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Area Calculator

Math

Calculate area of circles, rectangles, squares, triangles, trapezoids, and parallelograms instantly. Enter dimensions to get precise area and perimeter.

Reviewed by the thecalcu.com team · Last updated June 25, 2026

Shape

A = πr²

Radius (r)
units
0.1200

Circle — Area

—sq units

Formula: A = πr²

Area Formulas

CircleA = πr²
RectangleA = l × w
SquareA = s²
TriangleA = ½ × b × h
TrapezoidA = ½(a+b) × h
ParallelogramA = b × h

What is a Area?

The area calculator computes the enclosed two-dimensional space, and, where applicable, the perimeter or circumference, for six common geometric shapes: circle, rectangle, square, triangle, trapezoid, and parallelogram. Pick a shape, enter its dimensions, and the result updates instantly with the formula shown alongside it. Area is one of the most practical mathematical concepts in everyday life, whether you're figuring out how much flooring a room needs, how much paint covers a wall, or the size of a plot of land. This tool pairs naturally with the pythagorean-theorem-calculator when you're working with right triangles, use Pythagoras to find a missing side, then feed those dimensions straight into the area calculation. For triangles where you know all three sides instead of base and height, the triangle-calculator computes area via Heron's formula and gives you all three angles plus the perimeter too.

Why Use an Area Calculator?

Manual area calculation is straightforward for a single simple shape but gets error-prone fast once decimals, multiple shapes, or unit conversions enter the picture. A slipped digit in a multi-step calculation wastes time and can throw off a material order. The instant what-if capability matters most in practical planning: adjusting a circular garden bed's radius by a foot changes its area by 2πr square feet, which is a meaningful difference when you're buying turf or paving stone by the square foot. Trying a few room dimensions to hit a target area, say, fitting a 250 sq ft minimum for a workshop, is far faster when the result updates live instead of requiring a fresh calculation each time.

Who Should Use This Calculator?

Students studying geometry and mensuration can use the calculator to check homework answers, since the formula shown alongside each result reinforces the method rather than just handing over a number.

Homeowners and DIYers estimating material quantities, flooring, paint, carpet, wallpaper, where knowing the exact square footage of a surface avoids over-ordering and wasted material.

Architects, engineers, and draftspeople doing a quick area check during design review without setting up a full CAD computation for a simple verification.

Real estate professionals and property buyers working out the square footage of a room, lot, or floor plan when comparing listings or planning a build-out.

Landscapers and gardeners measuring beds, lawns, and hardscape areas, rectangular, circular, and trapezoidal shapes all cover common yard layouts.

How to use this Area calculator

  1. Select your Shape, Circle, Rectangle, Square, Triangle, Trapezoid, or Parallelogram. The input fields update to show only what's relevant.
  2. Enter the dimensions. Circle: radius, not diameter. Rectangle: length and width. Square: one side length. Triangle: base and perpendicular height, not the slant side. Trapezoid: both parallel bases and the perpendicular height. Parallelogram: base and perpendicular height.
  3. Read the Area result, shown in square units matching whatever unit you entered.
  4. Check Perimeter / Circumference, available for circle, rectangle, and square, useful for fencing, trim, or framing estimates.
  5. Switch shapes to compare, toggling between a circular and rectangular layout of similar dimensions is a fast way to see which uses more space.

Formula & Methodology

Circle: Area = πr², Circumference = 2πr, where r is the radius.

Rectangle: Area = l × w, Perimeter = 2(l + w).

Square: Area = s², Perimeter = 4s.

Triangle: Area = ½ × b × h, where h is the perpendicular height to the base.

Trapezoid: Area = ½ × (b₁ + b₂) × h.

Parallelogram: Area = b × h, using the perpendicular height, not the slant side.

Worked example, tiling a living room: a rectangular room measures 18 feet by 14 feet. Room area = 18 × 14 = 252 sq ft. Using 2 × 2-foot tiles (4 sq ft each), tiles needed = 252 ÷ 4 = 63, plus a 10% waste allowance brings the order to about 70 tiles. Perimeter for baseboard = 2(18 + 14) = 64 feet.

Common Mistakes to Avoid

Using the slant height instead of the true perpendicular height is the single most common mistake on triangles, trapezoids, and parallelograms, the formula specifically needs the straight-line distance between the base and the opposite side, not the length of an angled edge. Confusing radius with diameter on circle calculations throws the area off by a factor of four, since area scales with the square of whatever value gets entered. Mixing units within one calculation, entering length in feet and width in inches, for instance, produces a result that looks plausible but is wrong; convert everything to one unit first. Finally, forgetting that perimeter isn't computed for triangle, trapezoid, or parallelogram in this tool trips people up occasionally, that's because those shapes need side lengths the area formula doesn't require as direct inputs, so use the triangle-calculator or surface-area-calculator when perimeter or full surface detail is what you actually need.

Frequently Asked Questions

Six common shapes: circle, rectangle, square, triangle, trapezoid, and parallelogram, the shapes that show up most often in school geometry, construction, landscaping, and interior design. Switching shapes updates the input fields to only what's actually needed for that shape's formula.
Area = πr², where r is the radius and π ≈ 3.14159. Circumference (the perimeter) is 2πr. For a circular garden bed with a 7-foot radius, area = π × 7² ≈ 153.94 sq ft.
Area = length × width, and perimeter = 2(length + width). A room 12 feet long and 9 feet wide has an area of 108 sq ft and a perimeter of 42 feet, the single most common area calculation in flooring, painting, and construction estimates.
Area = ½ × base × height, using the perpendicular height, not a slanted side. For a triangular lot with a 20-foot base and 15-foot perpendicular height, area = ½ × 20 × 15 = 150 sq ft. If you know all three sides instead of the height, Heron's formula applies, see the [triangle-calculator](/triangle-calculator/) for that case.
Area is the two-dimensional space enclosed by a shape, measured in square units. Perimeter is the total length of the boundary around it, measured in linear units. A 10 × 5 rectangle has an area of 50 sq units but a perimeter of only 30 units, they measure entirely different things.
Area = ½ × (base₁ + base₂) × height, where base₁ and base₂ are the two parallel sides and height is the perpendicular distance between them. A trapezoid with parallel sides of 8 and 5 feet and a height of 4 feet has an area of ½ × (8 + 5) × 4 = 26 sq ft.
Area = base × height, using the perpendicular distance between the two parallel bases, not the slanted side length. A parallelogram with a 12-foot base and 7-foot perpendicular height has an area of 84 sq ft. Perimeter isn't calculated for a parallelogram since that requires the slant side, which isn't a direct input here.
No, it computes area from given dimensions, not the reverse. To back into dimensions from a known area, you typically set up an algebraic equation, for a rectangle with area 60 and length 4 more than width, w(w+4) = 60 gives the quadratic w² + 4w − 60 = 0, which the [quadratic-formula-calculator](/quadratic-formula-calculator/) can solve for w.
A square is a rectangle where all four sides happen to be equal. Rectangle area = length × width; square area = side², since both dimensions are identical. A square with a 10-foot side has an area of 100 sq ft and a perimeter of 40 feet, both shapes share right angles at every corner, the only difference is whether opposite sides or all four sides are equal.
1 square meter equals about 10.764 square feet, so multiply square meters by 10.764 to get square feet, or divide square feet by 10.764 to get square meters. A 100 sq m space works out to roughly 1,076 sq ft, a conversion that comes up often when comparing listings or specs quoted in different units.
Break it into regular sub-shapes, rectangles, triangles, circles, calculate each one's area with the appropriate formula, then add them together. An L-shaped room, for instance, splits cleanly into two rectangles. Subtract any cut-out sections, like a circular fountain inside a rectangular garden, from the total.
Also known as
shape areasquare arearectangle areacircle areaarea finderarea of shape