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Digit Sum & Digital Root Calculator

Find a number’s digit sum.

Result

35
8

How it is calculated

The tool keeps only the digits 0 to 9 of what you type, adds them to get the digit sum, and then repeats the process on the sum until a single digit remains, which is the digital root. For a whole number, the digital root equals the remainder after division by 9 (with 9 instead of 0 for nonzero multiples of 9), so root = 1 + (n − 1) mod 9 for n above zero. All other characters, including a minus sign, a decimal point or separators, are discarded, so 3.14 is treated as the digits 3, 1 and 4. Empty input or input with no digits gives no result. The digit sum is the basis of the divisibility check by 3 and 9.

Worked example

Number 98765. Digit sum: 9 + 8 + 7 + 6 + 5 = 35. The sum has two digits, so repeat: 3 + 5 = 8. The digital root is 8. As a check, 98,765 divided by 9 leaves a remainder of 8 (9 × 10,973 = 98,757; 98,765 − 98,757 = 8). Since 35 is not divisible by 3 or 9, neither is 98,765.

Try this example →

Common mistakes

  • Typing a decimal like 3.14 and expecting the dot to be respected. It is stripped, and 3, 1 and 4 are added.
  • Entering a negative number: the sign is dropped, so -57 gives the same result as 57.
  • Confusing the digit sum (35) with the digital root (8) when only one digit is wanted.
  • Using the digital root as proof that a calculation is correct. A matching root can still hide an error such as swapped digits.

About this calculator

This calculator adds up all the digits of a number to get its digit sum, then repeats the process on the result until a single digit remains — the digital root. The digital root is always equal to the number's remainder when divided by 9 (with a special case for multiples of 9).

It's used to teach the “casting out nines” checksum trick for spotting arithmetic errors, in numerology, and by programmers writing simple validation or puzzle-solving code where a quick digit-based check is useful.

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Comments (1)

  • Editorial team

    The digital root is the old accountant's trick of casting out nines: it equals the number's remainder when divided by 9, with 9 standing for an exact multiple. You can use it to catch arithmetic slips, since the root of a product should equal the root of the product of the two roots. The tool simply reads every digit it finds in the box, so a minus sign or spaces are ignored. What are you using it for?

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