# Perfect Square Calculator

URL: https://speedycalculator.com/calculators/math/perfect-square/
Last updated: 2026-10-30

> The perfect square calculator checks whether a number is a perfect square, gives its square root, the nearest squares and the quick digit tests that rule numbers out.

## Inputs

- Your number

## Results

- Result
- Square root
- Nearest perfect squares
- Quick checks

## Formula

```
N is a perfect square ⇔ √N is an integer
Squares end in 0, 1, 4, 5, 6 or 9 and have digital root 1, 4, 7 or 9
```

## Explanation

Perfect squares – 1, 4, 9, 16, 25 … – appear in geometry (areas of squares), the Pythagorean theorem and factoring. Quick checks on the last digit and digital root rule out most non-squares instantly.

### How to use the Perfect Square Calculator

- **Your number**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The integer square root is computed exactly for whole numbers of any length; the calculator also explains the last-digit and digital-root tests.

## Worked example

Inputs — Your number: 144.

Results — **Result = 144 is a perfect square: 12² = 144**; Square root = 12; Quick checks = Last digit 4 can end a square; digital root 9 is allowed (1, 4, 7 or 9).

## Key terms

- **Perfect square**: The square of an integer.

## FAQ

**Is 0 a perfect square?**
Yes, 0 = 0².

**Can a perfect square end in 2, 3, 7 or 8?**
Never.

**How many perfect squares are there below 100?**
Ten: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 (or nine positive ones).

**How many factors does a perfect square have?**
An odd number.


## Sources

- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)
- [Wolfram MathWorld – Prime factorization](https://mathworld.wolfram.com/PrimeFactorization.html)