Digit Sum Calculator
Find the sum of digits and the digital root.
Results update as you type.
How it works
Adding up the digits of a number and reducing to a single digit are common operations in math and puzzles, and this calculator does both. You enter a whole number, and it returns the sum of its digits and its digital root. The digit sum is simply the total of all the individual digits: for 12345, that is 1 plus 2 plus 3 plus 4 plus 5, which is 15. The digital root goes further, repeatedly summing the digits until only one digit remains: 15 becomes 1 plus 5, which is 6, so the digital root of 12345 is 6. There is a neat shortcut for the digital root: for any positive number it equals 1 plus (the number minus 1) modulo 9, which the calculator uses, reflecting the deep connection between digital roots and arithmetic modulo 9. This is the basis of the old accounting check called casting out nines, used to catch arithmetic errors, since a correct sum or product must have a matching digital root. Digit sums and digital roots appear in divisibility rules (a number is divisible by 3 if its digit sum is, and by 9 if its digital root is 9), in numerology, in recreational math and puzzles, and in checksum schemes. This calculator is handy for students, puzzle solvers, and anyone verifying divisibility or exploring number patterns. Enter a number to find its digit sum and digital root.
Digit sum = add all digits ; digital root = repeat until one digit
The digit sum adds up all the digits of a number. The digital root repeats that process on the result until a single digit remains, which equals 1 plus (n minus 1) mod 9 for positive n, or 0 for zero. The digital root reflects the number's value modulo 9.
Source:Number theory
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Worked example
How to use this calculator
- 1
Enter your values
Enter number.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Sum of digits updates instantly as you type — no button to press.
Frequently asked questions
What is a digit sum?
The digit sum is the total you get by adding up all the individual digits of a number. For example, the digit sum of 12345 is 1 plus 2 plus 3 plus 4 plus 5, which equals 15. It is a simple but useful quantity in divisibility rules, checksums, and recreational mathematics.
What is a digital root?
The digital root is the single digit you reach by repeatedly summing a number's digits until one digit remains. For 12345, the digit sum 15 reduces to 1 plus 5, giving a digital root of 6. It equals 1 plus (n minus 1) mod 9 for positive numbers, reflecting the number's value modulo 9.
How are digit sums used in divisibility rules?
A number is divisible by 3 if and only if its digit sum is divisible by 3, and divisible by 9 if and only if its digit sum (and hence digital root) is divisible by 9. These rules make it easy to test divisibility by 3 and 9 without doing the full division, which is a classic use of digit sums.
What is casting out nines?
Casting out nines is an old technique for checking arithmetic by comparing digital roots. Because digital roots follow the same arithmetic modulo 9, the digital root of a correct sum or product must match the result of the same operation on the inputs' digital roots. A mismatch reveals an error, though it cannot catch every mistake.
Where else are digital roots used?
Digital roots appear in numerology, in recreational math and number puzzles, in some checksum and error-detection schemes, and in exploring patterns in number sequences. Because the digital root captures a number's value modulo 9, it connects everyday digit manipulation to modular arithmetic, making it both a practical tool and a source of mathematical curiosity.