Base Calculator
Number Base Converter and Binary Calculator works out Result in the target base and Decimal value from Number, From base and To base. The default figures on this page give result in the target base of 10; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
2 steps
- "1010" read in base 2 is 10 in decimal.
- 10 in base 10 is 10.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Number Base Converter and Binary Calculator calculates
Converts whole numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36, and performs binary arithmetic and bitwise operations with two's complement fixed-width results.
How to use this Number Base Converter and Binary Calculator
Enter Number, From base, To base and Operation. Result in the target base updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Result in the target base, Decimal value and Binary.
The method follows Donald E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms, section 4.1 (Positional Number Systems), IEEE Std 754 / ISO/IEC 9899 (C) section 6.2.6.2 - integer representations and ECMA-262, ECMAScript Language Specification - BigInt.asUintN / BigInt.asIntN.
Binary 11010110 to decimal example
With Number: 11010110, From base: 2, To base: 10, the calculator returns Result in the target base: 214, Hexadecimal: d6, Octal: 326. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Result in the target base, Decimal value and Binary. The inputs you can vary are Number, From base, To base, Operation, Second number (B) and Word width.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to do base on a calculator?
Converts whole numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36, and performs binary arithmetic and bitwise operations with two's complement fixed-width results. Open “How this is worked out” beside the result to see each step for your own figures.
Do we use base 10 or 9?
Converts whole numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36, and performs binary arithmetic and bitwise operations with two's complement fixed-width results. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give 10.
What is base 7 of 100?
Converts whole numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36, and performs binary arithmetic and bitwise operations with two's complement fixed-width results. On this page it is computed from Number, From base and To base and shown as Result in the target base, Decimal value and Binary.
What is a base calculator used for?
It needs Number, From base, To base, Operation, Second number (B) and Word width. Nothing else is required, and the figures stay in your browser.
What information do I need for the Number Base Converter and Binary Calculator?
You need Number, From base, To base, Operation, Second number (B), Word width and Uppercase digits. The page opens with default figures that give result in the target base of 10, so you can see the scale before entering your own.
What does this Number Base Converter and Binary Calculator show?
It shows Result in the target base, Decimal value, Binary, Octal, Hexadecimal, Decimal value (numeric), Bits needed (magnitude) and Two's complement pattern, with the working and any warnings for your entries.