Living room floor: 18 ft × 12 ft rectangle
Area = 18 × 12 = 216 sq ft = 20.07 sq m. Enough for tile/paint quantity estimation. At ₹50/sq ft for vitrified tile, materials cost ₹10,800.
Area Calculator - Kostenloser Online-Rechner
Compute area for any common 2D shape - circle, square, rectangle, triangle, trapezoid, parallelogram, ellipse and sector. Useful for room measurements, tiling, painting, gardening and architectural planning.
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Area (Rectangle)
24
Result is in (input units)²
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Area Calculator verstehen
Area calculation is one of the most practical math skills with daily uses across Indian households, businesses and construction. Real estate listings advertise carpet area in square feet; property tax is assessed per square foot; tile and paint quantities depend on floor and wall area; agricultural land is measured in acres, hectares, gunthas, or bighas; gardens, balconies and roof terraces are measured for furniture, plants or shading. Understanding area formulas for the eight standard 2D shapes - square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, sector - covers nearly every real-world measurement need.
Class 5-10 mathematics teaches each formula at successive levels: rectangle and square in primary school, triangle and circle in middle school, parallelogram, trapezoid and combined figures by Class 9-10. JEE/NEET aspirants encounter advanced applications in coordinate geometry, mensuration of irregular shapes, and integration-based area between curves. This calculator gives instant answers with the formula shown so you can verify by hand and build geometric intuition - particularly valuable for students preparing for board exams and competitive tests.
Area Calculator in 3 Schritten nutzen
Pick the shape.
Enter the dimensions.
Read the area.
So funktioniert Area Calculator
Each shape has its own area formula derived from its geometry. Rectangle and square use length × width. Circles use πr². Triangles use ½ × base × height. Trapezoid averages the parallel sides times height.
Formula
Square: s² Rectangle: l × w Circle: πr² Triangle: ½ × b × h Trapezoid: ½ × (a+b) × h Parallelogram: b × h Ellipse: π × a × b
- sSide
- l, wLength, width
- rRadius
- b, hBase, height
- a, bSemi-axes (ellipse) or parallel sides (trapezoid)
Wie Area Calculator zum Ergebnis kommt
The eight standard area formulas: Square = side² (special case of rectangle with equal sides). Rectangle = length × width. Triangle = ½ × base × height (where height is perpendicular to base; for non-right triangles use Heron's formula if you only know sides). Circle = π × radius². Parallelogram = base × height (where height is perpendicular distance, not slanted side). Trapezoid = ½ × (parallel side 1 + parallel side 2) × height. Ellipse = π × semi-major axis × semi-minor axis. Sector = ½ × radius² × angle in radians.
Why does triangle have ½? A triangle is half of a parallelogram or rectangle when you mirror it across its hypotenuse. So if you can compute the rectangle area, halve it for the triangle. Similarly, the parallelogram formula (base × height) is the rectangle formula in disguise - sliding the parallelogram into a rectangle preserves area but changes the visible side lengths.
Unit consistency matters: if you enter dimensions in centimetres, the area comes out in cm². For square feet (the Indian real estate standard), enter dimensions in feet. To convert between units: 1 m² = 10.764 sq ft. 1 acre = 43,560 sq ft. 1 hectare = 10,000 m² = 2.471 acres. 1 sq yard (gaj) = 9 sq ft. Always verify which unit your final answer needs.
Gelöste Beispiele
Circular fountain: radius 1.5 m
Area = π × 1.5² = 7.07 m². Useful for landscape design - knowing surface area of pond/fountain helps with water capacity and chemical dosing.
Triangular plot: base 30m, height 20m
Area = ½ × 30 × 20 = 300 m² ≈ 0.07 acres. Useful for triangular boundary plots commonly encountered in older land parcels.
Wann Area Calculator nutzen
- Class 5-10 mathematics - mensuration chapter homework and exam prep.
- Real estate - converting between carpet, built-up and super built-up areas.
- Construction - tile, paint, flooring quantity estimation.
- Land measurement - converting between sq ft, sq m, acres, hectares, gunthas.
- Gardening and landscaping - bed area for plants, mulch and fertiliser.
- Civil engineering - material take-off for slabs, walls, roofs.
- Property tax computation - area-based tax assessment.
- Interior design - furniture layout planning based on room area.
Häufige Fehler und Stolperfallen
- Confusing perimeter with area. Perimeter is around the shape; area is inside.
- Using slanted side instead of perpendicular height for parallelogram or triangle.
- Forgetting unit consistency. Mixing feet and meters gives nonsense answers.
- Computing area of irregular shape as a single rectangle. Break it up first.
- Using diameter instead of radius for circle. Area uses radius, not diameter.
- Mixing up base and parallel sides for trapezoid. Trapezoid needs the two parallel sides plus perpendicular height between them.
Mehr aus diesem Tool herausholen
- For irregular shapes, decompose into known shapes (rectangles, triangles), compute each, sum.
- Use π ≈ 3.14159 for accurate circle calculations; π ≈ 3 only for rough estimates.
- Always verify unit consistency - convert all dimensions to the same unit before computing.
- For curved/free-form shapes, trace on graph paper and count squares as a check.
- Pair with the square footage, circle, triangle and volume calculators on this site for related work.
Fragen zu Area Calculator
What unit comes out?
Whatever unit you put in, squared. Inputs in metres → output in square metres. Inputs in feet → square feet.
How do I find irregular shape area?
Break it into rectangles and triangles you can compute, sum them. For complex curves, use integration or trace the shape on graph paper and count squares.
Square vs rectangle area?
Square is a special rectangle where all sides are equal. Same formula (l × w), but for a square l = w so it simplifies to s².
What's the difference between area and surface area?
Area is for 2D shapes (rooms, floors). Surface area is the total outer area of a 3D shape (box, ball). Use the Surface Area Calculator for those.
How is a parallelogram's area different from a rectangle's?
Same formula (base × height) but height is the perpendicular distance, not the slanted side. Cutting a triangle off one end and adding it to the other turns the parallelogram into a rectangle.
Why does triangle use ½?
A triangle is half a parallelogram. The full parallelogram has area base × height; the triangle is exactly half.
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