Digit Sum Calculator
Calculate sum of digits, digital roots, and check divisibility rules
Calculate Digit Sum
Enter a positive integer
Digit Sum Examples
Basic Examples
Simple Number
567 → 5 + 6 + 7 = 18
Repeating Digits
1111 → 1×4 = 4
Large Number
123456 → 1+2+3+4+5+6 = 21
Digital Root
Step 1
123 → 1+2+3 = 6
Multiple Steps
789 → 7+8+9 = 24 → 2+4 = 6
Complex
9999 → 36 → 9
Divisibility Rules
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Divisible by 3
If digit sum is divisible by 3
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Divisible by 9
If digit sum is divisible by 9
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Digital Root
Keep summing until single digit
Applications
Mathematics
Divisibility testing
Computing
Checksum algorithms
Number Theory
Digital root patterns
Tips & Tricks
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Digital root is always 1-9 (never 0)
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Multiples of 9 have digital root 9
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Use for quick divisibility checks
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Sum of 1 to 100 digits is 901
Understanding Digit Sum
What is Digit Sum?
The digit sum is calculated by adding all individual digits in a number, ignoring place values. For example, the digit sum of 567 is 5 + 6 + 7 = 18.
Digital Root
The digital root is obtained by repeatedly summing digits until a single digit remains. For 567: 5+6+7=18 → 1+8=9, so the digital root is 9.
Calculation Method
- • Count occurrences of each digit (0-9)
- • Multiply each digit by its count
- • Sum all partial products
- • For digital root, repeat until single digit
Divisibility Rules
- •Rule of 3: If digit sum is divisible by 3, the number is too
- •Rule of 9: If digit sum is divisible by 9, the number is too
- •Digital Root: Always between 1-9 for positive integers
Practical Applications
- • Quick divisibility testing
- • Checksum verification in computing
- • Error detection in data transmission
- • Number theory and mathematical analysis
- • Educational tool for understanding place value