About the Digital Root Calculator
The digital root of a number is what you get by adding its digits, then adding the digits of that sum, and so on until only one digit is left. It links to divisibility by nine and is the basis of the old check called casting out nines. This calculator gives the digital root, the sum of the digits, and the number of steps it took, even for numbers with hundreds of digits. Type a whole number and the digital root appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Digital Root Calculator
- 1Enter a whole number.
- 2Pick the units or options from the menus if the digital root tool offers them.
- 3Read the digital root in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the digital root
Teachers use digital roots for number puzzles and quick checks of arithmetic. Because the digital root of a product equals the digital root of the product of the roots, a wrong answer to a long multiplication is often caught in seconds.
The calculator also shows the multiplicative persistence: how many times you must multiply the digits together to reach one digit. The smallest number with a multiplicative persistence of 2 is 25.
How the digital root is worked out
Add the digits repeatedly until one remains. For a positive number the digital root is 1 + (n − 1) mod 9, so it is 9 for every multiple of 9. The number 987,654,321 has a digit sum of 45, which becomes 4 + 5 = 9, so its digital root is 9 and it took 2 steps. For 12,345 the digit sum is 15 and the root is 6. Multiplying the digits of 987,654,321 gives 362,880, then 0, in 2 steps.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Works for 1,000-digit numbers
- Digit sum and persistence
- Accepts commas and spaces
Mistakes to avoid with digital root
The check only proves an answer wrong, never right, because many wrong answers share the same digital root. The tool accepts digits only; commas and spaces are removed, but letters or decimal points are rejected.
On phone and computer
On a phone, type into the boxes one after another and read the digital root underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the digital root move. The digital root calculator works the same on both. Digital roots relate to remainders, so Modulo Calculator shows the same idea with division. Factor Calculator and Prime Number Calculator explore the number further, and Number to Words writes it out in letters.
Features
- Roots repeat every 9
- A check, not a proof
- Digits only
- Clear messages when the digital root inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate digital root?
Add the digits repeatedly until one remains. For a positive number the digital root is 1 + (n − 1) mod 9, so it is 9 for every multiple of 9. The number 987,654,321 has a digit sum of 45, which becomes 4 + 5 = 9, so its digital root is 9 and it took 2 steps. For 12,345 the digit sum is 15 and the root is 6. Multiplying the digits of 987,654,321 gives 362,880, then 0, in 2 steps.
What is the formula for digital root?
Add the digits repeatedly until one remains. For a positive number the digital root is 1 + (n − 1) mod 9, so it is 9 for every multiple of 9. The digital root calculator applies it exactly and rounds only the displayed answer to six significant figures.
What is the digital root of a multiple of 9?
Always 9, except for 0, whose root is 0.
What is casting out nines?
A way to check a sum or product by comparing digital roots. If they disagree, there is a mistake.
What is persistence?
The number of steps to reach a single digit, by adding (additive) or by multiplying (multiplicative) the digits.
Is this digital root calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.