Select a 2D shape, enter its dimensions, and get area and perimeter instantly with the formula and step-by-step calculation.
How to use this calculator
Select the 2D shape from the dropdown.
Enter the required dimensions — the fields update to match the shape.
Read area and perimeter (or circumference) instantly with the formula shown.
Switch shapes to compare areas across different geometries.
Formula & method
Area formulas by shape
Rectangle: A = l × w · Square: A = s² · Circle: A = πr² · Triangle: A = ½bh · Trapezoid: A = ½(a+b)h · Ellipse: A = πab
l = length, w = width, s = side, r = radius, b = base, h = height, a/b = semi-axes.
Example
Rectangle 10 × 5: Area = 50, Perimeter = 30. Circle r = 5: Area = π × 25 ≈ 78.54, Circumference ≈ 31.42.
Key insights
A circle encloses the maximum area for a given perimeter — this is why bubbles are spherical.
Doubling all linear dimensions of a 2D shape quadruples the area (area scales as the square of length).
The area of a trapezoid is the average of the two parallel bases multiplied by the height.
An ellipse with semi-axes a and b has area πab — a circle is the special case a = b = r.
How to interpret your result
Area vs perimeter
Area measures interior space (in squared units); perimeter measures total boundary length (in linear units). They are independent — a very long thin rectangle can have large perimeter but small area.
Unit consistency
All inputs must be in the same unit. If dimensions are in cm, area is in cm². Convert inputs before computing if your measurements are mixed.
Frequently asked questions
What is the formula for the area of a triangle?
Area = ½ × base × perpendicular height. If you know all three sides, use Heron's formula instead via the Triangle Calculator.
How do I calculate the area of an irregular shape?
Divide it into standard shapes (rectangles, triangles, circles), calculate each sub-area, and sum them.
What is the difference between area and surface area?
Area applies to 2D flat shapes. Surface area is the total area of all faces of a 3D solid — use the Surface Area Calculator for that.
Related calculators
Surface Area Calculator — Calculate total, lateral and base surface areas for spheres, cylinders, cones, cubes, rectangular prisms and tori.
Volume Calculator — Calculate volume and total surface area for spheres, cylinders, cones, cubes, rectangular prisms, pyramids and capsules.
Circle Calculator — Calculate radius, diameter, circumference, and area from any one circle measurement, plus arc length and sector area.
Triangle Calculator — Solve any triangle from sides or angles using SSS, SAS, ASA, or AAS — area, perimeter, angles and heights.