Digital Root Calculator

Work out digital root instantly with clear inputs, formula shown and shareable results.

About Digital Root Calculator

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.

Formula

Digital root

dr(v) = 1 + ((v − 1) mod (b − 1)) for v > 0, and 0 for v = 0

Worked example

With the default values below, Digital Root Calculator returns Digital root of 2. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number: 493,193
Digital root baseaccepts 2–36: 10

Results

Digital root: 2
Root found by repeated digit summing: 2
Summing steps needed: 3
Base minus one: 9

Step by step

1Values used
2Digital root
3Digital root= 2
4Root found by repeated digit summing= 2
5Summing steps needed= 3
6Base minus one= 9

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Digital root of 493193?

The digits sum to 29, then 11, then 2 — and the formula gives 1 + ((493193 − 1) mod 9) = 2 directly.

Why is the digital root of any multiple of 9 equal to 9?

Because multiples of 9 are congruent to 0 mod 9, and the formula maps that to 9 rather than 0.