Geometry Calculator

Calculate area, perimeter, and diagonal for all shapes including triangles, squares, rectangles, circles, ellipses, and trapezoids quickly and accurately.

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All Shapes in One Place

Comprehensive calculator for all geometric shapes including right triangles, equilateral triangles, isosceles triangles, general triangles, squares, rectangles, circles, ellipses, and trapezoids. Just input the required values and get all properties automatically calculated.

Triangle Calculations

Right triangles use the Pythagorean theorem (a² + b² = c²) to calculate the hypotenuse. Equilateral triangles only need one side to calculate height and area. Isosceles and general triangles use Heron's formula for accurate area calculation.

Quadrilateral Calculations

Squares calculate area, perimeter, and diagonal from one side length. Rectangles use width and length to find area, perimeter, and diagonal. The Pythagorean theorem is also used for diagonal calculations.

Circle and Ellipse Calculations

Circles calculate diameter, circumference (2πr), and area (πr²) from radius. Ellipses calculate area (πab) and approximate circumference from major and minor axes. Uses π = 3.14159265359.

Trapezoid Calculations

Trapezoids calculate area from top base, bottom base, and height. Formula: Area = (top + bottom) × height ÷ 2. Can also be used for parallelograms and other quadrilaterals.

Real-time Visualization

Results allow intuitive size comparison. Helpful for geometry education and quick calculations in practical work.

Frequently asked questions

Which shapes can this calculator handle?

It covers nine shapes — right triangle, equilateral triangle, isosceles triangle, general triangle, square, rectangle, circle, ellipse, and trapezoid — calculating area, perimeter (or circumference), and diagonal where applicable. Just select a shape and enter the required values.

Can I get the area of a general triangle from just the three side lengths?

Yes. General and isosceles triangles use Heron's formula, which calculates the exact area from the three side lengths alone, without needing any angles.

Why is the ellipse's circumference an approximation while the circle's isn't?

A circle's circumference has an exact formula (2πr), but there is no exact closed-form formula for an ellipse's perimeter, so an approximation is used instead. The ellipse's area (πab) is still calculated exactly.

How is the diagonal calculated for squares and rectangles?

Both use the Pythagorean theorem. A square's diagonal equals its side length times √2, while a rectangle's diagonal is √(width² + length²).

Can the trapezoid formula be used for other quadrilaterals?

The trapezoid area formula, (top base + bottom base) × height ÷ 2, also works for parallelograms and similar shapes where the top and bottom bases are equal.