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Algebra · Number systems

Number Base Converter (Bases 2–36)

Convert signed whole numbers between bases 2 and 36, validate every digit, and inspect the base-10 value used as the conversion bridge.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Exact conversion of signed integers using positional numeral systems

Place value

N = Σdᵢbⁱ

Allowed digits

0 ≤ dᵢ < b

Supported range

2 ≤ base ≤ 36A=10, …, Z=35
Algebra · Number systems

Convert an integer between bases

Whole numbers are converted exactly. Digits use 0–9 and A–Z; fractional parts are not supported.

N = Σdᵢbⁱ

Enter a signed whole number and choose source and target bases.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Digits 0–9 have values zero through nine and letters A–Z represent values ten through thirty-five. This reviewed version converts signed integers exactly and does not accept fractional parts.

Worked examples

See the method in practice

01

Hexadecimal to binary

FF in base 16 equals 255 in base 10 and 11111111 in base 2.

02

Binary validation

The input 102 is rejected in base 2 because digit 2 is not part of that numeral system.

Questions

Frequently asked

Why are letters used as digits?

Bases above ten need additional digit symbols; A represents ten, B eleven, through Z thirty-five.

Are results rounded?

No. Integer conversion uses exact whole-number arithmetic.

Can this convert fractions?

Not in this version; fractional expansions may repeat and require a separate precision policy.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

MDN — Number and radix

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology