Area Calculator for Squares, Circles & More

Find the Area of Any 2D Shape

Shape

Length unit

Dimensions

Side a

Square or rectangle side, ellipse semi-axis, or trapezoid side a.

Side b

Second side of the rectangle or trapezoid, second ellipse semi-axis.

Calculate automaticallyIf enabled, the result will update automatically when you change any value.

Area Results

AreaA

Area in square meters

Area in square feet

Area in square yards

Area in acres

Area in hectares

PerimeterP

Formula with your values

Shape diagram

Area Formula

Formula

\[ \begin{aligned} \text{Square / Rectangle:} \quad & A = a^2 \;\;(a = b) \qquad A = ab \\ \text{Triangle:} \quad & A = \tfrac{1}{2}\,b\,h \qquad A = \sqrt{s(s-a)(s-b)(s-c)},\; s = \tfrac{a+b+c}{2} \\ \text{Circle:} \quad & A = \pi r^2 \qquad \text{Semicircle: } A = \tfrac{1}{2}\pi r^2 \\ \text{Ellipse:} \quad & A = \pi a b \\ \text{Parallelogram:} \quad & A = b\,h \qquad \text{Trapezoid: } A = \tfrac{1}{2}(a+b)h \\ \text{Rhombus:} \quad & A = \tfrac{1}{2}\,d_1 d_2 \\ \text{Circular sector:} \quad & A = \tfrac{1}{2}\,r^2\theta \quad (\theta \text{ in radians}) \\ \text{Regular polygon:} \quad & A = \frac{n\,s^2}{4\tan(\pi/n)} \\ \text{Annulus (ring):} \quad & A = \pi(R^2 - r^2) \end{aligned} \]

Where:

\(a\), \(b\) — side lengths, semi-axes or parallel sides, depending on the shape
\(h\) — perpendicular height to the base
\(r\), \(R\) — radius (inner) and outer radius
\(d_1\), \(d_2\) — diagonals of the rhombus
\(\theta\) — central angle of the sector
\(n\), \(s\) — number of sides and side length of a regular polygon

Each formula multiplies two perpendicular lengths, so the area always comes out in the chosen length unit squared (for example \(\text{cm}^2\)). For the sector, the angle must first be converted from degrees to radians: \(\theta = \theta_{\text{deg}} \cdot \pi/180\).

Area – Calculation Example

Example: a rectangular room is 6 cm long and 4 cm wide on a floor plan (the calculator's default values), and the unit is set to cm.

\[ A = a \times b = 6 \times 4 = 24 \;\text{cm}^2 \]

\[ P = 2(a + b) = 2 \times (6 + 4) = 20 \;\text{cm} \]

Result: the area is 24 cm² (0.0024 m², about 0.258 ft²) and the perimeter is 20 cm. The same numbers in meters instead of centimetres would give an area of 24 m² — which is why the unit selector matters.

How to use the calculator

Choose a Shape from the dropdown — square, rectangle, triangle, circle, semicircle, ellipse, parallelogram, trapezoid, rhombus, circular sector, regular polygon or ring (annulus).
Select the Length unit (mm, cm, m, km, in, ft, yd or mi). Every dimension you type is interpreted in this unit, and the area is returned in this unit squared.
Only the fields the chosen shape needs are shown under Dimensions. Enter them as positive numbers — for example Side a and Side b for a rectangle, or Radius and Central angle for a sector.
For a triangle, first pick the Triangle input method: base and height, or three sides (Heron's formula).
Read the results: the area in your unit, conversions to square meters, square feet, square yards, acres and hectares, and the perimeter when the shape's dimensions fully define it. A step-by-step formula with your values and a scale diagram are shown at the bottom.

What is area and how to interpret the result

Area measures the size of a surface: how much two-dimensional space a shape covers. You meet it everywhere — floor space of a room, paint needed for a wall, land in a deed, material for a tarp or a garden bed. Whatever the shape, the underlying idea is the same: count how many unit squares fit inside the figure. A rectangle of 6 by 4 units contains exactly 24 unit squares, hence \(A = 24\) square units.

The formulas above are shortcuts for that count. Because each one combines two lengths, the result always carries squared units: centimetres give cm², feet give ft², kilometres give km². Mixing units without converting them is the single most common mistake, which is why the calculator fixes one unit for all inputs and then converts the result for you into m², ft², yd², acres and hectares — the five units most often used in construction, landscaping and surveying.

The perimeter, when shown, answers a different question: not how much space a shape covers, but how long its boundary is. Fence length is a perimeter problem; lawn, paint or tile quantity is an area problem. A long thin rectangle and a compact square can enclose the same area with very different perimeters.

Note that for some shapes, such as the circle, the perimeter is the circumference \(C = 2\pi r\), and for the sector it is the arc plus two radii. More specialised tools exist if you need to go deeper: the triangle area calculator covers more triangle cases, the circle calculator works out radius, diameter and circumference, and the sector area calculator and regular polygon area calculator focus on those two shapes in detail.

Assumptions, limits and practical tips

Units are shared by all inputs. If your plan mixes metres and centimetres, convert to a single unit first — or use the scientific calculator to do it quickly.
Heights must be perpendicular. For a triangle, parallelogram or trapezoid, enter the height measured at a right angle to the base, not the slant side.
A base-and-height triangle does not have a fixed perimeter. The area is determined, but the slant sides can vary, so the calculator hides the perimeter for this input method. With three sides (Heron's formula) it is simply \(a + b + c\).
Triangle sides must satisfy the triangle inequality: each side shorter than the sum of the other two. The calculator tells you when they do not.
The rhombus input uses diagonals, which must cross at right angles; for a rhombus they always do. The sector angle must be between 0° and 360° (0 and 2π rad).
The polygon must be regular (all sides and angles equal). For an irregular quadrilateral, split it into triangles and add their areas.
The annulus needs an inner radius smaller than the outer radius. The result is the area of the ring between the two circles.
Ellipse perimeter is approximate (Ramanujan's formula) — very accurate for typical shapes, but no exact elementary formula exists.
Acres and hectare conversions appear automatically, which is handy for land: 1 ha = 10,000 m² and 1 acre ≈ 4,046.86 m².

Frequently Asked Questions

How do I calculate area by hand without a calculator?

Pick the matching formula and multiply two perpendicular lengths. Rectangle: length × width. Triangle: ½ × base × height. Circle: π × radius² (use 3.14159 for π). For a circle, halve the diameter first — the radius, not the diameter, goes into the formula. Then convert units if needed: 1 m² = 10,000 cm², and 1 ft² = 144 in².

How do I convert between square meters, square feet, acres and hectares?

Because area units are squared, length conversion factors are squared too. 1 m² ≈ 10.764 ft², and 1 ft² ≈ 0.0929 m². For land: 1 hectare = 10,000 m², 1 acre ≈ 4,046.86 m² ≈ 43,560 ft², and 1 hectare ≈ 2.471 acres. The calculator shows all of these conversions automatically next to the result.

The sides of my room are in different units (e.g., meters and feet). Can I still use the calculator?

Convert everything to one unit before entering the values, because the calculator applies a single unit to all dimensions. Multiply feet by 0.3048 to get meters, or divide meters by 0.3048 to get feet. Never mix units directly in one formula — a room 6 m by 4 ft is a common mistake that produces a meaninglessly wrong area.

How do I find the area of an irregular shape like an L-shaped room or plot?

Split it into simple shapes, calculate each one, and add the results. An L-shaped room becomes two rectangles; an irregular quadrilateral becomes two triangles. For curved boundaries, approximate with sectors or break the region into narrow rectangles and sum them — the narrower the strips, the closer the estimate.

I know the width and height of my ellipse, not the semi-axes. What do I enter?

The calculator asks for semi-axes, which are half the full width and height. An ellipse 10 cm wide and 6 cm tall has semi-axes a = 5 cm and b = 3 cm, giving A = π × 5 × 3 ≈ 47.12 cm². Entering the full width instead of the semi-axis will overstate the area by a factor of four.

Can I find the area of a triangle when I only know the three side lengths?

Yes. Choose the “Three sides” input method and the calculator applies Heron's formula: with s = (a + b + c)/2, the area is √(s(s−a)(s−b)(s−c)). The sides must satisfy the triangle inequality — each side shorter than the sum of the other two — otherwise no triangle exists and the calculator will warn you.

How much paint or flooring do I need for a given area?

Multiply the area by the coverage rate on the product label. If a wall is 24 m² and a litre of paint covers 10 m² per coat, you need about 2.4 L per coat — buy extra for a second coat and touch-ups. For tiles or flooring, divide the area by one tile's area and add 5–10% for cuts and waste. Always check the manufacturer's figures, as coverage varies by product.