Perfect Square Calculator — Check & Find Square Roots
Enter any non-negative integer to find out instantly whether it is a perfect square, what its square root is, and which perfect squares are closest if it is not.
Perfect square — the square root is an exact integer
- 1
Square root √n
√144 = 12 - 2
Round to nearest integer k
12 - 3
Verify k² = n
12 × 12 = 144Equals n → perfect square - 4
Square root √n
12
How does this calculator work?
n is a perfect square when √n is an exact integer k (so k² = n). Enter n and the calculator verifies this with exact integer arithmetic, shows k if it exists, or identifies the adjacent perfect squares k² and (k+1)² when n is not a perfect square. Negative inputs are rejected because no real perfect square is negative.
Formula
How this is calculated
A perfect square is a non-negative integer that equals k² for some non-negative integer k. The sequence begins 0, 1, 4, 9, 16, 25, 36, 49 … A negative number can never be a perfect square in the real number system, so the calculator flags those inputs.
The check works by computing Math.sqrt(n), rounding to the nearest integer k, and then verifying with exact integer arithmetic that k × k === n. Using integer multiplication for the final test avoids false results from floating-point rounding in the square root computation. This is reliable for values up to about 9 × 10¹⁵ (the limit of IEEE 754 double-precision exact integer representation).
If n is not a perfect square the calculator finds the two adjacent perfect squares by taking k = floor(√n) — the square just below is k², and the square just above is (k+1)². The number line visualises exactly where n sits between them. If n is a perfect square, the square diagram illustrates the geometric meaning: a square with side k has area k² = n.
Frequently asked questions
0, 1, 4, 9, 16, 25, 36, 49, 64, 81. They are 0² through 9². The sequence continues: 100 (10²), 121 (11²), 144 (12²), etc.
Yes. 1 = 1² so its integer square root is 1. It is also a perfect cube (1³ = 1) and a perfect sixth power.
The calculator handles integers reliably up to about 9 × 10¹⁵ before floating-point precision limits are reached. For larger numbers, exact arbitrary-precision arithmetic would be needed, which is beyond this tool.
Also known as
TG we-Calculate Editorial Team. (2026). Perfect Square Calculator — Check & Find Square Roots [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/perfect-square-calculator
TG we-Calculate Editorial Team. "Perfect Square Calculator — Check & Find Square Roots." TG we-Calculate. 2026. https://we-calculate.com/calculator/perfect-square-calculator.
TG we-Calculate Editorial Team, "Perfect Square Calculator — Check & Find Square Roots," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/perfect-square-calculator
@misc{wecalculate_perfect_square_calculator, title = {Perfect Square Calculator — Check & Find Square Roots}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/perfect-square-calculator}}, year = {2026}, note = {TG we-Calculate} }
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