Calculate digital root instantly! Get step-by-step calculations, batch processing, and number analysis. Free tool for math, numerology & divisibility testing.
1. Calculate Digital Root
What is Digital Root?
The digital root is the single digit obtained by repeatedly summing all digits of a number until only one digit remains.
Formula: Digital Root = 1 + ((n – 1) mod 9), where n > 0
Special case: If n = 0, then Digital Root = 0
Formula: Digital Root = 1 + ((n – 1) mod 9), where n > 0
Special case: If n = 0, then Digital Root = 0
Result:
–
| Original Number: | – |
| Number of Iterations: | – |
| Digital Root: | – |
Step-by-Step Calculation:
📋 Quick Examples:
• 38: 3+8 = 11 → 1+1 = 2
• 123: 1+2+3 = 6 → 6
• 9999: 9+9+9+9 = 36 → 3+6 = 9
• 456: 4+5+6 = 15 → 1+5 = 6
2. Batch Digital Root Calculator
Batch Results:
| Range: | – |
| Total Numbers: | – |
💡 Note:
Maximum range is 100 numbers at a time for performance reasons.
3. Sum Multiple Numbers
Sum Result:
–
| Numbers Entered: | – |
| Count: | – |
| Sum of Numbers: | – |
| Digital Root of Sum: | – |
Calculation Process:
4. Digital Root Properties
Analysis:
| Original Number: | – |
| Digital Root: | – |
| Divisibility by 9: | – |
| Divisibility by 3: | – |
| Sum of Digits: | – |
| Number of Digits: | – |
📚 Digital Root Properties:
• If digital root = 9, the number is divisible by 9
• If digital root = 3, 6, or 9, the number is divisible by 3
• Digital root repeats in a cycle: 1,2,3,4,5,6,7,8,9…
• Digital root of 0 is always 0
• Adding two numbers: DR(a+b) = DR(DR(a) + DR(b))
📚 About Digital Root:
The digital root (also called repeated digital sum) is a single-digit value obtained by iteratively summing digits. It has applications in numerology, divisibility testing, and checksum validation. For example, credit card validation (Luhn algorithm) uses similar digit-sum principles.
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