Calculators
Neon Number Calculator
Check whether an integer equals the digit sum of its square with exact neon number arithmetic, privately in your browser.
A neon number equals the sum of the decimal digits of its square. For example, 9 squared is 81 and 8 + 1 = 9. Enter up to 1000 digits; leading zeros are removed. Calculations stay in your browser.
How to check a neon number
A neon number is a nonnegative integer equal to the sum of the base-10 digits of its square. For 9, the square is 81 and 8 + 1 = 9, so 9 qualifies. For 12, the square is 144 and 1 + 4 + 4 = 9, so 12 does not qualify. Zero and one also qualify under this definition. Enter 1 to 1000 decimal digits without signs, separators, decimals or exponent notation. Surrounding whitespace is accepted and leading zeros are removed: 0009 is checked as 9. The square uses exact integer arithmetic and its digits are summed once, without rounding. This is different from a digital root, which repeatedly sums digits until one remains, and from an automorphic number, whose square ends with its own digits. This calculator checks a single integer rather than searching for a sequence. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is a neon number?
A nonnegative integer equal to the sum of the decimal digits of its square. For example, 9 squared is 81 and 8 + 1 = 9.
Do zero and one qualify?
Yes. Their squares and the digit sums of those squares equal the original numbers.
Is this the same as a digital root?
No. This sums the digits of the square exactly once and compares the sum with the original number. A digital root repeatedly sums digits until one digit remains.
How are large numbers and leading zeros handled?
Up to 1000 entered digits are accepted. Leading zeros are removed, and exact integer arithmetic preserves every digit of the square. No input leaves your browser.