What is a cross sum?

A cross sum, also known as digit sum, is the result of adding all the individual digits of a number together. For example, the cross sum of 123 is 1 + 2 + 3 = 6. This simple mathematical operation has been used for centuries in numerology, checksum validation, and mathematical puzzles.

What is an iterated cross sum (digital root)?

An iterated cross sum, commonly called a digital root, is calculated by repeatedly summing the digits of a number until only a single digit remains. For 987, the cross sum is 9 + 8 + 7 = 24, and since 24 has two digits, we sum again: 2 + 4 = 6. The digital root of 987 is therefore 6. This single-digit result has interesting mathematical properties and is frequently used in divisibility tests.

Tool description

This calculator instantly computes both the cross sum and the iterated cross sum (digital root) of any number you enter. Results update in real-time as you type, making it easy to quickly check digit sums for multiple numbers. The tool handles numbers of any length and ignores non-numeric characters for convenience.

Examples

Input Cross Sum Iterated Cross Sum
12345 15 6
999 27 9
123456789 45 9
100 1 1
8675309 38 2

Features

  • Real-time calculation as you type
  • Computes both cross sum and digital root simultaneously
  • Handles arbitrarily large numbers
  • Copy results with one click
  • Paste numbers directly from clipboard

Use cases

  • Divisibility testing: A number is divisible by 9 if and only if its digital root is 9. Similarly, a number is divisible by 3 if its digital root is 3, 6, or 9
  • Checksum verification: Many identification systems use digit sums as part of their validation algorithms
  • Numerology calculations: Digital roots are fundamental in numerological analysis and life path number calculations
  • Mathematical education: Teaching addition, number properties, and iterative algorithms
  • Quick mental math verification: Cross-checking calculations by comparing digit sums