Area Calculator

Finding the area of a shape means remembering the right formula, and there is a different one for every shape. This calculator collects seven of the most common — rectangle, square, circle, triangle, trapezoid, parallelogram, and ellipse — into one tool that picks the right formula and does the math once you choose a shape and enter its dimensions.

Students use it to check geometry homework; people planning real projects use it to size a room, a garden bed, or a piece of material. It returns not just the area but the perimeter (or circumference, for a circle) and shows the formula and steps, so the result is something you can learn from rather than just copy.

Each shape has its own expression and the tool switches formula with the selector, showing which one it applied so the result can be checked by hand. The underlying set is the standard one from plane geometry: rectangles and squares multiply their sides, triangles take half the base times the perpendicular height, circles use pi times the radius squared, and trapezoids average the parallel sides before multiplying by the height.

Two inputs are commonly confused. A triangle's height is the perpendicular distance from base to opposite vertex, not the length of a sloping side — using a slant length overstates the area. And circles take the radius, so a diameter must be halved first; forgetting that quadruples the answer, since the radius is squared.

Area is always in squared units, and it scales as the square of any linear change. Doubling every dimension quadruples the area, which is why a pizza twice the diameter is four times the food.

Nothing in the real world is quite a textbook shape, and the standard approach is decomposition: split an awkward outline into rectangles and triangles, compute each, and add. Subtracting works equally well for holes and cutouts — calculate the full area, then remove the opening.

For materials, order more than the bare area suggests. Flooring, tiling, and wallpaper all need an allowance for cuts, waste, and pattern matching, and ten percent is a common rule of thumb, more for diagonal layouts or complex patterns. Measure the space rather than trusting a plan, since rooms are rarely as square as drawings imply.

Keep units consistent before calculating rather than converting afterwards, because squared units convert differently from linear ones — a square metre is ten thousand square centimetres, not a hundred. That factor catches people out regularly.