Area & Perimeter Calculator

Pick a shape; see area, perimeter, and the formula instantly. Square, rectangle, circle, triangle (Heron), trapezoid, parallelogram, ellipse, circular sector, and regular polygon — plus step-by-step solutions, feet/inches/meters/centimeters units, acre-hectare conversion, and volume (cube, cylinder, sphere, cone).

Length unit

Overage / waste (%) · opt.

π ≈ 3.14159Circle math constant

π · r²Circle area formula

43,560 ft²= 1 acre

2.47 acres= 1 hectare

📐 Calculation note: Every result is computed with the exact geometry formula for your selected shape, entirely in your browser (client-side) — no server or external service is used. Area is measured in square units (ft², m²), perimeter in plain length units (ft, m). Results are also shown together in square inches/feet/yards/meters and acres. Ellipse circumference uses Ramanujan's approximation (extremely high accuracy). Use a period for decimals (e.g. 12.5).

📐 Area & Perimeter Calculator — ToolPico ↗

What are area and perimeter, and how are they calculated?

A complete guide to area and perimeter formulas for squares, rectangles, circles, triangles, trapezoids, and parallelograms — with examples and unit rules.

Area is the size of the surface a shape covers, and it is always measured in square units (square feet ft², square meters m²). Perimeter is the total length of a shape's outer edges, measured in a plain length unit (feet, meters). Two shapes with the same perimeter can have very different areas, so each must be calculated separately. This tool gives you both the area and the perimeter for every shape, shows the formula used, and explains the result step by step.

How do you calculate the area of a rectangle and a square?

Quick answerFor a square, area is side²; for a rectangle it's long side × short side. Perimeter is 4 × side for a square and 2 × (a + b) for a rectangle. Example: an 8 ft × 5 ft rectangle has an area of 40 ft² and a perimeter of 26 ft.

Square: Area = a², Perimeter = 4a. Knowing one side is enough.
Rectangle: Area = a·b, Perimeter = 2(a+b). Requires two adjacent sides.
Square-footage estimates (rooms, flooring, tile) are almost always based on rectangular area.

How do you find the area and circumference of a circle?

Quick answerA circle's area is π × r², and its circumference is 2 × π × r; r is the radius. If you know the diameter, radius = diameter / 2. A circle with a 5 ft radius has an area of 78.54 ft² and a circumference of 31.42 ft.

Pi (π) is approximately 3.14159 and is the ratio of a circle's circumference to its diameter. When you select the "Circular sector" shape, the tool also calculates the arc length and sector area for a given angle.

How do you calculate the area of a triangle? (2 methods)

Quick answerThe most common method is (base × height) / 2. When only the three sides are known, use Heron's formula: take s = (a+b+c)/2, then Area = √(s(s−a)(s−b)(s−c)). For an equilateral triangle, Area = (√3 / 4) × a².

This tool has three separate options for triangles: base-height (fast area), Heron / 3 sides (area and perimeter together), and equilateral triangle (from a single side). In Heron mode, if the sides don't satisfy the triangle inequality (one side is greater than or equal to the sum of the other two), no valid triangle exists and the tool shows a warning.

Area of a trapezoid and a parallelogram

Quick answerTrapezoid: Area = ((bottom base + top base) / 2) × height. Parallelogram: Area = base × height. In a parallelogram, height is the perpendicular distance to the base, not the length of the slanted side.

Area and perimeter formulas table

Every shape's area and perimeter formula in one table — a copyable reference.

Geometric shapes · area and perimeter formulas (r = radius, a/b = side, h = height)
Shape	Area formula	Perimeter formula
Square	a²	4·a
Rectangle	a·b	2·(a+b)
Circle	π·r²	2·π·r
Triangle (base·height)	(base·h)/2	a+b+c
Triangle (Heron)	√(s(s−a)(s−b)(s−c))	a+b+c
Triangle (SAS)	(1/2)·a·b·sin(C)	a+b+c
Triangle (SSA)	(1/2)·a·b·sin(C)	a+b+c
Triangle (ASA/AAS)	c²·sin(A)·sin(B)/(2·sin(C))	a+b+c
Equilateral triangle	(√3/4)·a²	3·a
Trapezoid	((a+b)/2)·h	a+b+c+d
Parallelogram	base·h	2·(a+b)
Rhombus	(d1·d2)/2	4·a
Kite	(d1·d2)/2	2·(a+b)
Ellipse	π·a·b	≈ π·[3(a+b)−√((3a+b)(a+3b))]
Circular sector	(θ/360)·π·r²	arc + 2·r
Semicircle	(π·r²)/2	π·r + 2·r
Annulus (ring)	π·(R²−r²)	2·π·(R+r)
Regular polygon (n sides)	(n·a²)/(4·tan(180°/n))	n·a
Regular pentagon	(5·a²)/(4·tan(36°))	5·a
Regular hexagon	(3√3/2)·a²	6·a
Regular octagon	2·(1+√2)·a²	8·a

Volume and surface area formulas

Solids · volume and surface area (r = radius, h = height, l = slant height)
Solid	Volume	Surface area
Cube	a³	6·a²
Rectangular prism (box)	a·b·c	2·(ab+bc+ac)
Cylinder	π·r²·h	2·π·r·(r+h)
Sphere	(4/3)·π·r³	4·π·r²
Cone	(1/3)·π·r²·h	π·r·(r+l)

Popular calculations

Example area and perimeter values

Ready-made results for commonly used dimensions (unit: feet). Use the calculator above for exact figures.

Example shapes (unit: feet)
Shape / dimensions	Area	Perimeter
Square · side 5 ft	25 ft²	20 ft
Rectangle · 8 × 5 ft	40 ft²	26 ft
Circle · radius 5 ft	78.54 ft²	31.42 ft
Triangle · base 6, height 4 ft	12 ft²	—
Equilateral triangle · side 6 ft	15.59 ft²	18 ft
Trapezoid · 8 + 4, height 5 ft	30 ft²	—
Parallelogram · base 8, height 5, side 6 ft	40 ft²	28 ft
Circular sector · r 6 ft, 90°	28.27 ft²	21.42 ft

Unit & conversion tables

Conversions between area and length units, including acres and hectares commonly used for lots and land.

Area unit conversions
Unit	Equal to
1 sq ft	144 sq in = 0.0929 sq m
1 sq yd	9 sq ft
1 acre	43,560 sq ft = 4,047 sq m
1 hectare (ha)	2.471 acres = 10,000 sq m
1 sq mile	640 acres

In the US, land and lot sizes are typically measured in acres; 1 acre equals about 0.405 hectares.

Length (perimeter) unit conversions
Unit	Equal to
1 ft (foot)	12 in = 0.3048 m
1 yd (yard)	3 ft = 0.9144 m
1 mile (mi)	5,280 ft = 1,609.344 m
1 m (meter)	3.281 ft = 39.37 in
1 in (inch)	2.54 cm
1 mm (millimeter)	0.001 m = 0.0394 in
1 km (kilometer)	1,000 m = 0.6214 mi

Perimeter is a length; it is never expressed in square units (ft²).

Volume unit conversions
Unit	Equal to
1 cu ft	1,728 cu in
1 US gallon	231 cu in = 0.1337 cu ft
1 cu yd	27 cu ft
1 cu m	35.31 cu ft = 264.17 US gal

The "Volume & Surface" tab calculates volume and surface area together for cubes, prisms, cylinders, spheres, and cones.

Geometry terms glossary

Short definitions of the key terms used in area and perimeter calculations.

AreaThe size of the surface a shape covers. Measured in square units (ft², m²).

PerimeterThe total length of a shape's outer edges. Measured in a plain length unit (ft, m).

Radius (r)The distance from a circle's center to its edge. Half of the diameter.

DiameterThe longest straight line across a circle through its center; twice the radius.

Pi (π)The ratio of a circle's circumference to its diameter; approximately 3.14159.

BaseA shape's reference bottom side, used as the reference edge in area formulas.

HeightThe perpendicular distance measured from the base. Not to be confused with a slanted side.

Heron's formulaA formula that gives a triangle's area from its three side lengths alone.

Circular sectorThe "pie slice" portion of a circle corresponding to a given central angle.

Regular polygonA polygon with all sides and angles equal (e.g. a square, a regular hexagon).

AcreA US customary unit of land area equal to 43,560 square feet.

VolumeThe size of the space a solid object occupies. Measured in cubic units (ft³, m³, gallons).

Step-by-step guides

Detailed answers to the most common area and perimeter questions.

How do you calculate the area and circumference of a circle?

First determine the radius (r); if you know the diameter, divide it by two. In the formula Area = π × r², square the radius and multiply by π (≈3.14159). For example, at r = 5 ft the area is π × 25 = 78.54 ft².

For the circumference, use Circumference = 2 × π × r; this equals the diameter times π. At r = 5 ft, the circumference is 2 × π × 5 = 31.42 ft. In the tool, just select "Circle" and enter the radius — the step-by-step solution is shown automatically.

Area of a triangle from three sides: Heron's formula

When only the three sides (a, b, c) are known, area can be found without a height. First calculate the semi-perimeter s = (a + b + c) / 2. Then apply Area = √(s(s−a)(s−b)(s−c)).

Example: for a triangle with sides 3, 4, 5, s = 6, area = √(6·3·2·1) = √36 = 6 square units. If the sides can't form a triangle (the longest side equals or exceeds the sum of the other two), the result is invalid; the tool shows a warning in that case.

Converting square feet to acres

Lot and land areas are usually measured in square feet first, then converted to the units used in deeds and records. 1 acre = 43,560 square feet, and 1 hectare = 2.471 acres = 10,000 square meters.

For example, a 15,000 sq ft lot is 15,000 ÷ 43,560 ≈ 0.344 acres. This tool automatically shows any calculated area in square feet, square yards, square meters, and acres together, so no separate conversion is needed.

Frequently asked questions

How do you calculate the area of a rectangle?

The area of a rectangle is long side × short side, i.e. a × b. For example, an 8 ft × 5 ft rectangle has an area of 8 × 5 = 40 ft². Its perimeter is 2 × (a + b), which in the same example is 2 × 13 = 26 feet.

How do you find the area of a circle?

The area of a circle is π × r²; r is the radius (π ≈ 3.14159). A circle with a 5 ft radius has an area of π × 25 = 78.54 ft². If you have the diameter instead, use radius = diameter / 2.

What is the formula for the circumference of a circle?

The circumference of a circle is found with 2 × π × r, which equals π times the diameter. A circle with a 5 ft radius has a circumference of 2 × π × 5 = 31.42 ft. Area is measured in square units (ft²), circumference in a plain length unit (ft).

How do you calculate the area of a triangle?

The most common method is (base × height) / 2; for example, a base of 6 and a height of 4 gives an area of 12 square units. When only the three sides are known, use Heron's formula; for an equilateral triangle, use (√3 / 4) × a². This tool offers all three as separate options.

How do you calculate the area of a trapezoid?

The area of a trapezoid is ((bottom base + top base) / 2) × height. For example, with a bottom base of 8, top base of 4, and height of 5, the area is ((8 + 4)/2) × 5 = 30 ft². For the perimeter, add the lengths of all four sides.

How do you calculate the area of a parallelogram?

The area of a parallelogram is base × height. Height here is the perpendicular distance to the base, not the length of the slanted side. Its perimeter is twice the sum of two adjacent sides: 2 × (a + b).

How many square feet are in an acre?

1 acre = 43,560 square feet, or about 4,047 square meters (2.471 acres per hectare). This tool automatically shows any calculated area in square inches, square feet, square yards, square meters, and acres together.

How do you find the area of an equilateral triangle?

For an equilateral triangle, where all sides are equal, the area is (√3 / 4) × a². A triangle with a 6 ft side has an area of (1.732/4) × 36 ≈ 15.59 ft², and a perimeter of 3 × 6 = 18 ft.

How do you find a triangle's area from two sides and an angle (SAS)?

When you know two sides and the angle between them, the area is (1/2) × a × b × sin(C), where C is the included angle. The missing third side comes from the law of cosines: c = √(a² + b² − 2ab·cos(C)). This tool also offers SSA (two sides and a non-included angle) and ASA/AAS (two angles and a side) as separate triangle modes, both solved with the law of sines.

Methodology & accuracy

Area & Perimeter Calculator is a free, independent ToolPico calculator. Calculations are performed directly with the standard mathematical formula for your selected shape (square, rectangle, circle, triangle, trapezoid, parallelogram, ellipse, sector, regular polygon, and solids) entirely in your browser; no data is sent to a server.

Accuracy: π uses JavaScript's full-precision Math.PI constant. Since the ellipse has no closed-form circumference formula, it's calculated with Ramanujan's second approximation (typically an error smaller than one part in a million). Triangles use Heron's formula, and invalid side combinations are flagged. Last updated: July 21, 2026. Results are for educational and informational purposes.