Digital Root Calculator

Calculate the digital root

The digital root of a number is the single digit you get by repeatedly adding up its digits until only one digit is left. This calculator performs that repeated summing and shows each step. For twelve thousand three hundred and forty-five, the digits sum to fifteen, and the digits of fifteen sum to six, so the digital root is six. There is also a neat shortcut: the digital root equals one plus the remainder of the number minus one divided by nine.

The tool shows both the step-by-step process and the shortcut formula so you can see they agree.

Digital roots and casting out nines

Digital roots are closely tied to modular arithmetic, specifically to numbers modulo nine, which is why the shortcut formula works. This connection underlies the old technique of casting out nines, a quick way to check arithmetic by comparing digital roots. Digital roots also appear in numerology and recreational mathematics, and they are a simple, satisfying way to collapse any number down to a single digit.

Because of the link to nine, the digital root of any multiple of nine is always nine, and adding nine to a number never changes its digital root. All calculation happens locally in your browser.

Related tools

• Data Collection Analysis — Analyze app description to infer data collection.
• Dark Pattern Detector — Scan UX text for manipulative patterns.
• AI Risk Disclosure — Generate disclosure text for AI features.
• Maturity Radar — Generate a radar chart of security maturity.