Free base converter to convert numbers between any base from 2 to 36. Supports binary, octal, decimal, hexadecimal and custom bases, including fractional and negative values.
Use digits 0–9 and letters A–Z (for bases above 10). Only one decimal point is allowed.
Type your number exactly as it appears in the source base, choose the origin and target bases, then hit Convert number to refresh every panel. The helper buttons load the default example, swap the selected bases, or clear the entry so you can start over.
Conversions happen in two conceptual steps: the tool first parses the string into a precise integer or floating point value in decimal, then re-encodes that value into the requested base. Integer conversions use exact BigInt math so they stay precise, while fractional parts track digits with a capped precision to keep the output deterministic.
A number base (or radix) is the number of distinct digits used to write numbers in a positional numeral system. In everyday life we mostly use base 10 (decimal), which has digits 0–9. Computers, however, naturally work in base 2 (binary).
In any base b, digits run from 0 up to b − 1. For bases above 10, we use letters A, B, C, … to represent values 10, 11, 12, and so on. For example, in base 16:
A = 10, B = 11, C = 12, D = 13, E = 14, F = 15Any number in base b can be written as a sum of powers of b. For example, the decimal number 57 in base 10 can be written as:
57 = 5 × 10² + 7 × 10⁰In base 2, the binary number 1011₂ represents:
1011₂ = 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰ = 11₁₀When a decimal point is present, the part to the left is the integer part, and the part to the right is the fractional part. In base b, a number like:
dₖ … d₂ d₁ d₀ . f₁ f₂ … fₙcorresponds to
dₖ b^k + … + d₂ b² + d₁ b¹ + d₀ b⁰ + f₁ b⁻¹ + f₂ b⁻² + … + fₙ b⁻ⁿConverting between bases typically happens in two conceptual steps:
To convert from an arbitrary base b to decimal, multiply each digit by its positional weight (a power of b) and sum everything. For example, converting 7F₁₆ to decimal:
7F₁₆ = 7 × 16¹ + 15 × 16⁰ = 7 × 16 + 15 = 127₁₀To convert a decimal integer N to base b, repeatedly divide by b and collect remainders:
For the fractional part, repeatedly multiply by b and collect the integer part at each step.
A base converter is a digital tool that rewrites the same numeric value using a different numeral system. For example, it can show that 255₁₀ is the same value as FF₁₆, 11111111₂ and 377₈.
The selector allows any integer base from 2 up to 36. That includes binary (2), octal (8), decimal (10), hexadecimal (16) and many other custom bases that appear in coding puzzles or specialised algorithms.
Yes. You can start the number with a minus sign for negative values, and you may include one decimal point to represent fractions (for example -101.11 in base 2 or 3A.F in base 16). The converter processes both the integer and fractional parts.
The calculator validates your input and shows a clear error message if a digit is not allowed in the selected base (for example, using 8 in base 8 or G in base 16). Correct the digit or change the base and try again.
Base conversions are everywhere in computing: encoding and decoding data, working with bitmasks, reading memory dumps, interpreting color codes, writing low-level drivers and debugging network protocols. Being fluent with binary, decimal and hexadecimal is a core skill for developers and computer engineers.