Number Base Arithmetic Calculator

This number base arithmetic calculator adds, subtracts or multiplies two whole numbers written in base 2 (binary), base 8 (octal), base 12 (duodecimal) or base 16 (hexadecimal), instead of the base 10 you use every day. You enter a first number and a second number, choose whether to add, subtract or multiply them, and pick the base both numbers are written in. Every digit is checked against that base, since a base 2 number can only contain 0s and 1s and a base 16 number can only use 0 to 9 and A to F, and the calculator flags anything that does not fit before it works out an answer. Once your entries are valid, it returns the result written back in the same base you chose, plus the equivalent decimal value and a label confirming which base is in use, so you can double-check the answer in whichever number system you read most easily. This is handy for programming and computer science study, digital electronics work, exam preparation, or simply building a feel for how place value carries across bases other than base 10. To use it, type your two numbers, choose the operation and base, and the result updates automatically as you go. Try the binary example already loaded, 1010 plus 11, to see how the tool converts between bases and checks its own working in decimal.

First number

Second number

Operation

Base

1101 (base 2)

Result (decimal)13

Basebase 2

The formula

Each number is read in the chosen base, the operation is carried out, and the result is written back in that base. A digit must be less than the base, so base 2 allows only 0 and 1, base 16 allows 0 to 9 and A to F.

Worked example

In binary, 1010 + 11 means 10 + 3 in decimal, which is 13, written 1101 in binary. Enter 1010 and 11 with base 2 and plus to confirm.

Frequently asked questions

What bases can I use?

This tool offers base 2, 8, 12 and 16, the most common non-decimal bases in computing and maths.

What if I type an invalid digit?

The calculator flags it. Each digit must be smaller than the base, so 2 is not allowed in binary.

Why show the decimal too?

So you can check the result, since most people read decimal more easily than other bases.

Who this calculator is for

This calculator is for students, programmers and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid input.
The standard algorithm is applied.
Results are rounded for display.

Formula and sources

Related calculators

Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Prime Factorisation Calculator: factor a number into primes.

If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.

Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.

Calculate.co.nz is the sister site of CalculatorHub.com, the world's largest calculator website by tool count.

All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.

Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.

Calculate.co.nz is also partnered with Health Based Building and Premium Homes to promote informed choices that lead to better long-term outcomes for Kiwi households.

Calculate.co.nz is hosted in Auckland by SiteHost New Zealand.

All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.

About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use

Reviewed and maintained. Last reviewed 2026-08-15 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.