Decimal to senary (base 6) converter
Type a decimal number and see it in senary (base 6) 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 × 6 + r, where the remainder r (0 to 5) is the next digit from the right; repeat on q until it reaches 0. Example: 2026 = 13214 in base 6.
Example
Inputs: Decimal number = 2026. Result: Result in base 6: 13214; Number of digits: 5.
2026
13214
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 senary by hand?
Divide by 6 and write down the remainder, then divide the quotient by 6 again until it reaches 0, and read the remainders from last to first. For example 2026 becomes 13214.
Why is base 6 handy for fractions?
Because 6 = 2 × 3, both 1/2 and 1/3 terminate in base 6: a half is 0.3 and a third is 0.2, while a third repeats forever in decimal.
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 5. A negative number is converted by its absolute value and keeps its minus sign.