Area Calculator - Square, Rectangle, Triangle, Circle, Trapezoid

An area calculator answers how much flat space a region covers. That is a two-dimensional question: length times length, or an equivalent formula that still produces square units. A garden bed, a rectangular room, a circular patio, a triangular sail, and an elliptical running track all have area. They do not have volume until you add thickness, and they do not have surface area in the solid-geometry sense until you wrap a 3-D object.

This page handles seven plane figures: square (A = s²), rectangle (A = l × w), triangle (A = ½bh or Heron from three sides), parallelogram (A = bh), trapezoid (A = (a+b)/2 × h), circle (A = πr²), and ellipse (A = πab). The default load is a rectangle 8 by 5, which is exactly 40 square units - useful as a sanity check that the tool is multiplying, not adding (8+5=13) and not doubling a perimeter (26).

Arithmetic stays in the browser. If you need the full set of circle quantities (diameter, circumference, arc, sector), open the circle calculator. If the “area” you actually wanted is the skin of a box or tank, that is surface area, not this page. If you needed how much the tank holds, that is the volume calculator.

Using this square rectangle triangle circle area tool takes four steps:

1. Pick the shape that matches the region. A square is not “almost a rectangle” for the formula: you still use s², which is the special case l = w. A rhombus that is not a square belongs under parallelogram with perpendicular height, not under square.
2. Enter every required length as a positive number in the same unit. Height for a triangle, parallelogram, or trapezoid is the perpendicular distance, not a slanted side. Circle wants radius, not diameter.
3. Read the formula, the plugged-in substitution, and the numeric area. The number is square in whatever unit you used for the lengths.
4. Copy the result or clear the fields. Shape and dimensions are stored locally for up to 30 days.

Note: there is no unit dropdown. 3 cm and 3 m are both “3” to the formula, but 3² cm² is not 3² m². Convert first. Irregular polygons, composite L-shapes, and GIS polygons are not implemented.

A rectangle is a four-sided figure with right angles. Opposite sides are equal. Area is the product of two adjacent sides. The default on this page is l = 8, w = 5, so A = 40. If you swap length and width you still get 40; order does not matter. If a problem gives perimeter and one side, you do not yet have area: you must recover the other side first. Perimeter of the default rectangle is 2(8+5) = 26, which is not 40 and must not be reported as area.

Worked example - 8 × 5:

• Identify length 8 and width 5 in the same unit.
• Multiply: 8 × 5 = 40.
• Attach square units: 40 m² if the sides were metres, 40 ft² if they were feet.

Worked example - square of side 6:

• A square is the special rectangle with l = w = s.
• A = 6² = 36, not 24 (that would be the perimeter 4s).

Scaling: if you double both sides of an 8 × 5 rectangle you get 16 × 10 = 160, which is four times 40, not twice. Area scales with the square of a linear scale factor. That is why a drawing at 1:100 is not “one percent of the real area”; it is one ten-thousandth.

The school formula A = (1/2) b h needs a chosen base b and the perpendicular height to that base. A slanted side is not h. If you only have the three side lengths, switch this tool to Heron: let s = (a+b+c)/2, then A = √[s(s−a)(s−b)(s−c)]. The sides must form a genuine triangle (strict triangle inequality). Degenerate sticks laid end to end have area 0 and are rejected.

Worked example - base 6, height 4:

A = (1/2) × 6 × 4 = 12. If someone forgets the 1/2 they report 24, which is the parallelogram with the same base and height, not the triangle.

Worked example - sides 3, 4, 5 (Heron):

s = 6. A = √[6(6−3)(6−4)(6−5)] = √[6 × 3 × 2 × 1] = √36 = 6. That matches (1/2)×3×4 for a right triangle. For a general SSS case that is not right, use the triangle calculator if you also need angles; this area page only returns the number of square units.

Heron can be numerically unhappy on extremely skinny triangles (one tiny height, sides almost collinear). IEEE-754 square roots will still run; the result may lose digits. For ordinary homework sides it is exact enough.

A disk of radius r has A = π r². This calculator uses JavaScript Math.PI (about 3.141592653589793), not 3.14 and not 22/7. Diameter is 2r. Typing diameter into the radius field overstates area by a factor of four because (2r)² = 4r². Circumference 2πr is a length around the rim; it is not area. If a problem gives circumference C, recover r = C/(2π) first, or use the circle calculator which does that inversion for you.

Example: r = 7 gives A = 49π ≈ 153.93804002589985. Example: r = 1 gives π itself. An ellipse with semi-axes a and b has A = πab; when a = b = r the ellipse formula collapses to the circle. Semi-axes are half the full width and full height of the bounding rectangle, not the full diameters.

A parallelogram with base 10 and perpendicular height 3 has area 30. The same parallelogram with a slanted side of 5 is still 30 if the height is 3; multiplying 10 × 5 would be wrong unless that 5 happens to be the perpendicular height. A trapezoid with parallel sides 3 and 5 and height 4 is (3+5)/2 × 4 = 16. The non-parallel legs are not entered.

• Reporting perimeter as area. 8 × 5 is 40 square units, not 26 linear units. The words “around” and “covers” are different questions.
• Using a slanted side as triangle or parallelogram height. Height is the perpendicular drop to the base line.
• Forgetting 1/2 on a triangle and getting the parallelogram instead.
• Putting diameter in the circle radius box and getting 4× too much area.
• Mixing cm and m. Convert to one unit. Area conversion is the square of the length conversion: 1 m² = 10,000 cm².
• Calling volume “area.” A tank’s capacity is cubic. A label’s printed face is square.

Two lengths multiplied produce a square unit: m², cm², in², ft². One metre by one metre is a square metre, regardless of whether the region is a circle or a triangle - the unit does not change with the shape, only the numeric factor does. This tool never converts among those names. If l is in inches and you wanted square feet, divide the inch-area by 144 yourself.

Changing all linear dimensions by a factor k changes area by k². Triple every side of a square and the area becomes nine times larger. That scaling is why model drawings and full-size floors do not share a 1:1 area ratio with their scale factor.

Area (this page) is 2-D measure of a region in a plane. Surface area is the total of the faces of a solid - still square units, but you are wrapping a 3-D object. Volume is cubic. A cube of side 4 has face area 16 per square, six faces 96 (surface area), and interior 64 (volume). People search “area of a cube” when they mean surface area; this calculator will not invent a sixth dimension for a square. Use the matching tool.

A circle is not a sphere. πr² is the disk. 4πr² is the sphere’s skin. (4/3)πr³ is the ball’s volume. Mixing those three is the most common exam error when a word problem mentions “round.”

• Seven plane shapes only. No regular pentagon, no sector (use the circle calculator’s central angle), no annulus, no composite L-shape.
• Perpendicular heights. Triangle, parallelogram, and trapezoid h is altitude, not a side.
• No unit conversion and no paint-coverage litres. The output is a pure number in square input-units.
• IEEE-754 π for circle and ellipse. Very large r² can overflow to Infinity.
• Positive lengths only. Empty, zero, and negative dimensions error. Coordinates of polygons are not accepted.