🔢 Digital Root Calculator
Calculate digital root and sum of digits
How to Use This Calculator
Enter an Integer
Type any whole number (positive or negative). The calculator will use the absolute value.
Click Calculate Digital Root
Press the button to find the digital root and sum of digits instantly.
View Results
See the digital root (1-9), sum of digits, and step-by-step explanation.
Formula
Digital Root(n) = n mod 9 (if n mod 9 ≠0), else 9
Alternative: Repeatedly sum digits until single digit
Example 1: Digital Root of 12345
Method 1: 12345 mod 9 = 6
Method 2: 1+2+3+4+5 = 15 → 1+5 = 6
Answer: 6
Example 2: Digital Root of 99
Method 1: 99 mod 9 = 0, so digital root = 9
Method 2: 9+9 = 18 → 1+8 = 9
Answer: 9
Example 3: Digital Root of 7
Already single digit, so digital root = 7
Answer: 7
About Digital Root Calculator
The Digital Root Calculator finds the digital root of any number by repeatedly summing digits until reaching a single digit. The digital root is always between 1 and 9, except for 0 which has digital root 0.
When to Use This Calculator
- Error Checking: Use "casting out nines" for arithmetic verification
- Number Theory: Study digital root patterns and properties
- Mathematics: Solve problems involving digit sums
- Educational Use: Learn number properties and patterns
- Competitions: Solve competitive math problems
Why Use Our Calculator?
- ✅ Fast Method: Uses mod 9 formula for instant results
- ✅ Multiple Methods: Shows both formula and manual approach
- ✅ Step-by-Step: Explains how the digital root is calculated
- ✅ Educational: Learn digital root properties
- ✅ Completely Free: No registration required
Understanding Digital Root
The digital root is the single-digit result of repeatedly summing the digits of a number.
- Always 1-9 (except 0 for zero itself)
- Equal to n mod 9, or 9 if divisible by 9
- Preserves addition: Dr(a+b) = Dr(Dr(a) + Dr(b))
- Used for arithmetic error checking
Real-World Applications
Casting Out Nines: Verify additions by checking if digital root of sum equals digital root of sum of digital roots.
Checksums: Use digital roots for data verification in some systems.
Tips for Using This Calculator
- Digital root is always 1-9 (or 0 for zero)
- Multiples of 9 have digital root 9
- Works with any positive integer
- Use mod 9 for fastest calculation
Frequently Asked Questions
What is a digital root?
The digital root is the single-digit result (1-9) obtained by repeatedly summing the digits of a number. For example, 38 → 3+8=11 → 1+1=2.
Why is the digital root of 99 equal to 9, not 0?
Special rule: If a number is divisible by 9 (like 99), its digital root is 9, not 0. Only 0 itself has digital root 0.
What's the fastest way to calculate digital root?
Use n mod 9: If the result is 0 (and n ≠0), digital root is 9. Otherwise, digital root = n mod 9.
What is "casting out nines"?
An error-checking method using digital roots. Check if Dr(a + b) = Dr(Dr(a) + Dr(b)) to verify addition.
Can digital root be negative?
No, digital root is always 0-9. Use the absolute value when calculating digital root of negative numbers.
What's the digital root of 0?
The digital root of 0 is 0. This is the only number with digital root 0.