AnyTool
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How do I calculate the area of a shape?

Pick the shape and apply its formula to your measurements. AnyTool’s Area Calculator does it live for 11 shapes: square (s²), rectangle (l × w), triangle (½ × base × height, or Heron’s formula from three sides), circle (π × r²), ellipse (π × a × b), trapezoid (½ × (a + b) × h), parallelogram (b × h), rhombus (½ × d₁ × d₂), regular polygon (¼ × n × s² × cot(π/n)), circle sector (½ × r² × θ) and annulus ring (π × (R² − r²)). Choose a length unit (mm to miles), type the dimensions, and it shows the area in that unit squared with the exact formula filled in, the perimeter or circumference where it makes sense, and the same area converted to m², ft², acres and hectares. It is pure planar geometry, computed entirely in your browser — nothing is uploaded.

  • 11 shapes — square, rectangle, triangle, circle, ellipse, trapezoid, parallelogram, rhombus, polygon, sector, annulus
  • Shows the exact formula with your own numbers substituted in
  • Triangle by base × height OR Heron’s formula from three sides
  • Any length unit in; area out in that unit² plus m², ft², acres, hectares
  • 100% in your browser — no upload, no signup, works offline

What is

Area (of a 2D shape)

Area is the amount of flat (planar) surface a two-dimensional shape covers, measured in square units such as square metres or square feet. Each shape has its own formula: a square is the side squared (s²); a rectangle is length × width; a triangle is half the base times the perpendicular height (or Heron’s formula from the three side lengths); a circle is π times the radius squared; an ellipse is π × a × b for its two semi-axes; a trapezoid is half the sum of the two parallel sides times the height; a parallelogram is base × height; a rhombus is half the product of its diagonals; a regular polygon with n sides of length s is ¼ × n × s² × cot(π/n); a circle sector is ½ × r² × θ for an angle θ in radians; and an annulus (ring) is π × (R² − r²). Area is distinct from perimeter (the boundary length) and from floor area used for rooms and buildings.

Calculators

Related terms

PerimeterCircumferenceSquare unitsHeron’s formulaPi (π)Floor area

Frequently Asked Questions

Area = ½ × base × height, using the perpendicular height. If you only know the three side lengths, use Heron’s formula: A = √(s(s−a)(s−b)(s−c)) where s is half the perimeter.

The standard formula for a triangle’s area is one-half times the base times the perpendicular height, A = ½ × b × h — the height must be the straight-up distance from the base to the opposite vertex, not a slanted side. When you do not know the height but do know all three side lengths a, b and c, use Heron’s formula: first find the semi-perimeter s = (a + b + c) / 2, then A = √(s(s−a)(s−b)(s−c)). AnyTool’s Area Calculator accepts either input — enter base and height, or leave them blank and enter the three sides — and shows the exact formula with your numbers filled in, plus the perimeter when all three sides are given.

Area = π × r², where r is the radius (half the diameter). A circle of radius 7 has an area of about 153.94 square units; its circumference is 2 × π × r.

A circle’s area is pi times the radius squared, A = π × r², where the radius r is the distance from the centre to the edge — half the diameter, so if you measured across the full width, halve it first. For example, a radius of 7 gives π × 49 ≈ 153.94 square units. The matching boundary length is the circumference, C = 2 × π × r ≈ 43.98 for that circle. AnyTool’s Area Calculator computes both from the radius, shows the formula with your number substituted, and also converts the area to square metres, square feet, acres and hectares so large circles read sensibly.

A trapezoid is ½ × (a + b) × h, half the sum of the two parallel sides times the height. A parallelogram is simply base × height. Both use the perpendicular height.

For a trapezoid (a quadrilateral with one pair of parallel sides), the area is one-half times the sum of the two parallel sides times the perpendicular distance between them: A = ½ × (a + b) × h. For a parallelogram, the area is just the base times the perpendicular height, A = b × h — the same as a rectangle of equal base and height, because shearing a rectangle into a parallelogram does not change its area. In both cases the height is the perpendicular (straight-across) distance, never a slanted edge. AnyTool’s Area Calculator computes either from those measurements and can also report the perimeter when you add the slanted sides.

One square metre is about 10.7639 square feet, and one acre is 4,046.86 square metres (about 43,560 ft²). One hectare is 10,000 m². Multiply by the right factor or let the tool do it.

Area conversions square the length factor: because one foot is 0.3048 metres, one square foot is 0.3048² = 0.09290304 square metres, and one square metre is about 10.7639 square feet. For land, an acre is 4,046.8564224 square metres (43,560 square feet), and a hectare is exactly 10,000 square metres (about 2.471 acres). AnyTool’s Area Calculator shows your result in the input unit squared and simultaneously in square metres, square feet, acres and hectares, so a small tile and a large field both read in familiar units without any manual conversion.

Detailed Explanation

Methodology

How the Area Calculator Works

The calculator applies the exact closed-form formula for the selected shape to the dimensions entered, returning the area in the chosen length unit squared. Square is s²; rectangle is l × w; triangle is ½ × base × height, with a Heron-of-Alexandria fallback A = √(s(s−a)(s−b)(s−c)) from three sides; circle is π × r²; ellipse is π × a × b; trapezoid is ½ × (a + b) × h; parallelogram is b × h; rhombus is ½ × d₁ × d₂; a regular n-gon of side s is ¼ × n × s² × cot(π/n); a circle sector is ½ × r² × θ (θ in radians, or (θ/360) × πr² in degrees); and an annulus is π × (R² − r²). Where a closed boundary is meaningful the tool also reports the perimeter or circumference (the ellipse uses Ramanujan’s high-accuracy approximation), and the area is converted to square metres, square feet, acres and hectares by squaring the length factor.

  • Square s² · rectangle l·w · triangle ½bh or Heron · circle πr² · ellipse πab
  • Trapezoid ½(a+b)h · parallelogram bh · rhombus ½d₁d₂
  • Regular polygon ¼·n·s²·cot(π/n) · sector ½r²θ · annulus π(R²−r²)
  • 1 ft² = 0.09290304 m²; 1 acre = 4046.8564224 m²; 1 ha = 10,000 m²
  • All math is client-side JavaScript with no server round-trip
Use Cases

Pure Geometry, the Formula and the Units

Unlike a single-shape box, this tool covers eleven common shapes in one place and shows the exact formula with the user’s own numbers substituted in, which makes it useful for homework, design and quick double-checks as well as practical measuring. Each shape asks only for the dimensions it needs — a circle wants a radius, a rhombus wants its two diagonals, a regular polygon wants the side count and side length, a sector wants a radius and an angle — and a live pure-SVG diagram shows what each measurement means. Because the result is also expressed in square metres, square feet, acres and hectares simultaneously, the same tool serves a tile, a garden bed and a field. For the floor area of rooms and a whole home, the companion Room Area Calculator sums real footprints instead.

  • Eleven shapes with the exact formula displayed, not just a number
  • Triangle accepts base × height OR three sides (Heron)
  • Sector angle entered in degrees or radians
  • Area shown in input-unit² plus m², ft², acres and hectares
  • Live SVG diagram shows what each dimension means
Limitations

Exact Planar Math, Real-World Measuring

The output is the exact area of an idealised flat shape, so its accuracy is bounded entirely by the measurements supplied. Real objects deviate from ideal geometry: corners are rarely truly square, circles are rarely perfectly round, and a triangle’s height must be the perpendicular height rather than a slanted side. The radius — not the diameter — is what a circle, sector and annulus expect, and a rhombus is defined here by its diagonals. The ellipse perimeter uses Ramanujan’s approximation because a true ellipse has no elementary perimeter formula, though the area π × a × b is exact. Unit conversions assume the input length unit is exact. This tool is pure geometry and is not a substitute for the Room Area Calculator, which handles building floor area, costs and per-room totals.

  • Exact formulas; accuracy limited by your measurements
  • Use the perpendicular height for triangle and parallelogram
  • Circle / sector / annulus expect the radius, not the diameter
  • Ellipse perimeter is a very-accurate approximation; its area is exact
  • For room and building floor area use the Room Area Calculator
Privacy & Security

Privacy and Offline Use

All computation runs in the browser, so the shape and dimensions entered are never sent to a server, there is no account or tracking, and the page works offline after first load. The calculator is built on a shared, unit-testable area-shape engine, so its per-shape formulas and unit conversions behave consistently, and the full result — the area, the exact formula used, the perimeter or circumference, and the conversions to m², ft², acres and hectares — can be copied to the clipboard with one tap.

Area: in-browser (AnyTool) vs typical online area calculators
CapabilityAnyToolTypical online area calculators
ProcessingRuns in your browserOften server-side
Shapes11 (incl. sector, annulus, polygon)Often a handful
Formula shownExact formula with your numbersResult only
Triangle from 3 sidesYes (Heron’s formula)Rarely
Perimeter / circumferenceWhere meaningfulSometimes
Length unitsmm to milesOften fixed
Area conversionsm², ft², acres, hectares at onceUsually one unit
Live diagramPure-SVG per shapeStatic image or none
Works offlineYes (PWA)No
Cost / signupFree, no signupOften ad-heavy or gated

AnyTool computes the area locally and uploads nothing. Comparison as of June 2026.