1. What is Digit Sum?

The digit sum of a number is the value obtained by adding all the digits in the number. For example, the digit sum of 123 is 1 + 2 + 3 = 6.

2. How Does the Calculator Work?

The calculator uses the digit sum formula:

Where:

• \( d_1 \) to \( d_n \) — Individual digits of the number
• \( n \) — Number of digits

Explanation: The calculator breaks down the number into its individual digits and sums them sequentially.

3. Importance of Digit Sum

Details: Digit sums are used in mathematics for divisibility tests, digital roots, checksums, and various number theory applications.

4. Using the Calculator

Tips: Enter any positive whole number. The calculator will display the sum of all digits and show step-by-step how the sum was calculated.

5. Frequently Asked Questions (FAQ)

Q1: What's the digit sum of 0?
A: The digit sum of 0 is 0.

Q2: How is this different from digital root?
A: Digital root is the recursive sum until you get a single digit (e.g., 99 → 9+9=18 → 1+8=9).

Q3: What are practical uses of digit sums?
A: Used in checksums for error detection, numerology, and some mathematical proofs.

Q4: Can I calculate digit sums for decimal numbers?
A: This calculator works with whole numbers only. For decimals, you could sum digits ignoring the decimal point.

Q5: What's the maximum number this calculator can handle?
A: It's limited by PHP's integer size, typically up to 9,223,372,036,854,775,807 on 64-bit systems.