Area Calculator

Area of any plane figure — rectangle, triangle, circle, sector, trapezoid, polygon and more — drawn to scale with your dimensions on it.

Your measurements

Shape

Units

Length (l)

Decimals are fine — 12 ft 6 in is 12.5.

Width (w)

Rectangle, 20 ft long and 15 ft wide, drawn to scale

Area

300 ft²

A = l × w = 20 × 15

Rectangle · 20 ft long and 15 ft wide

Perimeter

70 ft

All dimensions in ft. The area is in ft².

An L-shaped room is two rectangles. Measure each, run this twice, and add the two areas.

Every measure of this shape

Measure	Value	How it was worked out
Area	300 ft²	A = l × w = 20 × 15
Perimeter	70 ft	2(l + w) = 2 × (20 + 15)
Diagonal	25 ft	sqrt(l² + w²) = sqrt(20² + 15²)

Column three is the arithmetic with your numbers in it, so you can check any line by hand.

This area in other units

Unit	Amount
Square centimetres (cm²)	278,709
Square metres (m²)	27.87
Square kilometres (km²)	0.0000279
Hectares (ha)	0.0028
Square inches (in²)	43,200
Square feet (ft²)	300
Square yards (yd²)	33.33
Acres	0.0069

Factors from NIST SP 811, all exact. For any other conversion, the area converter linked below has ten units.

Area and perimeter formulas for all 12 shapes

Shape	Area	Perimeter	What we ask for
Rectangle	l × w	2(l + w)	Length and width
Square	a²	4a	One side
Triangle	½ b h, or Heron from 3 sides	a + b + c (3 sides only)	Base × height, 3 sides, or 2 sides + angle
Circle	π r²	2π r	Radius, diameter or circumference
Circle sector	½ θ r²	2r + r θ	Radius and central angle
Ellipse (oval)	π a b	Ramanujan II (approximate)	Both semi-axes
Trapezoid	½ (b1 + b2) h	not fixed by these inputs	Both bases and the height
Parallelogram	b h, or a b sin θ	2(a + b) (2 sides + angle only)	Base × height, or 2 sides + angle
Rhombus	½ p q, or a h	4a, or 2 sqrt(p² + q²)	Both diagonals, or side + height
Regular polygon	n a² / (4 tan(π/n))	n a	One side and the number of sides
Annulus (ring)	π (R² − r²)	2π(R + r), both boundaries	Both radii
Rectangular border	L W − (L − 2t)(W − 2t)	2(L + W) + 2(L' + W')	Outer size and the border width

The shape you have picked is highlighted.

Unit factors from NIST SP 811; formulas from Wolfram MathWorld. Checked 25 August 2026.

Need to convert an area you already have? Use the area converter.

Area calculator. Area and perimeter of a rectangle, circle, triangle, trapezoid, sector or polygon.

An area calculator turns measured dimensions into the area a shape covers; this one adds the perimeter and draws the figure you are measuring. Twelve figures share one form — rectangle, circle, triangle, trapezoid, sector, polygon and six more — and every answer is repeated in ft², yd², in², cm², m², km², hectares and acres.

What Area Means, and Which of the Twelve Shapes Yours Is

Area is the amount of flat surface a shape covers, counted in squares of whatever unit you measured in. Measure a room in feet and the answer arrives in square feet; measure the same room in meters and it arrives in square meters. A 20 × 15 ft room holds 300 one-foot squares, which is the same floor as 27.87 one-meter squares or 33.33 one-yard squares. Perimeter measures that shape a different way — the distance around the outside, in plain feet rather than square feet. For the same room it is 70 ft, and the two figures buy different things: 300 ft² of flooring, 70 ft of baseboard.

Most of the work in an area calculation goes into picking the shape and the route into it rather than into the arithmetic. Shape offers twelve figures, and How you measured it offers eighteen routes across them, because four of the twelve accept more than one set of measurements. A circle opens from Radius (r), Diameter (d) or Circumference (C), so a tape run once around a tree trunk or a water tank is enough on its own. A triangle opens from Base × height, 3 sides or 2 sides + angle. A parallelogram and a rhombus take two routes each. Competing pages narrow this further than you would expect: Calculator.net's area page asks a triangle for three sides and offers nothing else, so a builder holding a base and a height has nowhere to type them, and Omni Calculator's dedicated area-of-a-circle page accepts a radius or a diameter and stops there.

The four biggest general-purpose area calculators ranking for this query all illustrate the figure with a picture prepared in advance, while this one draws yours from the numbers in the form. Inch Calculator emits eighteen shape illustrations at 1280 × 854 and switches between them with a CSS class, so its trapezoid looks identical whether you type 20 × 15 or 2 × 900; Calculator.net, Omni and GIGAcalculator follow the same pre-drawn pattern. Here the drawing is built from your dimensions and ships inside the page's HTML, under the caption "Computed from your numbers, not a stock illustration." Change one side of a three-sided triangle and the drawn triangle changes shape with it. The same measurements are written out as text in "Every measure of this shape", the table sitting open underneath, so a screen reader and a search crawler both get what the picture is showing.

The perimeter card is the other thing this page does that the rest of the field leaves out. Checked against their live pages on 25 August 2026, Calculator.net, Omni Calculator, GIGAcalculator and Inch Calculator each output an area and stop, although all four already hold the sides they would need. Fifteen of the eighteen routes on this page return a perimeter: 70 ft around the default room, 45 ft around a 20/15/10 ft triangle, 60 ft around a hexagon of 10 ft sides. Three routes withhold it on purpose and say why on screen — "Base and height don't fix the perimeter: the two slanted sides could be any length. Switch to 3 sides to get it."

Much of the first page of Google for "area calculator" is land measurement rather than geometry. Map Developers and CalcMaps both rank there, and both work the same way: outline a plot on a satellite image and read the acreage back. Neither accepts a typed dimension for a named shape, and Daft Logic's Google Maps area tool ranks alongside them on the same principle. This page answers the other half of that query, the one where you are standing in a room or a yard with a tape measure. Where the two halves meet is the units table, which repeats every answer in acres and hectares alongside ft², yd², in², cm², m² and km²: that 20 × 15 ft plot is 0.0069 acres. For an area you already have and only need converted, the area converter does that job on its own.

Which Shape to Pick for What You Are Measuring

What you are measuring	Shape	How you measured it	What you type
A room, patio or driveway with square corners	Rectangle	Length × width	Length (l), Width (w)
A square paver, tile field or garden square	Square	Side	Side (a)
A round patio or fire-pit pad you can reach across	Circle	Diameter	Diameter (d)
A circular flower bed you can reach the middle of	Circle	Radius	Radius (r)
A tree trunk, tank or silo you can only tape around	Circle	Circumference	Circumference (C)
A gable end, a roof face or a triangular corner bed	Triangle	Base × height	Base (b), Height (h)
A triangular lot with three sides you measured	Triangle	3 sides	Side a, Side b, Side c
A pie-slice bed or a quarter-round lawn corner	Circle sector	Radius + angle	Radius (r), Central angle (θ)
A yard that tapers between two parallel ends	Trapezoid	Two bases + height	Base 1 (b1), Base 2 (b2), Height (h)
A leaning plot or a sheared panel	Parallelogram	Base × height	Base (b), Height (h)
A diamond tile or a kite-shaped bed	Rhombus	Diagonals	Diagonal p, Diagonal q
A hexagonal deck or an octagonal gazebo floor	Regular polygon	Side + number of sides	Side (a), Number of sides (n)
An oval table top or a track infield	Ellipse (oval)	Two semi-axes	Semi-major axis (a) — the long one, Semi-minor axis (b) — the short one
A border ringing a round pond, or a pipe wall end on	Annulus (ring)	Two radii	Outer radius (R), Inner radius (r)
A walkway framing a rectangular patio	Rectangular border	Outer size + border	Outer length (L), Outer width (W), Border width (t)

Using the Form: Shape First, Then How You Measured It

Nothing needs pressing. Both cards, the drawing and the three tables move as you type, and a link you copy reopens the same shape with the same measurements in it.

1. Choose the figure at Shape. The twelve options are Rectangle, Square, Triangle, Circle, Circle sector, Ellipse (oval), Trapezoid, Parallelogram, Rhombus, Regular polygon, Annulus (ring) and Rectangular border. The form underneath rebuilds for whichever you pick, so no field appears that the shape does not need.

2. Say how you took the measurement at How you measured it. Four shapes give you a choice: a triangle takes Base × height, 3 sides or 2 sides + angle; a circle takes Radius, Diameter or Circumference; a parallelogram takes Base × height or 2 sides + angle; a rhombus takes Diagonals or Side + height. The other eight have one route each, from Side on a square to Outer size + border on a rectangular border.

3. Type the one to three dimensions that route asks for. Every field accepts decimals, and the hint under it says so: "Decimals are fine — 12 ft 6 in is 12.5." That is how a tape reading in feet and inches gets in, and how a 6-inch border on a patio measured in feet becomes 0.5.

4. Set Units once. A single selector governs every dimension in the form — in, ft, yd, mi, mm, cm, m and km — and the answer comes back as the square of whichever you chose. Feet is the default. Giving each dimension its own unit is what makes competing answers ambiguous: fed 30 feet by 20 meters, Calculator.net returns "1968.5039370079 feet²" and "182.88 meters²", two answers to a question that has one.

5. On a Circle sector, and on either route that takes an angle between two sides, a second control appears for Degrees or Radians. Degrees is the default. If your plan states the angle the other way, the angle converter turns it round.

6. Read the Area card first. Its subtitle is your own formula with your numbers already substituted, so the arithmetic is visible rather than asserted, and the copy button puts the figure on the clipboard. The note under it names the shape and the dimensions it used. Perimeter sits below, and vanishes entirely on the three routes that cannot determine one.

7. Under the cards comes the drawing, and under that the three tables. Every measure of this shape is open by default and carries the derived quantities — an apothem, a semi-perimeter, a midsegment, an arc, a chord, a diagonal, the interior angles, whatever that shape has, with a third column carrying the arithmetic that produced each one, so any line can be checked by hand. This area in other units and Area and perimeter formulas for all 12 shapes are collapsed until you open them; the second highlights the row for the shape you picked.

Eight Shapes, Read Off the Live Calculator

The default state: a 20 by 15 foot room is 300 square feet

The page opens on Rectangle, Length × width, 20 ft by 15 ft, and has answered before you touch anything:

Area 300 ft², noted underneath as Rectangle · 20 ft × 15 ft
Perimeter 70 ft, which is the baseboard rather than the flooring
Diagonal 25 ft in the measures table, which makes it a 15-20-25 right triangle, the 3-4-5 scaled by five

Open This area in other units and the same floor reads 27.87 m², 33.33 yd², 43,200 in², 278,709 cm², 0.0028 hectares, 0.0069 acres and 0.0000279 km². The yd² row is the one a carpet quote wants, since carpet in the US is sold by the square yard and 300 ÷ 9 is 33.33.

A cluster of single-purpose domains ranks for "how many square feet is a 20x15 room" — calculateme.com, propertycalcs.com, squareroot.info and half a dozen more. PropertyCalcs answers 300 and repeats it in acres, m² and hectares, and stops there: no perimeter, no diagonal, not even yd². The 70 ft of perimeter, the 25 ft diagonal and the 33.33 yd² are the same room measured three more ways, and all three cost money at a checkout.

A round patio, three ways in

A patio 12 ft across is the same patio whether or not you can reach the middle of it.

Circle, Diameter, d = 12 ft → 113.1 ft², perimeter 37.7 ft
Circle, Radius, r = 6 ft → the identical 113.1 ft² and 37.7 ft
Circle, Circumference → for the trunk, tank or silo you can get a tape around but not across

Putting a diameter into Radius (r) multiplies the answer by four rather than by two, because the radius is squared. Having all three routes on the form removes any need to halve something in your head first: type what the tape actually said.

Scale it up and the perimeter becomes the interesting number. A circle of r = 20 ft covers 1,257 ft² and takes 125.66 ft of edging around it. What to pour on a pad that size is a separate question — the concrete calculator takes a round pad's diameter and thickness and returns bags.

A triangle three ways, and the one the perimeter refuses

Three routes, three different amounts of information, and only two of them close the outline.

Base × height, b = 20 ft, h = 10 ft → 100 ft². No perimeter card appears, and a line says why: "Base and height don't fix the perimeter: the two slanted sides could be any length. Switch to 3 sides to get it." Slide the apex anywhere along a line parallel to the base and the area holds at 100 ft² while the two slanted sides lengthen without limit. Infinitely many triangles share that base and that height, and they do not share a perimeter.

3 sides, 20 / 15 / 10 ft → 72.62 ft², perimeter 45 ft. The measures table adds the semi-perimeter of 22.5 that Heron's formula runs on, interior angles of 104.48°, 46.57° and 28.96°, and the height to the 20 ft side, 7.26 ft. This is the only triangle route Calculator.net offers on its area page.

2 sides + angle, 20 ft and 15 ft at 90° → 150 ft², perimeter 60 ft. The third side comes back as 25 ft and the angles as 90°, 53.13° and 36.87° — the 3-4-5 right triangle again, scaled by five.

An L-shaped room: run it twice, or run it once and subtract

The most-asked practical question about area has no shape of its own here, and does not need one. A permanent note on the page says how: "An L-shaped room is two rectangles. Measure each, run this twice, and add the two areas."

Take a main room of 20 × 15 ft with a 12 × 10 ft section off one end. Run Rectangle twice — 20 × 15 gives 300 ft², 12 × 10 gives 120 ft² — and the L covers 420 ft².

The subtraction route suits a room with a corner bitten out of it instead. The same 20 × 15 ft rectangle with a 12 × 10 ft notch taken from one corner is 300 − 120 = 180 ft², which is 20 yd² of carpet.

The perimeter of that notched room behaves in a way worth knowing before you buy trim. Cutting a rectangular notch out of a corner removes two wall segments and adds two of exactly the same lengths, so the L keeps the perimeter of the rectangle it came from: 70 ft, the figure the calculator gives for 20 × 15. Calculator Academy's L-shape page publishes the same rule as P = 2 × (outer length + outer width). Floor area falls by 40%; baseboard does not move at all.

A room that is not an L — a bay window, an angled wall, a five-sided lot — comes apart the same way, into rectangles and triangles, run one at a time and added.

A tapered back yard: the trapezoid and its second refusal

A yard running 20 ft along the back fence, 15 ft along the house and 10 ft between them is a Trapezoid, Two bases + height: 175 ft².

The measures table adds the midsegment, 17.5 ft — the width halfway up, which is the average of the two parallel ends and the number that makes the formula obvious. That yard is a rectangle 17.5 ft wide and 10 ft deep, rearranged.

The perimeter card is absent here for the same reason as the base-and-height triangle: two parallel ends and a perpendicular height say nothing about how far the slanted sides lean. Shift the top edge sideways and the area stays at 175 ft² while both legs get longer.

One naming trap comes with this shape. In British usage a "trapezium" is what American English calls a trapezoid, and a British "trapezoid" is a quadrilateral with no parallel sides at all. Charles Hutton's 1795 dictionary transposed the two terms, British English reverted around 1875, and American English kept the swap. When the vocabulary is in doubt, the shape drawn on screen is the thing to check against.

A pie-slice bed: the sector, and the edging trap

A quarter-circle bed cut from a 20 ft radius is Circle sector, Radius + angle, r = 20 ft, θ = 90°: 314.16 ft², perimeter 71.42 ft.

The measures table opens it up: the arc is 31.42 ft, the chord across the open ends is 28.28 ft, the slice is 25% of a full turn, and the whole circle it was cut from would be 1,257 ft².

The trap sits in the perimeter. Edging a pie slice takes the curve plus both straight radii, 31.42 + 20 + 20 = 71.42 ft, so ordering the arc alone leaves you 40 ft short at the till. The arc row also answers an arc-length question on its own, without reaching for a second tool.

A hexagonal deck, an octagonal gazebo, and the twelve-side ceiling

Regular polygon, Side + number of sides, a = 10 ft, n = 6: 259.81 ft², perimeter 60 ft. The measures table adds the apothem, 8.66 ft (center to the middle of a side, which is what a decking layout works from), the circumradius, 10 ft (center to a corner, equal to the side length on a hexagon), interior angles of 120°, exterior angles of 60°, and 9 diagonals.

Change n to 8 and the same 10 ft board length gives an octagon of 482.84 ft², perimeter 80 ft, apothem 12.07 ft, circumradius 13.07 ft, interior angles of 135° and 20 diagonals. Two more boards of the same length buy 223 ft² more deck.

Number of sides (n) accepts 3 to 12, the range that covers a triangular corner bed through to a twelve-sided gazebo; beyond it, Circle is the shape being approached. GIGAcalculator hard-codes an octagon as its own menu entry and offers no general polygon at all, while Omni and Inch Calculator both keep separate pentagon, hexagon and octagon entries beside a general polygon that already takes a side count.

Same area, different perimeter

Two shapes can cover the same floor and need different amounts of edging around it, which is exactly why both cards are on the page. Every row below comes off this calculator with feet as the unit.

Shape and route	What you type	Area	Perimeter
Triangle, 2 sides + angle	20 ft, 15 ft, 90°	150 ft²	60 ft
Rhombus, Diagonals	p = 20 ft, q = 15 ft	150 ft²	50 ft
Regular polygon	a = 10 ft, n = 6	259.81 ft²	60 ft
Parallelogram, 2 sides + angle	20 ft, 15 ft, 60°	259.81 ft²	70 ft
Square	a = 12 ft	144 ft²	48 ft
Rhombus, Side + height	a = 12 ft, h = 10 ft	120 ft²	48 ft

The first pair covers 150 ft² each and differs by 10 ft of boundary. The second pair covers 259.81 ft² each and differs by 10 ft the other way. The third pair shares an identical 48 ft perimeter and differs by 24 ft² of floor: a rhombus is a square pushed over, and pushing it over costs area while leaving all four sides the length they were. The general rule behind all three pairs is that among shapes of a given perimeter the circle encloses the most area, and among four-sided ones the square does.

Where an Area Measurement Goes Wrong

Typing a diameter into Radius (r). The radius is squared, so a measurement taken across the circle instead of to its center comes back four times too big. All three ways in are on the form — Radius, Diameter, and Circumference for a tape you could only get around the outside — so enter what you measured rather than halving it in your head first.
Measuring the slant instead of the height. On a triangle, a trapezoid and a parallelogram, Height (h) is the perpendicular distance from the base — to the far corner on a triangle, to the opposite edge on the other two — not the length of the sloping side. The slope is the longer of the two, so this error overstates the area. If a sloping edge is what you have on a triangle, switch to 3 sides and let Heron's formula take all three.
Mixing units inside one shape. One Units selector governs the whole form, and that is a correctness decision rather than a missing feature. Fed 30 feet by 20 meters, Calculator.net returns "1968.5039370079 feet²" and "182.88 meters²" — two answers to a question that has one. Convert to a single unit before typing; the field hint covers the fractional part, since 12 ft 6 in is 12.5.
Reading a British trapezium as an American trapezoid. They name the same quadrilateral with one pair of parallel sides, the other way round on either side of the Atlantic, and a British trapezoid has no parallel sides at all. When the figure that draws is not the figure in front of you, the vocabulary is usually the reason.
Expecting a perimeter the measurements cannot contain. Base and height on a triangle, base and height on a parallelogram, and two bases plus a height on a trapezoid each pin down an area and leave the outline free to move. The card is withheld rather than guessed at. Measure the remaining sides and change route.
Running Regular polygon on an irregular one. The formula behind that option assumes every side and every interior angle are equal. A five-sided lot whose sides differ is not a pentagon in this sense: split it into triangles, run Triangle with 3 sides on each, and add the areas.
Measuring the room instead of the floor. A chimney breast, a kitchen island, a closet doorway and a bay window all change what a flooring order should be. Measure at floor level, run each rectangle separately, and subtract whatever you are not covering. The drawing here is a check on the shape, not on what is standing inside it.
Ordering material straight off the raw area. Carpet in the US is quoted by the square yard, so a 300 ft² room is a 33.33 yd² order before anything is added, and flooring quotes then allow for pattern match, seams and offcuts on top. The units table gives the yd² figure directly; the allowance is a number your supplier sets, not one the geometry knows.

Where This Calculator Stops

It runs forwards only. Dimensions go in, area and perimeter come out. There is no route back from an area to a side, a radius or a diagonal. Solving in that direction is a different form with different fields, and folding both directions into one page would hand every visitor a form built for somebody else's question.

Three routes cannot give a perimeter. Base and height on a triangle, base and height on a parallelogram, and two bases plus a height on a trapezoid fix an area without fixing an outline. The card disappears and a line names the fix instead of printing a guess.

Regular polygons stop at twelve sides. Number of sides (n) takes 3 to 12, covering a triangular bed through to a twelve-sided gazebo. Past that, Circle is the shape being approached anyway.

The ellipse perimeter is an approximation, and says so. The note beside it says so in full: "The ellipse perimeter has no closed form; this is Ramanujan's second approximation, within 0.03 % for any shape drawn here." The area, π times the two semi-axes, is exact: an ellipse of 20 ft and 15 ft semi-axes covers 942.48 ft², with a perimeter of 110.52 ft.

The drawing clamps at extreme proportions. A shape many times longer than it is wide would render as a hairline, so the figure holds the proportions back and posts a badge — "Not to scale — the real proportions are more extreme." The numbers stay exact; only the picture is held.

There is no map and no material list. Tracing a property boundary on a satellite image is what Map Developers, Daft Logic and CalcMaps do. Totalling several rooms into one order, with a price and a waste allowance, is a flooring job rather than a geometry one. This page takes one shape at a time and reports it in eight units.

It is not a survey. A tape measure and a plane figure will get a lawn, a lot or a roof face close enough to buy materials against. A boundary in a deed is a surveyor's work, and the acreage on this page is arithmetic on what you typed.

Terms the Measures Table Uses

Apothem

The distance from the center of a regular polygon to the midpoint of one of its sides. It is what a decking or paving layout works from, and it gets its own row for any regular polygon: 8.66 ft for a hexagon of 10 ft sides, 12.07 ft for an octagon of the same side.

Circumradius

The distance from the center of a regular polygon to any corner, which is the radius of the circle the polygon fits inside. On a hexagon it equals the side length exactly, so a hexagon of 10 ft sides has a circumradius of 10 ft; an octagon of the same side has 13.07 ft.

Semi-perimeter

Half the perimeter of a triangle, written s. Heron's formula uses it to get an area from three sides with no angle and no height involved. For sides of 20, 15 and 10 ft, s is 22.5 and the area is 72.62 ft².

Midsegment

The line halfway between a trapezoid's two parallel sides, whose length is their average. It equals the width of the rectangle with the same height and the same area, so a trapezoid with 20 ft and 15 ft ends has a midsegment of 17.5 ft.

Central angle (θ)

The angle at the center of a circle through which a sector opens, entered in degrees or radians. A 90° central angle is a quarter of a full turn and takes a quarter of the circle's area with it.

Arc and chord

Two different distances across the open end of a sector. The arc follows the curve; the chord cuts straight across. On a 20 ft radius opened to 90° the arc is 31.42 ft and the chord is 28.28 ft, and edging follows the arc.

Annulus (ring)

The area between two circles that share a center: a pipe wall seen end on, a washer, a running-track lane, or a garden border around a round pond. With an outer radius of 20 ft and an inner radius of 15 ft, the band is 5 ft wide and covers 549.78 ft².

Semi-major and semi-minor axis

The two half-widths of an ellipse, measured out from its center: the long one and the short one. They play the part the radius plays in a circle, and the area is π times the two multiplied together.

Square unit

The unit an area is counted in, always the square of a length unit. One yd² is 9 ft² because a yard is 3 ft and 3 squared is 9, and one acre is 43,560 ft². Doubling every dimension of a shape multiplies its area by four rather than by two.

Area and Perimeter — Frequently Asked Questions

How do I find the area of an L-shaped room?

Split it into two rectangles, run this calculator once for each, and add the areas. A 20 by 15 ft main room plus a 12 by 10 ft section is 300 ft² plus 120 ft², or 420 ft² in total. The alternative is to take the whole enclosing rectangle and subtract the missing corner.

How many square feet is a 20x15 room?

300 square feet. The same room has a perimeter of 70 ft and a diagonal of 25 ft, and its floor is 33.33 yd², 27.87 m² or 0.0069 acres.

Is a trapezium the same as a trapezoid?

In British English a trapezium is the quadrilateral American English calls a trapezoid: one pair of parallel sides. A British trapezoid has no parallel sides at all. Charles Hutton's 1795 dictionary swapped the two terms, British usage reverted around 1875, and American usage did not.

How do I convert square feet to square yards for carpet?

Divide by 9, because a yard is 3 feet and 3 squared is 9. A 300 ft² room is 33.33 yd². The units table under the result does it for you, alongside in², cm², m², km², hectares and acres.

How many square feet are in an acre?

43,560 square feet, which is also 4,840 square yards or 4,046.8564224 m². Every result on this page is repeated in acres, so a 20 by 15 ft plot reads 0.0069 acres.

Can I get the perimeter of a triangle from its base and height?

No, and that is a property of triangles rather than a limit of the calculator. Slide the apex along a line parallel to the base and the area stays put while the two slanted sides lengthen without bound, so infinitely many triangles share any given base and height. Switch to 3 sides, or to 2 sides + angle, and the perimeter appears. The same holds for a parallelogram given a base and a height, and for a trapezoid given two bases and a height.

What is the difference between area and perimeter?

Area is the surface a shape covers, measured in square units; perimeter is the distance around its outside, measured in plain length units. Two shapes can share an area and differ in perimeter: a right triangle with 20 ft and 15 ft legs and a rhombus with 20 ft and 15 ft diagonals both cover 150 ft², but they take 60 ft and 50 ft of boundary.

How do I find the area of a triangle when I only know the three sides?

Pick Triangle, then 3 sides, and type them in. The calculator runs Heron's formula: sides of 20, 15 and 10 ft give a semi-perimeter of 22.5 and an area of 72.62 ft², with a perimeter of 45 ft and interior angles of 104.48°, 46.57° and 28.96° listed in the measures table.

How do I find the area of a circle if I can only measure around it?

Choose Circle, then Circumference, and enter the distance around the outside. That route exists for tree trunks, tanks, silos and any circle whose center you cannot reach. Radius and diameter are the other two ways in, and a 12 ft diameter and a 6 ft radius both return 113.1 ft².

Why is there only one unit selector for the whole form?

Because a shape measured in two different units has no single area. Calculator.net gives every dimension its own unit selector, and a rectangle entered as 30 feet by 20 meters comes back as 1968.5039370079 feet² and 182.88 meters², which is two answers. One selector for the form means one answer. When part of a measurement is in inches, enter it as a decimal: 12 ft 6 in is 12.5.

Can this calculator work backwards, from an area to a side?

No. It goes one way: dimensions in, area and perimeter out. Working back from an area to a side, or from a circumference to a radius, belongs to shape-specific tools with their own forms, and putting both directions on one page would double the fields for everybody.

How do I measure a room that is not a rectangle or an L?

Break it into pieces the calculator does have. Most rooms come apart into rectangles and triangles: run each piece, note its area, and add them. An angled wall gives you a triangle with three measurable sides, which the 3 sides route takes directly. An angled bay window bump-out is a trapezoid; a square one is a rectangle.

Is this area calculator free to use?

Yes, and there is nothing to sign up for. All twelve shapes, all eighteen measurement routes, the perimeter, the drawing, the eight-unit table and the formula reference are open to anyone, and the calculator can be embedded on another site. The conversion factors come from NIST Special Publication 811 and the formulas from Wolfram MathWorld, both listed under the tool.

How accurate are the results?

The area formulas are exact: every one was re-derived from its primary source — Wolfram MathWorld for the regular polygon, Heron's formula, the ellipse, the sector and the annulus — and seven of them were re-run against Calculator.net's live engine, which returned the same figures. Displayed answers are rounded for reading: four decimals below 1, two decimals from 1 up, whole numbers from 1,000 up. A circle of 20 ft radius therefore reads 1,257 ft² here where Calculator.net prints 1256.6370614359 for a measurement taken with a tape. The one approximation on the page is the ellipse perimeter, which has no closed form and is flagged where it appears.

What do I do with the square footage once I have it?

Convert it into the unit your supplier quotes in before you shop: carpet by the square yard, which is the area divided by 9, land by the acre, which is the area divided by 43,560, and most of Europe by the square meter. Then settle the allowance for offcuts with the supplier rather than with the calculator, since it depends on the material and the pattern. Keep the perimeter figure as well, because baseboard, edging, fencing and trim are bought by the running foot and none of them scales with the area.

Sources & References

Content verified by the Smart Calculators Team