Work out digital root instantly with clear inputs, formula shown and shareable results.
The digital root is what you get by summing digits repeatedly until one digit remains. In base b it equals 1 + ((v − 1) mod (b − 1)) for positive v, so no iteration is really needed.
Digital root
dr(v) = 1 + ((v − 1) mod (b − 1)) for v > 0, and 0 for v = 0
The digits sum to 29, then 11, then 2 — and the formula gives 1 + ((493193 − 1) mod 9) = 2 directly.
Because multiples of 9 are congruent to 0 mod 9, and the formula maps that to 9 rather than 0.