What is a Digit Sum?
The digit sum of a number is simply the total you get by adding all of its individual decimal digits together. For example, the digit sum of 12345 is \(1 + 2 + 3 + 4 + 5 = 15\). This Digit Sum Calculator computes that total instantly, and also reports how many digits the number has and its digital root.
How to use it
Type any whole number into the input box and submit. The calculator strips any non-digit characters, adds up the remaining digits, and displays three results: the digit sum, the digit count, and the digital root.
The formula explained
The digit sum is the sum of each digit \(d_i\).
$$\text{Digit Sum} = \sum_{i=1}^{k} d_i \quad\text{where } d_i \text{ are the digits of } \text{Number}$$The digital root is found by repeatedly applying the digit sum until only one digit is left. There is also a closed form: for any positive integer \(n\), the digital root equals \(1 + ((n - 1) \bmod 9)\).
$$\text{Digital Root} = 1 + \left(\left(\sum_{i=1}^{k} d_i\right) - 1 \bmod 9\right)$$The digital root is closely related to the value of a number modulo 9, which is why it powers the classic "casting out nines" check.
Worked example
Take 987654. The digit sum is
$$9 + 8 + 7 + 6 + 5 + 4 = 39$$It has 6 digits. To get the digital root, sum 39's digits: \(3 + 9 = 12\), then \(1 + 2 = 3\). So the digital root of 987654 is 3.
FAQ
Does the digit sum work for very large numbers? Yes — just enter all the digits and they will be added.
What is a digital root used for? It is used in checksum and error-detection tricks like casting out nines, and in recreational mathematics.
What is the digital root of 0? The digital root of 0 is 0.
