Geometry Area & Perimeter Calculator
Calculate area and perimeter for rectangles, circles, triangles, and trapezoids — pick a shape, enter its dimensions, and get an instant result.
Area
50
Perimeter
30
Rectangle: area = length × width. Perimeter = 2 × (length + width).
About this tool
How to use it
- Pick a shape — rectangle, circle, triangle, or trapezoid.
- Enter its dimensions in the fields that appear (they change to match the shape you picked).
- Press Calculate Area, or just keep typing — the results update live.
- Read the area and perimeter (or circumference for a circle), plus a note on the exact formula used.
Why it matters
Each shape has its own area and perimeter formula, and it's easy to mix them up or forget one (especially Heron's formula for a triangle from just its three sides, which most people don't have memorized). Picking the shape and getting the right formula applied automatically removes that step entirely.
When to use it
Useful for checking geometry homework, for a quick real-world measurement (flooring, fencing, land area), or for working out a triangle's area when you only know its three side lengths and don't want to first calculate a height.
Good to know
Rectangle and circle are straightforward — a single well-known formula each. Triangle uses Heron's formula, which computes area from all three side lengths without needing a separate height measurement; the three sides must satisfy the triangle inequality (each side shorter than the sum of the other two) or no such triangle can exist, and the calculator hides the result rather than showing a nonsensical answer if they don't. Trapezoid needs the two parallel side lengths and the height for area, plus the two non-parallel leg lengths for the perimeter.
Common questions
What is Heron's formula?
Heron's formula computes a triangle's area directly from its three side lengths (a, b, c), without needing to know the height: with s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)). It's useful whenever you know all three sides but not the height.
Why does the triangle option sometimes hide the result?
Three lengths only form a real triangle if each side is shorter than the sum of the other two — this is called the triangle inequality. If the three numbers you entered can't actually form a triangle, the calculator hides the result rather than showing a made-up answer.
What's the difference between the trapezoid's parallel sides and its legs?
A trapezoid has exactly one pair of parallel sides (used for the area formula, along with the height between them) and two non-parallel sides, called legs, which only matter for the perimeter — they don't affect the area calculation at all.
Why is a circle's second measurement called circumference instead of perimeter?
Circumference is simply the standard name for a circle's perimeter — the distance around its curved edge. The calculator uses the term specific to whichever shape is selected.