Number Converter
About Balanced Ternary
Balanced ternary is a base-3 system using the digits T (−1), 0 (0) and 1 (+1). It represents positive numbers, negative numbers and zero all in one notation — no separate minus sign required.
Negating a number is wonderfully simple: just swap every 1 with a T and every T with a 1. For example, 1T0 equals 6, so its negative T10 equals −6.
Balanced Ternary Calculator
Type with your keyboard: 1 0 T · + − * / % · Enter = · ⌫ delete · Esc clear
How it works
Each operand is read as a balanced ternary integer, the arithmetic is done exactly, and the answer is shown both in balanced ternary and (in orange) its decimal value. Division uses integer (truncated) division; use mod for the remainder.
Handy Utilities
Negator
Flip the sign instantly by swapping every 1 ↔ T.
Increment / Decrement
Step a balanced ternary number up or down by one.
Comparator
Compare two balanced ternary numbers side by side.
The Balance Scale
Balanced ternary gets its name from an old puzzle: weigh any whole number of grams using weights of 1, 3, 9, 27 … placed on either side of a two-pan scale. Each digit says where its weight goes — 1 on the empty pan, T on the object's pan, 0 set aside.
Left pan · holds the object
Right pan · counterweights
The conversion algorithm, step by step
Repeatedly divide by 3, but keep the remainder balanced in {−1, 0, +1}. A remainder of 2 becomes −1 (digit T) with a carry of +1 to the next division.
Reference & Charts
Value chart (−13 to 13)
Decimal, balanced ternary, and standard ternary (base-3 with digits 0,1,2) side by side. Standard ternary has no representation for negative numbers.
| Decimal | Balanced Ternary | Standard Ternary |
|---|
Powers of three
The place values of every balanced ternary digit.
| Place | Decimal value | Balanced ternary |
|---|