Decimal to septenary (base 7) converter
Type a decimal number and see it in septenary (base 7) 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 × 7 + r, where the remainder r (0 to 6) is the next digit from the right; repeat on q until it reaches 0. Example: 2026 = 5623 in base 7.
Example
Inputs: Decimal number = 2026. Result: Result in base 7: 5623; Number of digits: 4.
2026
5623
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 septenary by hand?
Divide by 7 and write down the remainder, then divide the quotient by 7 again until it reaches 0, and read the remainders from last to first. For example 2026 becomes 5623.
How does base 7 relate to weeks?
The last base 7 digit is the days left over after whole weeks. For example 30 days is 42 in base 7, which means 4 weeks and 2 days.
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 6. A negative number is converted by its absolute value and keeps its minus sign.