Digital Root Calculator
Use our digital root calculator to find the digital root of a number instantly. Includes digital root meaning, the digital root concept, digital root examples, the digital root formula, and how to find digital root of a number step by step (including the Vedic maths digital root idea).
What is Digital Root?
The digital root of a number is the single-digit value you get by repeatedly adding the digits of the number until only one digit remains.
If you’re searching for digital root meaning or digital root concept, it’s basically “keep summing digits until you get a single digit.” For example, 987 → 9+8+7 = 24 → 2+4 = 6, so the digital root is 6.
Digital root is also commonly discussed in Vedic maths, where the same idea is used to do quick checks (often connected to casting out nines).
Digital Root Formula
You can compute a digital root by repeated digit sums, or using a shortcut formula based on modulo 9.
This works for any non-negative integer.
This is the common digital root formula using mod 9.
So the digital root of a number 493 is 7.
Same result using the shortcut digital root formula.
How to Use the Digital Root Calculator
- 1
Enter a whole number n.
- 2
The calculator adds the digits of n.
- 3
If the sum has more than one digit, it repeats the digit-sum process.
- 4
The final single digit is the digital root of the number.
Frequently Asked Questions
Digital root is the single-digit value obtained by repeatedly summing a number’s digits until one digit remains.
It’s the final single digit after repeatedly adding the digits of that number.
Add the digits. If you get a multi-digit number, add those digits again. Repeat until one digit remains.
dr(n) = 0 if n = 0, otherwise dr(n) = 1 + ((n − 1) mod 9).
Yes. The mod 9 shortcut makes it easy even for very large values.
It’s often used as a quick “casting out nines” check. The digital root relates to a number’s remainder modulo 9 (with a special case for 0).
Yes, only when the number is 0. Otherwise the digital root is 1 through 9.
Because powers of 10 are congruent to 1 modulo 9, digit sums preserve the same remainder mod 9.