Do exact arithmetic in ANY base from 2 to 36 – pick the base, pick the operation, and get the result in that base with a decimal cross-check.
Show calculation steps
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Pick a base, then compute
This calculator makes the base a parameter: choose 2 through 36, enter both operands IN that base, and add, subtract, multiply or divide exactly — results in the same base with decimal verification. It is the generalisation the specific binary/octal/hex calculators instantiate.
Working natively in an unusual base is rarely a daily need — but when it is (checking base-32 arithmetic, teaching positional systems, puzzle work), nothing else substitutes.
Worked example
Base 16: FF + A = 109 (255 + 10 = 265) Base 8: 755 + 22 = 777 (493 + 18 = 511) Base 36: zz + 1 = 100 (1295 + 1 = 1296 = 36²)
One value, many coats
The decimal check line is the constant reminder: arithmetic happens on VALUES, notation merely displays them. zz+1 rolling over to 100 in base 36 is the same event as 99+1→100 in decimal — a place overflowing — seen through a different digit alphabet.
Division semantics
Quotient and remainder both print in the working base, satisfying q×divisor + r = dividend exactly. Mixed-base arithmetic (base-7 plus base-12) requires converting one operand first — the Any Base Converter feeds this page naturally.
Privacy
Exact BigInt arithmetic in your browser; operands never leave it.
How to use the Base-N Calculator
- Choose the working base (2-36).
- Enter both numbers IN that base.
- Pick the operation and click "Calculate".
- Results are in the working base with decimal verification.
Frequently asked questions
What does "working base" mean here?
Both operands are read, and the result written, in the base you select – true base-N arithmetic. FF + A in base 16 is 0x109; the same digits in base 20 would mean different values entirely.
Which bases does it support?
Every base from 2 to 36, using 0-9 then a-z case-insensitively. That covers binary through the densest case-insensitive alphabet.
Why does the same digit string change value across bases?
Positional notation weights digits by powers of the base, so "21" means 2×base + 1: in base 3 it is 7, in base 8 it is 17, in base 16 it is 33 – and in base 2 it is not a number at all, since the digit 2 does not exist there. The base declares the weights; the calculator makes that declaration explicit.
What is division's output?
Integer quotient and remainder, both in the working base – the identity q×divisor + r = dividend holds exactly in every base.
Is mixed-base arithmetic possible – add base 7 to base 12?
Not directly, and no calculator can dodge the mathematics: convert one operand first (Any Base Converter), then compute in a single base. Numbers add; notations do not.
How do letters behave in high bases?
As ordinary digits – in base 36, z is 35, so z + 1 = 10 (one-zero, i.e. 36). The cross-check line translates every such result to decimal.
Where does the base-N arithmetic run?
Locally in your browser, exact at any operand size.
