Calculators
Automorphic Number Calculator
Check whether an integer is automorphic with its exact square and matching decimal suffix, privately in your browser.
An automorphic number is a nonnegative integer whose square ends with the same decimal digits. Enter up to 1000 digits; leading zeros are removed. Calculations stay in your browser.
How to check an automorphic number
An automorphic number is a nonnegative integer whose square ends with the same base-10 digits. For example, 76 squared is 5776, which ends in 76, so 76 is automorphic. By contrast, 12 squared is 144, which does not end in 12. The exact test is n² mod 10^d = n, where d is the digit count of n. Zero and one both 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 before counting digits: 00076 is checked as 76 with two digits. The square and remainder use exact integer arithmetic without rounding. The suffix is padded to the input digit count to make the comparison clear. This calculator checks one 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 an automorphic number?
A nonnegative integer whose square ends with its own decimal digits. For example, 25 squared is 625, so 25 qualifies.
Do zero and one qualify?
Yes. Zero squared is zero and one squared is one, so both satisfy the suffix test.
How are leading zeros handled?
Leading zeros are removed before counting digits. Thus 00076 is checked as 76, whose square is 5776.
Are large numbers rounded?
No. The calculator uses exact integer arithmetic for up to 1000 entered digits. No input is sent to a server.