Ternary (base 3) to decimal converter
Paste a number in ternary (base 3) to get its decimal value, worked out place by place. Handy for exercises and for checking encoded values.
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How to use it
- Enter number in base 3.
- 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
Value = sum of (digit × 3^position), with position 0 at the far right. Example: 2210001 = 2×3^6 + 2×3^5 + 1×3^4 + 0×3^3 + 0×3^2 + 0×3^1 + 1×3^0 = 2026.
Example
Inputs: Number in base 3 = 2210001. Result: Decimal value: 2026; With thousands separators: 2,026; Decimal digits: 4.
2210001
2026
Limits and caveats
- Whole numbers only, up to 1000 digits; a radix point is not accepted here.
- The place value table appears for inputs up to 60 digits.
Questions about this tool
How do I convert ternary to decimal by hand?
Multiply each digit by 3 raised to its position, starting at position 0 on the right, then add the results. For example 2210001 in base 3 equals 2026.
Why does ternary need fewer digits than binary?
Each ternary digit carries about 1.585 bits (log2 3), so 255 is 100110 in ternary, six digits against eight in binary.
Which symbols are allowed in base 3?
The digits 0 to 2; spaces are ignored. Any other symbol triggers a message that names it.