Digital Root Calculator
This calculator finds the digital root of any non-negative integer — the recursive sum of its digits until a single digit is obtained. It’s widely used in number theory, numerology, and checksum validations.
Digital Root Finder
Digital Root Formula
\[
\text{Digital Root}(n) =
\begin{cases}
0, & \text{if } n = 0 \\
9, & \text{if } n \bmod 9 = 0 \\
n \bmod 9, & \text{otherwise}
\end{cases}
\]
The digital root is the single-digit value obtained by iteratively summing the digits of a number. Alternatively, it can be calculated directly using modulo 9.
Digital Root – Calculation Example
Find the digital root of 9875:
- 9 + 8 + 7 + 5 = 29
- 2 + 9 = 11
- 1 + 1 = 2
Digital root = 2
The digital root is useful in simplifying arithmetic checks, divisibility rules, and recreational math puzzles. It is also used in some ancient systems of numerology. This calculator supports both step-by-step addition and fast modulo-based computation.