Decimal to ternary (base 3) converter
Type a decimal number and see it in ternary (base 3) right away, with the working shown. Useful for math and computer science students checking an exercise.
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How to use it
- Enter decimal number.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Repeated division: n = q × 3 + r, where the remainder r (0 to 2) is the next digit from the right; repeat on q until it reaches 0. Example: 2026 = 2210001 in base 3.
Example
Inputs: Decimal number = 2026. Result: Result in base 3: 2210001; Number of digits: 7.
2026
2210001
Limits and caveats
- Whole numbers only, up to 1000 digits. For fractions use the fractional base converter.
- The step table appears when the result has 60 digits or fewer.
Questions about this tool
How do I convert decimal to ternary by hand?
Divide by 3 and write down the remainder, then divide the quotient by 3 again until it reaches 0, and read the remainders from last to first. For example 2026 becomes 2210001.
What is balanced ternary?
A variant that uses the digits 1, 0 and -1 instead of 0, 1 and 2, so negative numbers need no minus sign. The Soviet Setun computer used it in 1958, and this tool shows it as an extra result where T stands for -1.
Does it handle large and negative numbers?
Yes. It uses exact whole-number math up to 1000 digits with no rounding, and the result uses the digits 0 to 2. A negative number is converted by its absolute value and keeps its minus sign.