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Number Base Converter

Converts an integer written in one base (2–36) to another, using exact arbitrary-precision arithmetic, and always shows the binary, octal, decimal and hexadecimal forms.

When to use

You need to convert between binary, octal, decimal, hexadecimal or any positional base up to 36, including large integers.

Do not use when: The value has a fractional part, you need Roman numerals (use roman-numeral) or byte/bit unit conversions (use data-storage).

Formula

value = Σ dᵢ × from_base^i (digits read right to left); the result digits are the remainders of repeated division by to_base

Inputs

Parameter	Type	Required	Description
`value`	string	yes	Integer written in the source base, e.g. 'ff' or '1010'. Letters a–z stand for digits 10–35 (case-insensitive); an optional leading '-' and the prefixes 0x, 0o, 0b are accepted.
`from_base`	integer	default 10	Base of the input value. Range: ≥ 2, ≤ 36
`to_base`	integer	default 2	Base of the result. Range: ≥ 2, ≤ 36

Outputs

Output	Type	Description
`result`	string	The number written in to_base (digits above 9 as uppercase letters).
`decimal`	string	Exact base-10 representation (a string so that very large values are not rounded).
`decimal_value`	number	Base-10 value as a number; omitted when it exceeds 2^53.
`binary`	string	Base-2 representation.
`octal`	string	Base-8 representation.
`hexadecimal`	string	Base-16 representation.

Example

ff (hex) to decimal: {"value":"ff","from_base":16,"to_base":10} → {"result":"255","decimal":"255","decimal_value":255,"binary":"11111111","octal":"377","hexadecimal":"FF"}

1010 (binary) to hex: {"value":"1010","from_base":2,"to_base":16} → {"result":"A","decimal":"10","decimal_value":10,"binary":"1010","octal":"12"}

GET https://tttkmbb.com/api/v1/calculate/base-converter?value=ff&from_base=16&to_base=10

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/base-converter (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/base-converter · Markdown: https://tttkmbb.com/math/base-converter.md · JSON definition: https://tttkmbb.com/math/base-converter.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="base-converter"
OpenAPI operationId: convert_number_base
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Radix (reference)
Wikipedia – Positional notation (reference)
Wolfram MathWorld – Base (reference)

FAQ

Are negative numbers supported?

Yes, with a leading minus sign (sign-magnitude form). Two's-complement bit patterns are not interpreted.

What about fractions like 0.1 in binary?

Not supported; only integers are converted. Multiply by a power of the base first if you need fixed-point digits.

Related calculators

Modulo Calculator — Remainders used by the conversion algorithm.
Data Storage Converter — Convert between bits, bytes and larger units.
Roman Numeral Converter — A non-positional numeral system.