Square Number Calculator

How it is calculated

The input must be a whole number between −3,037,000,499 and 3,037,000,499; a value such as 2.5, or one outside that range, shows no result. The tool then does three things. It squares the number, n² = n × n, which is also correct for negative n. It tests whether n itself is a perfect square by taking the integer square root r and checking whether r × r = n; if so it reports "Yes" with the root (for example "Yes √=7"), otherwise "No". Finally it finds the perfect square closest to n by comparing the square just below and just above and taking the nearer one; there are no ties, because the gap between consecutive squares is always odd. Negative numbers are never perfect squares, and for them the nearest square is reported as 0. The displayed square is a floating-point value, so for results above about 9 × 10¹⁵ the last digits are rounded.

Common mistakes

• Mixing up the two questions. The first result is n², the square of what you typed; the Yes/No answer is about n itself being a perfect square. To test whether 2,500 is a square, enter 2500, not 50.
• Typing a decimal such as 2.5. The tool only accepts whole numbers, and a fraction gives no result at all instead of a rounded one.
• Expecting a negative number to have a real square root. The tool says "No" for negative inputs, because no whole number squared is negative, while still showing n² as positive.
• Reading "nearest" as the next larger square. It can be below or above n, whichever is closer; for 50 it is 49, the one below.
• Trusting the last digits of a very large square. Once n² passes roughly 9 × 10¹⁵ (n above about 95 million) the shown digits are rounded, so use exact big-integer arithmetic for those.