Calculators

Digital Root Calculator

Find the digital root of a whole number with exact digit-sum steps privately in your browser.

Repeatedly add decimal digits until one digit remains. Large integers are handled exactly. Your data stays in your browser.

Enter a non-negative whole number of up to 100 digits. Use digits only, without commas or exponent notation. Zero returns zero.

Your digital root will appear here.

Reduce a number by repeatedly adding its digits.

The base-10 digital root is the single digit obtained by repeatedly summing decimal digits. For 9875, add 9 + 8 + 7 + 5 = 29, then 2 + 9 = 11, then 1 + 1 = 2. The digital root is 2 after three addition rounds; this round count is also called additive persistence. Zero has digital root zero and needs no rounds. For positive integers n, the equivalent formula is 1 + ((n − 1) mod 9); positive multiples of nine have digital root nine, not zero. Enter 1 to 100 digits with no signs, separators, decimals or exponent notation. Surrounding whitespace and leading zeros are accepted; leading zeros are removed before counting rounds. The calculator operates directly on digit strings to preserve integers beyond floating-point precision. It shows each addition round and runs entirely in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

What is a digital root?

It is the single digit left after repeatedly adding the decimal digits of a non-negative integer. For 9875 the steps are 29, 11 and 2, so its digital root is 2.

Is a digital root the same as a remainder modulo nine?

For positive integers, use 1 + ((n − 1) mod 9). Positive multiples of nine have digital root 9. Zero has digital root 0.

What does the addition round count mean?

It counts the digit-sum operations needed to reach one digit, also called additive persistence. Single-digit numbers need zero rounds. Leading zeros are removed first.

Which numbers can I enter?

Enter a non-negative integer of 1 to 100 digits. Leading zeros and surrounding whitespace are accepted. Signs, commas, decimals and scientific notation are rejected. All processing stays in your browser without rounding large integers.