Calculate the iterative sum of a number's digits until a single-digit value is reached.
Last updated: March 2026 | By ForgeCalc Engineering
The digital root (also called the repeated digital sum) of a non-negative integer is the value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.
For example, the digital root of 65,536 is 7, because 6 + 5 + 5 + 3 + 6 = 25, then 2 + 5 = 7. In modular arithmetic, the digital root is related to the remainder when a number is divided by 9.
This formula allows you to find the digital root of any number $n$ without performing iterative additions.
Let's find the digital root of 49,382:
Step 1: 4 + 9 + 3 + 8 + 2 = 26
Step 2: 2 + 6 = 8
Using the formula:
1 + ((49382 - 1) mod 9) = 1 + (49381 mod 9) = 1 + 7 = 8.
Final Answer: 8
The digital root of any multiple of 9 (except 0) is always 9. This is why the 'casting out nines' method works for checking arithmetic.
Only if the original number is 0. For all other positive integers, the digital root is a value between 1 and 9.
It's a technique used to check the accuracy of addition, subtraction, multiplication, and division by comparing the digital roots of the operands and the result.
It is a very simple form of a checksum. While it can catch some errors, it won't catch errors where digits are transposed (e.g., 12 vs 21) because the sum remains the same.
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