Digital Root Calculator

About this calculator

The digital root of a number is found by repeatedly summing its digits until only a single digit remains — for example, 9875 becomes 9+8+7+5=29, then 2+9=11, then 1+1=2, so its digital root is 2. The number of summing steps it takes to get there is called its additive persistence, a separate and less commonly discussed property of the same number.

There’s a shortcut behind the repeated addition: the digital root of any positive integer equals that number modulo 9 (with a digital root of 9, not 0, for exact multiples of 9). This is exactly the basis of the old “casting out nines” technique accountants and students once used to spot-check arithmetic by hand, and it still underlies certain checksum and divisibility-by-9 tricks used in computer science and numerology, where digital roots are treated as a number’s fundamental “essence.”

Enter any whole number and this calculator reduces it step by step to its single-digit digital root, showing you exactly how many summing iterations it took.