Ternary to Decimal Converter
Type a ternary number of any length to see it in decimal, with every step of the working.
Ternary to decimal table
| Ternary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 10 | 3 |
| 11 | 4 |
| 12 | 5 |
| 21 | 7 |
| 22 | 8 |
| 101 | 10 |
| 120 | 15 |
| 121 | 16 |
| 1012 | 32 |
| 2101 | 64 |
| 10201 | 100 |
| 11201 | 127 |
| 11202 | 128 |
| 100110 | 255 |
| 100111 | 256 |
| 1101001 | 1000 |
| 1101221 | 1024 |
Worked examples
10 in decimal
101 (ternary)
10 (decimal)
Decimal value 10.
255 in decimal
100110 (ternary)
255 (decimal)
Decimal value 255.
2026 in decimal
2210001 (ternary)
2026 (decimal)
Decimal value 2026.
About Ternary to Decimal Converter
This converter turns ternary numbers into decimal and shows how. To convert ternary to decimal, multiply each ternary digit by its place value, which is a power of 3, and add the results. For example, 101 in ternary is 10 in decimal, and 2210001 is 2026.
Ternary, or base 3, uses the digits 0, 1 and 2. It is rare in computing, though the Soviet Setun computer of 1958 used a balanced form of it, and it turns up often in maths puzzles. Decimal is the base 10 system we count in every day, with place values of ones, tens, hundreds and so on. Numbers of any length are converted exactly, because the tool works with whole numbers digit by digit instead of rounding.
How to use Ternary to Decimal Converter
- Type or paste a ternary number into the first box. Spaces, underscores and prefixes such as 0x are ignored.
- Read the decimal result straight away in the second box, grouped for easier reading if you leave the box ticked.
- Look at the working table to see each step of the method.
- Copy the result, or use the swap button to convert decimal back to ternary.
Common uses
- Maths puzzles such as the balance scale weighing problem
- Learning how number bases work beyond binary
- Reading about the Setun ternary computer built in 1958
- Coding exercises and competitions
Frequently asked questions
How do I convert ternary to decimal by hand?
Multiply each ternary digit by its place value, which is a power of 3, and add the results. The working table on this page shows exactly these steps for the number you type.
What is 100110 in decimal?
100110 in ternary is 255 in decimal. In decimal it is 255, the largest number that fits in one byte.
What is 2210001 in decimal?
2210001 in ternary is 2026 in decimal.
Can it convert very large numbers?
Yes. Whole numbers with up to 4,096 digits are converted exactly. The working table shows the first rows when a number is very long.
Does it handle fractions or negative numbers?
Negative whole numbers are converted with their minus sign kept. Fractions are not supported, because many fractions that end in one base repeat for ever in another.