Sum of Digits Calculator

Enter any integer to calculate the sum of its digits, see the digit breakdown, running sum, and digital root.

Enter a Number

Result

Sum of Digits
35
Number of Digits 5
Digital Root 8

Digit Breakdown & Running Sum

What Is the Sum of Digits?

The sum of digits of a number is obtained by adding each individual digit together. For example, the sum of digits of 1234 is 1 + 2 + 3 + 4 = 10. This concept is fundamental in number theory and has applications in divisibility tests, checksum algorithms, and mathematical puzzles.

Key Concepts

Digit Sum

Add all digits of a number together to get a single result.

S = d1 + d2 + ... + dn

Digital Root

Repeatedly sum the digits until you get a single digit (1-9). Also called the iterated digit sum.

DR = 1 + ((n - 1) mod 9)

Running Sum

A cumulative sum showing the total as each digit is added from left to right.

R(k) = d1 + d2 + ... + dk

Divisibility Rules Using Digit Sums

The sum of digits has a close relationship with divisibility. A number is divisible by 3 if its digit sum is divisible by 3. Similarly, a number is divisible by 9 if its digit sum is divisible by 9. The digital root provides a quick modular arithmetic check.

Applications

  • Divisibility testing for 3 and 9.
  • Casting out nines for arithmetic verification.
  • ISBN and credit card checksum validation (Luhn algorithm).
  • Numerology and recreational mathematics.