Digital Root Calculator
Repeatedly sum digits until you reach a single digit — same full-width layout as our conversion calculators.
Digits only — sums digits repeatedly until one digit remains.
The digital root compresses a positive integer by replacing it with the sum of its digits until the value fits in one digit. It connects directly to divisibility patterns for 3 and 9.
Iteratively replace n with the sum of its decimal digits until n < 10. Equivalently dr(n) = 0 when n = 0; otherwise dr(n) = 1 + ((n − 1) mod 9) for n ≥ 1 in the mapping that sends multiples of 9 to 9.
5+8+9+3+4 = 29 → 2+9 = 11 → 1+1 = 2. Digital root 2.
For positive integers, repeated digit sums yield the same residue class as dividing by 9, except multiples of 9 collapse to 9 rather than 0 in the usual recreational definition.
Digit sums expose arithmetic mistakes quickly and reinforce place-value reasoning when teaching divisibility patterns.
For modulo-9 intuition and classroom shortcuts, see What Is a Digital Root?.
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