Digit Sum Calculator

This calculator adds up the individual digits of any whole number and works out its digital root, the single digit you reach by repeatedly summing the digits until only one remains. Type a whole number into the input box and it instantly returns three results: the digit sum itself, shown as the main figure, the digital root, and the total number of digits you entered. For example, entering 12345 gives a digit sum of 15 (1 + 2 + 3 + 4 + 5), a digital root of 6 (from 1 + 5), and a digit count of 5. Behind the scenes it uses the exact integer algorithm rather than an approximation, and the digital root follows the neat shortcut of 1 plus the remainder when the number minus 1 is divided by nine. Digit sums have genuine practical uses beyond curiosity: they underpin the quick mental test for divisibility by 9, since a number splits evenly by 9 only when its digit sum does too, and they turn up in checksum routines used to catch data entry errors. Students, programmers and anyone exploring number theory use this tool to check working by hand, verify code, or simply satisfy curiosity about a number's properties. Just enter a whole number and read the results, which update live as you type.

Whole number

Digit sum = 15

Digital root6

Number of digits5

The formula

The digit sum adds each digit once. The digital root is found by repeating that until one digit remains, and equals 1 + (n minus 1) mod 9 for any positive n, or 0 when n is 0.

Worked example

For 12345 the digits add to 1 + 2 + 3 + 4 + 5 = 15, and summing again gives 1 + 5 = 6, the digital root. The number has 5 digits. Enter 12345 to confirm.

Frequently asked questions

What is a digit sum?

The total you get by adding all the digits of a number, for example 1 + 2 + 3 = 6 for 123.

What is the digital root?

The single digit reached by repeatedly summing the digits. For 12345 it is 6.

How does this check divisibility by 9?

A number is divisible by 9 exactly when its digit sum is, which is why the digital root of a multiple of 9 is 9.

Who this calculator is for

This calculator is for students, programmers and anyone exploring number theory.

What this calculator assumes

You enter a whole number within the stated range.
The exact integer algorithm is used.
Very large results are shown grouped for readability.

Formula and sources

Related calculators

Prime Factorization Calculator: break a number into prime factors.
LCM Calculator: lowest common multiple.
GCF Calculator: greatest common factor.

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