Quick answer
A number is a perfect square if its square root is an integer. 49 is a perfect square (7 × 7). 0 and 1 are also perfect squares.
Enter a number. The calculator says whether it is a perfect square and gives the square root.
Related tools: Slope Calculator: Slope, angle, distance and line equation through two points. LCM Calculator: Least common multiple of two or more numbers. Factor Calculator: List every factor of a positive whole number.
How to use the Perfect Square Calculator
- Enter number (a whole number, between 0 and 1000000000000000).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Number | A whole number | ≥ 0, ≤ 1000000000000000 |
Formula and method
Formula
n is a perfect square if √n is an integer
IEEE-754 double precision; shown to at most 6 decimal places.
Integer square root check.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Number = 49.
| Result | Value |
|---|---|
| Perfect square? | Yes |
| Square root | 7 |
Example 2
Inputs: Number = 50.
| Result | Value |
|---|---|
| Perfect square? | No |
| Nearest squares | 49 and 64 |
The first line is the headline result (perfect square?). Below it the perfect Square Calculator lists square root, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Recognising them
Perfect squares end in 0, 1, 4, 5, 6 or 9, never in 2, 3, 7 or 8. The first few are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. The difference between consecutive squares is the odd numbers 3, 5, 7 …
Uses
Simplifying square roots, solving quadratics by factoring and tiling puzzles. A non-square integer has an irrational square root, for example √50 ≈ 7.071.
How the result changes with number
Holding every other input at the first worked example, this table changes only number. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Number | Perfect square? | Square root |
|---|---|---|
| 25 | Yes | 5 |
| 49 | Yes | 7 |
| 196 | Yes | 14 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number: entering "-1" shows "Number must be at least 0." beside that field and no result.
Choosing between the Perfect Square Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
| [Factor Calculator](/math/factor-calculator/) | number | Factors |
| [Quadratic Formula Calculator](/math/quadratic-formula-calculator/) | a, b and c | Roots |
| [Log Calculator](/math/log-calculator/) | number x and base b | log base 2 of 8 |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- 0 and 1 are perfect squares
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number to confirm this.
Frequently asked questions
Is 50 a perfect square?
No. √50 ≈ 7.07 is not a whole number, so 50 isn't a perfect square.
Is 0 a perfect square?
Yes. 0 = 0 × 0, so zero counts as a perfect square, as does 1.
What is the next square after 49?
The next square after 49 (7²) is 64 (8²).
What does the Perfect Square Calculator calculate?
Check whether a number is a perfect square. It returns Perfect square? and Square root.
What formula does the Perfect Square Calculator use?
n is a perfect square if √n is an integer. Integer square root check.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. 0 and 1 are perfect squares.
What is an example of a perfect Square result?
With number 49, the perfect square? is Yes.
Related calculators
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
- Quadratic Formula Calculator — Solve ax² + bx + c = 0, including complex roots.
- Log Calculator — Logarithm of a number to any base.
- GCF Calculator — Greatest common factor (greatest common divisor) of two or more numbers.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.