Calculate the area of common 2D shapes instantly using accurate formulas, step-by-step explanations, worked examples and easy-to-use tools.
Area is the amount of surface a shape covers, and it is always measured in square units. For a rectangle multiply length × width; for a triangle use ½ × base × height; for a circle use πr². Pick a shape below, enter its dimensions, and the calculator returns the area plus the perimeter, a scale diagram, the working, and the same area converted into square metres, square feet, hectares and more.
Choose a shape:
Enter the dimensions and the results update as you type. Any unit works — the answer comes back in that unit squared, plus conversions.
| Property | Value |
|---|
| Unit | Area |
|---|
Hectares and acres are included because Australian land is quoted in hectares for rural blocks and square metres for suburban ones.
Area is the amount of flat surface a shape covers. Because it measures two dimensions at once — length and width — it is always expressed in square units: square millimetres, square metres, square feet. A square metre is literally the space covered by a square measuring one metre on each side, and an area of 20 m² means twenty of those squares would fill the shape exactly.
That is why area formulas nearly always multiply two lengths together. Multiply metres by metres and the result is metres squared. It is also why you can never mix units mid-calculation: a room measured 4 m by 350 cm must become 4 m by 3.5 m before multiplying, or the answer is meaningless.
Area is the number that turns a measurement into a quantity you can buy, cost or plan. Flooring, turf, tiles, paint and topsoil are all sold by area, so the calculation sits between a tape measure and a materials order. Councils set building limits using site coverage ratios, property is valued and rated by land area, solar output is estimated from roof area, and agricultural inputs are applied per hectare. Get the area wrong and every figure downstream is wrong with it.
| Shape | Formula | Variables |
|---|---|---|
| Rectangle | A = l × w | l = length, w = width |
| Square | A = s² | s = side length |
| Triangle | A = ½ × b × h | b = base, h = perpendicular height |
| Circle | A = πr² | r = radius (π ≈ 3.14159) |
| Parallelogram | A = b × h | b = base, h = perpendicular height |
| Trapezoid | A = ½(a + b) × h | a, b = parallel sides, h = height between them |
| Rhombus | A = ½ × d₁ × d₂ | d₁, d₂ = diagonals |
| Kite | A = ½ × d₁ × d₂ | d₁, d₂ = diagonals |
| Ellipse | A = πab | a, b = semi-major and semi-minor axes |
| Circle sector | A = ½r²θ | θ = angle in radians, or (θ°/360) × πr² |
| Regular polygon | A = ns² / (4 tan(π/n)) | n = number of sides, s = side length |
| Regular hexagon | A = (3√3 / 2) s² | s = side length |
| Annulus (ring) | A = π(R² − r²) | R = outer radius, r = inner radius |
A = l × w. The base case every other formula relates back to: length times width. It is why floor plans and land titles are usually broken into rectangles before anything gets measured. A room 8 m by 5 m is 40 m².
A = s². A square is a rectangle with equal sides, so s × s = s². A side of 10 gives 100 square units, and the diagonal is always s√2 ≈ 1.414s.
A = ½ × b × h. A triangle is exactly half the rectangle drawn around the same base and height, which is where the ½ comes from. The height must be measured perpendicular to the base — a sloping side is longer and overstates the area. Knowing all three sides instead? Use Heron's formula, which the triangle calculator applies for you.
A = πr². This needs the radius, not the diameter — substituting the diameter makes the answer four times too large. A radius of 7 gives π × 49 ≈ 153.94 square units, and the circumference is 2πr.
A = b × h. A parallelogram slides into a rectangle of the same base and height, so there is no fraction involved. The height is the straight-line distance between the parallel sides, never the slanted edge. Base 15 and height 9 gives 135 square units.
A = ½(a + b) × h. Average the two parallel sides, then multiply by the perpendicular height between them. Sides of 8 and 12 with a height of 6 give ½ × 20 × 6 = 60 square units. The midline of a trapezoid equals that same average, (a + b)/2.
A = ½ × d₁ × d₂. The diagonals of a rhombus cross at right angles, so half their product gives the area. Diagonals of 10 and 6 give 30 square units. Because a rhombus is also a parallelogram, base × perpendicular height works equally well.
A = ½ × d₁ × d₂. Identical to the rhombus formula, for the same reason: a kite's diagonals also meet at right angles. Diagonals of 12 and 8 give 48 square units. The perimeter, however, needs the four side lengths — the diagonals alone will not give it.
A = πab. Here a and b are the semi-axes, meaning half of each full axis. Semi-axes of 10 and 6 give π × 60 ≈ 188.5 square units. Set a equal to b and the formula collapses back to πr². The perimeter has no simple closed form, so approximations such as Ramanujan's are used.
A = ½r²θ with θ in radians, or equivalently (θ°/360) × πr². A sector is a slice of a circle, so its area is the whole circle scaled by the fraction of 360° it occupies. A 90° sector of radius 8 is a quarter of the circle: ≈ 50.27 square units.
A = ns² / (4 tan(π/n)). Works for any regular polygon with n equal sides of length s — pentagon, octagon, decagon and beyond. Six sides of length 5 give ≈ 64.95 square units. The interior angle is (n − 2) × 180 ÷ n, and the apothem is s ÷ (2 tan(π/n)).
A = (3√3 / 2) s² ≈ 2.598s². A regular hexagon is common enough in tiling, engineering and nature to have earned its own shortcut, though the general polygon formula gives the same result. A side of 6 gives ≈ 93.53 square units, with a width across flats of s√3 and across corners of 2s.
A = π(R² − r²). An annulus is a circle with a smaller concentric circle removed, so subtract the inner area from the outer. Radii of 10 and 6 give π × 64 ≈ 201.06 square units. This is the formula for pipe wall cross-sections, washers and circular garden borders.
| Field | What area is used for | Worked example |
|---|---|---|
| Construction | Concrete slabs, formwork, plasterboard, roofing sheets | A 10 m × 6 m slab is 60 m²; at 100 mm thick that is 6 m³ of concrete |
| Flooring | Tiles, timber, carpet, vinyl — all priced per m² | A 5 m × 4 m room is 20 m²; order about 22 m² to allow 10% for cuts and waste |
| Painting | Wall area minus openings, then divide by coverage | 36 m² of wall at 10 m²/L needs 3.6 L per coat, so about 8 L for two coats |
| Landscaping | Turf, mulch, topsoil, paving | A 12 m × 8 m lawn is 96 m² of turf; mulch at 75 mm deep needs 7.2 m³ |
| Architecture | Floor area ratios, site coverage, compliance | A 180 m² house on a 600 m² block is 30% site coverage |
| Surveying | Land parcels, easements, subdivision | Irregular blocks are split into triangles, each measured, then totalled |
| Solar and roofing | Panel layout and generation estimates | A typical panel is about 1.9 m²; 20 panels need roughly 38 m² of clear roof |
| Education | Geometry, measurement and unit conversion | Australian Curriculum measurement strands from primary school onward |
Perimeter is the distance around the outside; area is the surface inside. Perimeter is in plain units, area in square units. Fencing and skirting are perimeter jobs; turf and tiles are area jobs.
The two are not tied together in the way most people assume. Two shapes with the identical perimeter can enclose very different areas: a 1 m × 9 m rectangle and a 5 m × 5 m square both have a 20 m perimeter, yet they enclose 9 m² and 25 m². Of all shapes with a given perimeter, the circle encloses the most area, which is why bubbles and tanks are round.
Area conversion factors are the square of the length factors. Since 1 m = 100 cm, it follows that 1 m² = 100² = 10,000 cm². Missing that squaring step is the single most common conversion error.
| Conversion | Factor | Notes |
|---|---|---|
| 1 m² | = 10,000 cm² = 1,000,000 mm² | The metric chain squares 100 and 1,000 |
| 1 hectare | = 10,000 m² (100 m × 100 m) | Standard for Australian rural land |
| 1 km² | = 1,000,000 m² = 100 hectares | Used for regions and catchments |
| 1 ft² | = 0.092903 m² | 1 ft = 0.3048 m exactly, then squared |
| 1 m² | ≈ 10.7639 ft² | Handy for imperial plans |
| 1 in² | = 645.16 mm² | 1 in = 25.4 mm exactly |
| 1 yd² | = 0.836127 m² | Older carpet and turf quotes |
| 1 acre | = 4,046.86 m² ≈ 0.4047 ha | Still used in older land titles |
Measuring area is one of the oldest applications of mathematics, and it began with tax and flooding. Each year the Nile inundated Egyptian farmland and erased boundary markers, so surveyors known as rope-stretchers re-measured fields using knotted cords. The Rhind and Moscow papyri, dating from roughly 1800 BCE, record working methods for the areas of rectangles, triangles and circles — the circle rule used there is equivalent to taking π as about 3.16.
Greek mathematicians turned those practical recipes into proofs. Around 300 BCE Euclid's Elements established area through rigorous geometric argument rather than measurement, and Archimedes pushed further, bounding the area of a circle between inscribed and circumscribed polygons to obtain remarkably tight limits on π. Heron of Alexandria later gave the formula for a triangle's area from its three sides alone, still in daily use by surveyors.
Modern practice rests on standardised units. The metric system, introduced in revolutionary France in the 1790s, defined the metre and with it the square metre, and the International System of Units now defines area as a derived quantity in square metres. Australia converted to metric during the 1970s, which is why land is quoted in square metres and hectares today, while acres survive on older titles.
| Mistake | Why it goes wrong | How to avoid it |
|---|---|---|
| Mixing units in one calculation | Metres × centimetres produces a meaningless number | Convert everything to one unit before multiplying |
| Using the diameter as the radius | πd² is four times too large | Halve the diameter first: r = d ÷ 2 |
| Using a sloping side as the height | The height must be perpendicular to the base | Measure at right angles, or use Heron's formula |
| Forgetting the ½ for triangles and trapezoids | Doubles the answer | Write the formula out before substituting |
| Squaring the length factor incorrectly | 1 m² is 10,000 cm², not 100 | Square the linear conversion factor |
| Confusing area with perimeter | They answer different questions and use different units | Check whether the units are squared |
| Confusing area with surface area | Surface area covers all faces of a 3D object | Use the surface area calculator for solids |
| Ordering materials with no allowance | Cuts, waste and pattern matching consume extra | Add roughly 5–10%, more for diagonal or patterned layouts |
| Treating an irregular block as a rectangle | Overstates or understates the real area | Split it into triangles and rectangles, then add |
A = l × w | Square: A = s²A = ½bh | Heron: A = √(s(s−a)(s−b)(s−c))A = πr² | Sector: A = (θ°/360)πr²A = π(R² − r²)A = bh | Trapezoid: A = ½(a+b)hA = ½d₁d₂ | Ellipse: A = πabA = ns² / (4 tan(π/n))A = (3√3/2)s²×k on lengths → ×k² on area1 m² = 10,000 cm², 1 ha = 10,000 m², 1 m² ≈ 10.764 ft²
1) 9 × 4 = 36 m² 2) 7² = 49 cm² 3) ½ × 10 × 6 = 30 cm² 4) π × 25 ≈ 78.54 m² 5) 12 × 5 = 60 m²
1) ½ × (14 + 10) × 7 = ½ × 24 × 7 = 84 m² 2) r = 9, so π × 81 ≈ 254.47 cm² 3) 250 × 10.7639 ≈ 2,690.98 ft² 4) 24 + 6 = 30 m²; order about 33 m² 5) ½ × 16 × 9 = 72 cm²; side = √(8² + 4.5²) = √84.25 ≈ 9.18 cm 6) (120/360) × π × 81 = 27π ≈ 84.82 cm² 7) 400 × 250 = 100,000 m² = 10 hectares 8) Outer radius 5, so π(25 − 16) = 9π ≈ 28.27 m²
What is area?
Area is the amount of flat surface a two-dimensional shape covers, measured in square units such as square metres or square feet. Because it accounts for two dimensions at once, an area of 20 m² means the shape would be exactly filled by twenty squares each measuring one metre on every side.
How do you calculate area?
Multiply the relevant dimensions according to the shape. A rectangle is length × width, a triangle is ½ × base × perpendicular height, and a circle is π × radius². For less regular shapes, split the outline into rectangles and triangles, calculate each piece, then add them together. Always convert every measurement to the same unit first.
What is the formula for area?
There is no single formula — each shape has its own. The most used are A = l × w for rectangles, A = s² for squares, A = ½bh for triangles, A = πr² for circles, A = bh for parallelograms and A = ½(a + b)h for trapezoids. What they share is that two lengths are always multiplied, which is why the result is in square units.
How do I find the area of a rectangle?
Multiply the length by the width. A rectangle 8 units long and 5 wide has an area of 8 × 5 = 40 square units. For a room measured 5 m by 4 m, the floor area is 20 m². Make sure both measurements use the same unit — 4 m by 350 cm must become 4 m by 3.5 m before multiplying.
How do I calculate the area of a triangle?
Use A = ½ × base × perpendicular height. A triangle with a base of 12 and a height of 8 has an area of ½ × 12 × 8 = 48 square units. The height must be measured at right angles to the base, not along a sloping side. If you know two sides and the angle between them use A = ½ab·sin(C), and if you know all three sides use Heron's formula.
What is the area of a circle?
A = πr², where r is the radius and π is about 3.14159. A circle with a radius of 7 has an area of π × 49 ≈ 153.94 square units. If you were given the diameter, halve it first — using the diameter in place of the radius makes the answer four times too large.
How do I calculate area in square metres?
Measure every dimension in metres, then apply the shape's formula. A 6.5 m by 4 m room is 26 m². If you measured in centimetres, either divide each measurement by 100 first, or calculate in cm² and divide the result by 10,000. The calculator on this page reports square metres automatically in its conversion table whatever unit you enter.
How do I convert square feet to square metres?
Multiply square feet by 0.092903, since one foot is 0.3048 m and 0.3048² = 0.092903. So 1,500 ft² ≈ 139.35 m². Going the other way, multiply square metres by about 10.7639.
What is the difference between area and perimeter?
Perimeter is the distance around the outside of a shape, measured in plain units. Area is the surface inside it, measured in square units. Fencing a yard is a perimeter job; laying turf on it is an area job. The two are independent: a 1 m × 9 m rectangle and a 5 m × 5 m square share a 20 m perimeter but enclose 9 m² and 25 m² respectively.
How do I calculate the area of a trapezoid?
Add the two parallel sides, halve the total, then multiply by the perpendicular height between them: A = ½(a + b)h. With parallel sides of 8 and 12 and a height of 6, the area is ½ × 20 × 6 = 60 square units. The height is the gap between the parallel sides, not the length of a slanted edge.
How do I find the area of an ellipse?
Use A = πab, where a and b are the semi-major and semi-minor axes — half of each full axis. An ellipse with semi-axes of 10 and 6 has an area of π × 60 ≈ 188.5 square units. When a equals b the ellipse is a circle and the formula reduces to πr². The perimeter of an ellipse has no simple exact formula, so approximations such as Ramanujan's are used instead.
How do I calculate the area of a parallelogram?
Multiply the base by the perpendicular height: A = b × h. A parallelogram with a base of 15 and a height of 9 has an area of 135 square units. There is no ½ because a parallelogram can be rearranged into a rectangle with the same base and height. The height is the straight-line distance between the parallel sides, never the sloping side.
What is the area formula for a rhombus?
A = ½ × d₁ × d₂, using the two diagonals. Diagonals of 10 and 6 give ½ × 60 = 30 square units. Because a rhombus is also a parallelogram, A = base × perpendicular height works equally well if that is what you have measured. The same diagonal formula applies to a kite, since both shapes have diagonals that meet at right angles.
What units are used for area?
Metric areas use square millimetres, square centimetres, square metres, hectares and square kilometres. Imperial areas use square inches, square feet, square yards and acres. Australia uses the metric system, with square metres for buildings and suburban blocks and hectares for rural land, though acres still appear on older titles.
Why is area measured in square units?
Because area is the product of two lengths. Multiplying metres by metres gives metres squared, in the same way that multiplying 3 by 3 gives 3². Physically, the unit describes the tile being counted: one square metre is the space covered by a square one metre on each side, and an area figure tells you how many of those tiles fit.
Can one calculator find the area of different shapes?
Yes. This page covers thirteen shapes — circle, rectangle, square, triangle, parallelogram, trapezoid, rhombus, kite, ellipse, sector, regular polygon, hexagon and annulus — each with its own formula and inputs. Select the shape, enter its dimensions, and the calculator applies the correct formula, shows the working, draws a scale diagram and converts the result into other units.
How do builders calculate floor area?
By breaking the plan into rectangles, calculating each one, and adding the results, then subtracting voids such as stairwells where required. Measurements are taken in metres to two decimal places and areas quoted in square metres. Definitions matter: gross floor area, net lettable area and site coverage each include different parts of a building, so check which one a council or contract is asking for.
How is land area measured?
Suburban land is quoted in square metres — a typical Australian block is roughly 400 to 700 m² — while rural land is quoted in hectares, where one hectare is 10,000 m². Irregular parcels are divided into triangles, each measured, and the results totalled. Registered land areas come from a licensed surveyor's plan, and that plan is the figure that counts legally.
How do surveyors calculate area?
For a parcel with straight boundaries, surveyors use coordinate geometry: they record the coordinates of each corner and apply the shoelace formula, which sums cross-products of consecutive coordinate pairs. Curved boundaries are handled with arc segments, and modern practice uses total stations or GNSS equipment feeding directly into software. Splitting the parcel into triangles and using Heron's formula gives the same answer by hand.
How do I calculate flooring and allow for waste?
Work out the floor area, then add an allowance for offcuts and pattern matching. Around 5–10% is typical for straight-laid tiles or boards, 10–15% for diagonal or herringbone layouts and for patterned material that must be aligned. A 5 m × 4 m room is 20 m², so ordering 22 m² covers a 10% allowance. Buying in the same batch also avoids visible colour differences later.
How do I find the area of an irregular shape?
Divide it into shapes you can calculate — rectangles, triangles, and circle segments — then add the areas. Subtract any cut-outs such as garden beds or a pool. For a block with several straight boundaries, splitting it into triangles and measuring each one is the standard approach, and it is exactly what surveyors do before totalling the parts.
What is the difference between area and surface area?
Area applies to flat two-dimensional shapes. Surface area applies to three-dimensional objects and totals the area of every face or curved surface — a cube of side 2 has a surface area of 6 × 4 = 24 square units. Both use square units, so check whether the object is flat or solid before choosing a formula.
What are common mistakes when calculating area?
Mixing units in one calculation, using the diameter instead of the radius for circles, using a sloping side instead of the perpendicular height, forgetting the ½ in triangle and trapezoid formulas, and converting units without squaring the factor. Another frequent one is assuming that doubling the dimensions doubles the area — it quadruples it, because area scales with the square of length.
Does this area calculator show the formula and steps?
Yes. For every shape it displays the formula being applied, the substituted working line by line, the perimeter and related properties such as diagonals, apothem or arc length, and a scale diagram of the shape. It also converts the result into square millimetres, centimetres, metres, kilometres, inches, feet, yards, hectares and acres, and results update live as you type.
A one-page reference covering all thirteen shapes, the scaling rule and the unit conversions. Use the button to print it or save it as a PDF — everything else on the page is hidden from the printout.
MegaCalcOnline.com · 2D shape areas, perimeters and unit conversions
| Shape | Area formula | Perimeter / notes |
|---|---|---|
| Rectangle | A = l × w | P = 2(l + w); diagonal = √(l² + w²) |
| Square | A = s² | P = 4s; diagonal = s√2 |
| Triangle | A = ½bh | Heron: A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 |
| Circle | A = πr² | C = 2πr; use the radius, not the diameter |
| Parallelogram | A = bh | h is perpendicular to the base |
| Trapezoid | A = ½(a + b)h | Midline = (a + b)/2 |
| Rhombus | A = ½d₁d₂ | Side = √((d₁/2)² + (d₂/2)²) |
| Kite | A = ½d₁d₂ | Diagonals meet at right angles |
| Ellipse | A = πab | a, b are semi-axes; perimeter needs an approximation |
| Sector | A = ½r²θ = (θ°/360)πr² | Arc length = rθ (θ in radians) |
| Regular polygon | A = ns² / (4 tan(π/n)) | P = ns; interior angle = (n−2)180/n |
| Regular hexagon | A = (3√3 / 2)s² | P = 6s; across flats = s√3 |
| Annulus (ring) | A = π(R² − r²) | Ring width = R − r |
| Unit conversions | Factor |
|---|---|
| 1 m² | = 10,000 cm² = 1,000,000 mm² |
| 1 hectare | = 10,000 m² |
| 1 km² | = 1,000,000 m² = 100 hectares |
| 1 m² | ≈ 10.7639 ft² |
| 1 ft² | = 0.092903 m² |
| 1 acre | = 4,046.86 m² ≈ 0.4047 ha |
| Scaling rule | multiply lengths by k → area × k² |
Educational use only. For legal land areas, rely on a registered surveyor’s plan.