Calculate the area of a circle, triangle, rectangle, square, trapezoid, parallelogram, ellipse or regular polygon — instantly, with the formula shown.
Choose a shape, enter its dimensions, and calculate to see the area
This free area calculator finds the area of nine common two-dimensional shapes — circle, triangle (by base and height, or by three sides using Heron's formula), rectangle, square, trapezoid, parallelogram, ellipse, and regular polygon — showing the exact formula behind every result. Area measures the flat space enclosed by a shape's boundary, always expressed in square units, whether square feet for a room, square meters for a plot of land, or square centimeters for a craft project. Instead of memorizing nine separate geometry formulas, this area calculator lets you pick a shape, enter its dimensions, and get an instant, formula-transparent answer for homework, flooring, land measurement, or any project where getting the area right matters.
Area is a two-dimensional measurement — it quantifies how much flat surface a shape covers, not the distance around its edge (that's perimeter) or how much space it occupies in three dimensions (that's volume). Because area multiplies two linear measurements together (or their geometric equivalent), the result is always reported in square units: cm², m², ft², or acres, for example. Doubling every linear dimension of a shape doesn't just double its area — it quadruples it, since area scales with the square of length.
This area calculator is built for students checking geometry homework, homeowners and DIYers estimating paint, flooring, or turf for a project, contractors and architects sizing rooms and lots, land surveyors and real-estate professionals computing parcel size, packaging and manufacturing engineers sizing flat stock or labels, and hobbyists working in CAD or 3D printing who need a cross-sectional area. Anyone who needs a fast, formula-transparent area calculation without deriving it from scratch can use it.
Area translates directly into cost and material quantity: paint coverage, flooring cartons, fabric yardage, fertilizer per square foot of lawn, and price per square meter of land all depend on an accurate area figure. Getting area wrong compounds quickly on large projects — a small measurement error on a room's length or width becomes a much larger error in the squared result, which is why this calculator shows the exact substitution used for every shape.
Contractors use rectangle and trapezoid area to estimate flooring, tiling, and paint coverage. Farmers and land surveyors use polygon and rectangle area to size fields and parcels. Packaging engineers use circle and ellipse area for lids, gaskets, and labels. Interior designers use area to plan rugs, furniture layout, and material budgets. Students and teachers use every shape here, including Heron's formula, to verify geometry coursework.
How this area calculator turns your dimensions into a square-unit result, shape by shape
Every area result is expressed in square units (cm², m², ft², acres). Never mix units — convert all dimensions first, then compute.
Circle and ellipse formulas use JavaScript's full-precision Math.PI (≈3.14159265358979), more accurate than the classroom shortcuts 3.14 or 22/7.
Heron's formula first finds s, the semi-perimeter (half the triangle's total perimeter), before computing area from the three sides alone.
From picking a shape to reading a verified result
Open the Shape dropdown and select circle, triangle (base/height or 3 sides), rectangle, square, trapezoid, parallelogram, ellipse, or regular polygon.
The input fields update automatically for your chosen shape — radius, base and height, three side lengths, or number of sides, all in the same unit.
The calculator substitutes your values into that shape's area formula and computes the result instantly.
The result panel shows the numeric area in square units alongside the exact formula and substitution used to reach it.
Pick a different shape from the dropdown to reset the input fields and calculate another area without reloading the page.
Sanity-check by rounding your inputs and estimating mentally, or rework the formula by hand for a simple case.
Finding the area of a circle with radius 5 — the calculator's default shape
A circular table top has a radius of 5 units. What is its surface area?
Explanation: The result is in square units because area always multiplies two linear dimensions together — here, radius by itself. If the radius were measured in feet, the area of 78.5398 would be reported in square feet. Doubling the radius to 10 would not double the area; it would quadruple it to ≈314.1593, since area scales with the square of a linear dimension.
Unit conventions and sanity checks for each shape
| Shape | Unit Convention | Sanity Check |
|---|---|---|
| Circle | Square units of the radius entered (e.g. r in m → m²) | Area should be roughly 3.14 × r² — much larger than r itself for r > 1 |
| Triangle (base/height) | Square units of base/height | Should equal half the rectangle formed by the same base and height |
| Triangle (3 sides) | Square units of the side lengths | Semi-perimeter s must exceed every individual side, or the result is invalid |
| Rectangle / Square | Square units of length × width (or side²) | A square's area is always a perfect square of its side length |
| Trapezoid | Square units of parallel sides × height | Should sit between the areas of rectangles formed by each parallel side and the height |
| Parallelogram | Square units of base × height | Equal to a rectangle with the same base and height, regardless of slant |
| Ellipse | Square units of semi-axes a × b | Equal to πr² when a = b (a circle is a special-case ellipse) |
| Regular polygon | Square units of side length | Approaches πr² (a circle) as the number of sides n grows large |
Reading the result: the number shown is always in whatever unit you entered, squared — enter meters and get square meters, enter feet and get square feet.
Typical ranges: area should always be a positive number; a result of zero or an error message signals a zero, negative, or invalid input (such as a triangle that fails the triangle inequality).
Manual verification: the fastest sanity check for a rectangle or square is to picture unit squares tiling the shape and counting roughly how many fit — for a circle, the area should be a bit more than 3 times the radius squared.
Where a fast, accurate area calculation genuinely helps
Check area homework for circles, triangles, and polygons, including Heron's formula problems.
Measure a room as a rectangle or trapezoid to estimate tile, laminate, or carpet quantity.
Calculate wall area to estimate cans of paint or rolls of wallpaper needed.
Size a rectangular or trapezoidal slab footprint before ordering concrete or forms.
Estimate parcel or lot area from a rectangle, trapezoid, or regular polygon boundary.
Calculate the area of a rectangular or irregular field split into simpler shapes for seed or fertilizer planning.
Determine flat material needed for circular lids, elliptical gaskets, or polygon panels.
Estimate the cross-sectional area of a print layer or design for material and cost planning.
Plan rug, furniture footprint, or rectangular/oval table sizing relative to a room's area.
Size a lawn, garden bed, or circular flower bed for mulch, sod, or seed coverage.
Compute the cross-sectional area of a beam, pipe, or duct for material and flow calculations.
Calculate fabric area for rectangular panels or triangular gussets before cutting.
Quickly size a shelf, panel, or custom-cut piece of material for any home project.
What this area calculator does well, and where manual judgment is still needed
Formula and typical use, side by side
| Shape | Formula | Typical Use |
|---|---|---|
| Circle | A = πr² | Round tanks, pipes, wheels, lids |
| Triangle (base/height) | A = ½bh | Roof sections, gussets, sails |
| Triangle (3 sides) | Heron's: A = √(s(s−a)(s−b)(s−c)) | Land wedges, surveying without a height measurement |
| Rectangle | A = l × w | Rooms, panels, screens, lots |
| Square | A = s² | Tiles, patios, square plots |
| Trapezoid | A = ½(a+b)h | Angled walls, ramps, garden beds |
| Parallelogram | A = b × h | Slanted panels, some roof and land shapes |
| Ellipse | A = πab | Oval rugs, gaskets, running tracks |
| Regular polygon | A = ns²/(4tan(π/n)) | Hex tiles, decking, gazebos, bolt patterns |
Summary: This area calculator gives you an instant, free way to find the area of a circle, triangle, rectangle, square, trapezoid, parallelogram, ellipse, or regular polygon — with the formula and substitution shown for every result. Pair it with the Perimeter Calculator and Volume Calculator for a complete picture of a shape's edges, surface, and solid capacity.
Common questions about area formulas and this area calculator
Trusted educational references to go deeper on the math behind area formulas
Explore other geometry tools