all four bases simultaneously.
  4. Digits for bases above 10 use letters A–Z (A=10, B=11, ... Z=35).
  5. Toggle the conversion steps to see the detailed working.

Formula

d2d1d0(b) = d2 × b² + d1 × b¹ + d0 × b³

To convert from base b to decimal, multiply each digit by b raised to the power of its position and sum the results. To convert decimal to base b, repeatedly divide by b and collect remainders.

Examples

IP Networking

192.168.1.1 in binary is 11000000.10101000.00000001.00000001 — essential for understanding subnet masks.

Color Codes

CSS uses hex like #FF5733 where FF=255, 57=87, 33=51 in decimal. Each pair represents one RGB channel.

File Permissions

Unix permissions use octal: chmod 755 means rwxr-xr-x. 7=111 (rwx), 5=101 (r-x) in binary.

Frequently Asked Questions

What is a number base?

A number base (or radix) determines how many unique digits are used. Base 10 (decimal) uses 0–9, base 2 (binary) uses 0–1, and base 16 (hex) uses 0–9 plus A–F.

Why is hexadecimal used in computing?

Hex represents 4 bits with a single digit, making binary data more compact and human-readable. One hex digit = exactly 4 binary digits.

What is the 0x prefix?

The prefix 0x (e.g., 0xFF) is a common convention in programming to indicate that a number is written in hexadecimal.

What bases can I convert between?

Any base from 2 to 36 is supported. For bases above 10, letters A through Z represent values 10 through 35.

Disclaimer: This converter is for educational and general-purpose use. For production systems requiring precise base arithmetic, use verified libraries.