Area Calculator
Calculate the area and perimeter of common 2D shapes including circles, triangles, and polygons.
| Shape | Area Formula | Perimeter |
|---|---|---|
| Square | a² | 4a |
| Rectangle | l × w | 2(l+w) |
| Triangle | ½ × b × h | a+b+c |
| Circle | πr² | 2πr |
| Trapezoid | ½(a+b)h | a+b+c+d |
| Ellipse | πab | ≈2π√((a²+b²)/2) |
| Parallelogram | b × h | 2(b+s) |
| Reg. Pentagon | (5/4)a²tan(54°) | 5a |
| Reg. Hexagon | (3√3/2)a² | 6a |
| Sector | (θ/360)πr² | 2r+(θ/360)2πr |
Calculate the area and perimeter of ten common 2D shapes — squares, rectangles, triangles, circles, trapezoids, ellipses, parallelograms, regular pentagons and hexagons, and circle sectors.
How Area Calculator Works
Selecting a shape from the dropdown loads its own formula: a square's area is a², a rectangle is length×width, a triangle is ½×base×height, and a circle is πr² — each shape asks only for the specific dimensions its formula actually needs.
Perimeter is calculated with a matching formula wherever it can be determined from the entered dimensions alone — for example 4a for a square or 2πr for a circle's circumference — but for a general triangle, trapezoid, or parallelogram, only base and height were entered, so the full perimeter (which needs every side length) isn't shown.
The regular pentagon and hexagon formulas come from splitting each polygon into equal triangles radiating from its center, and use trigonometric identities to relate one side length to the whole shape's area; a circle sector's area simply scales the full circle's area (πr²) by the fraction of 360° that its central angle represents.
See It In Action
Who Uses Area Calculator and Why
- Estimating flooring, carpet, or paint coverage needed for a square or rectangular room.
- Calculating an irregular land plot's area from a trapezoid or parallelogram's base and height.
- Figuring out a pizza slice or sprinkler coverage area from a circle sector's central angle.
- Laying out a regular hexagon or pentagon paver pattern using each shape's side-length-based area formula.
Mistakes to Avoid
- Expecting a perimeter result for a triangle, trapezoid, or parallelogram when only base and height were entered — a true perimeter needs every side length, which those minimal inputs don't provide.
- Entering a diameter value where the calculator expects a radius for a circle or sector, doubling or halving the resulting area unintentionally.
- Assuming the ellipse's perimeter figure is mathematically exact — there's no simple closed-form formula for it, so the calculator uses a well-known approximation instead.
Tips for Best Results
- Remember a circle sector's area is always the full circle's area scaled by the fraction of 360° its central angle covers — double-check the angle unit is degrees.
- For shapes where perimeter didn't display, you'd need to know every individual side length, not just base and height, to calculate it.
Fixing Common Problems
The perimeter field is blank or missing for my shape. — Some shapes (general triangle, trapezoid, parallelogram) only need base and height for area, but a true perimeter requires every side length — which those minimal inputs don't supply.
Terms Explained
Sector: A 'slice' of a circle bounded by a central angle, whose area is the full circle's area scaled by that angle's fraction of 360°.
Regular polygon: A shape (like a regular pentagon or hexagon) with all sides and angles equal, whose area formula comes from splitting it into equal triangles from its center.