Digital Root Calculator

How it is calculated

Enter a whole number. The tool adds its digits, then adds the digits of that sum, and repeats until one digit is left. That digit is the digital root; the number of rounds it took is the additive persistence, shown as the second result. A number that already has one digit needs 0 rounds, and 0 gives a root of 0. The sign is ignored. Typed as plain digits, the number is processed digit by digit, so even a 20-digit value is exact. A decimal such as 98.7 shows no result, as does text or a thousands separator like 1,234; a decimal that is really whole, such as 98.0, is accepted. For a positive integer the root equals n mod 9, with 9 instead of 0 for multiples of 9.

Common mistakes

• Stopping after one round. For 9875 the first sum, 29, still has two digits, so you must keep going to reach 2.
• Assuming multiples of 9 have root 0. A positive multiple of 9, such as 123456789, has root 9; only 0 itself gives 0.
• Mixing up the two outputs. The digital root is the final single digit; the additive persistence is how many rounds it took to reach it.
• Typing a decimal or a number with separators, such as 98.7 or 1,234. The tool wants plain whole digits and shows nothing otherwise.