Geometry Calculators

How a Rectangle's Diagonal Is Calculated

A rectangle's diagonal is the square root of its length squared plus its width squared — the Pythagorean theorem applied to the right triangle formed by two adjacent sides and the diagonal itself.

How the Pythagorean Theorem Finds a Right Triangle's Hypotenuse

The Pythagorean theorem says the hypotenuse of a right triangle is the square root of the sum of its two legs squared: c = √(a² + b²) — it only works for right triangles, where the two legs meet at exactly 90°.

How to Calculate the Area of a Circle, Square, and Rectangle

A circle's area is π times its radius squared, a square's area is its side squared, and a rectangle's area is length times width — three different formulas for the same basic question, "how much surface does this shape cover?"

How to Solve a Right Triangle for Area and Angles

Beyond the hypotenuse, a right triangle's area is half the product of its two legs, and its two acute angles come from the arctangent of the legs' ratio — the two angles always add up to exactly 90°.

Perimeter vs Area: What Each One Tells You

Perimeter measures the distance around a shape's boundary; area measures the surface it covers — they're independent measurements, so shapes with the exact same perimeter can have very different areas.