How this calculator works
Add the decimal digits. If the sum still has more than one digit, repeat. The last single digit is the digital root, and the number of digit-sum operations is called additive persistence. This calculator works with non-negative safe integers, so every entered integer digit is represented reliably.
Formula
dr(0) = 0. For n > 0 in base ten, dr(n) = 1 + ((n - 1) mod 9).
Worked example
9876 gives 9 + 8 + 7 + 6 = 30, then 3 + 0 = 3. Its digital root is 3 and its persistence is 2. The digital root of 18 is 9.
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Frequently asked questions
Why is the digital root of 9 not zero?
Positive multiples of 9 end at 9. The remainder formula treats that case differently from the number zero.
Does this prove an arithmetic answer is correct?
No. Matching digital roots is only a partial check; many different numbers share the same root.
Can I enter a decimal or a negative number?
This tool uses the standard non-negative integer definition. Remove a sign or choose an integer deliberately before using it.