Area Calculator

Calculate and combine areas for common 2D shapes

Select a shape, enter its measurements in one linear unit, and choose the square unit for the answer. This calculator handles rectangles, squares, triangles from base and height, triangles from three sides, circles, ellipses, parallelograms, trapezoids, and circular sectors. For an irregular room, add each non-overlapping section to the running total; sections are converted before they are combined. It also reports supporting measurements such as perimeter, circumference, semiperimeter, or arc length when the entered dimensions determine them.

What area measures

Area is the amount of two-dimensional surface inside a boundary. Because two lengths are multiplied, area is expressed in square units such as square inches, square feet, square meters, acres, or hectares. A rectangle that is 20 feet long and 12 feet wide has 240 square feet of area. Its perimeter is a linear measurement of 64 feet; square feet and feet describe different quantities and cannot be interchanged.

Rectangle and square area

For a rectangle, multiply length by width. A square uses the same formula, but all four sides have the same length, so its area is the side length squared.

rectangle area = length x width
square area = side²

A 20-foot by 12-foot rectangle has area 20 x 12 = 240 square feet. Its perimeter is 2 x (20 + 12) = 64 feet. A square with a 10-foot side has area 100 square feet and perimeter 40 feet.

Triangle area from base and height

A triangle occupies half the area of a parallelogram with the same base and perpendicular height. The height must meet the base at a right angle. A slanted side is not the height unless it is perpendicular to the chosen base.

triangle area = base x perpendicular height / 2

A triangle with a 12-foot base and an 8-foot perpendicular height has area 48 square feet. Base and height alone do not determine the other two sides, so this mode cannot produce a unique perimeter.

Triangle area from three sides

When all three side lengths are known, choose the three-side option. The calculator first checks the triangle inequality: every pair of sides must add to more than the remaining side. It then uses Heron's formula, where s is the semiperimeter.

s = (a + b + c) / 2
triangle area = sqrt(s(s - a)(s - b)(s - c))

For sides 3, 4, and 5, the semiperimeter is 6 and the area is 6 square units. The perimeter is 12 units. Use the dedicated triangle calculator when you also need angles, altitudes, inradius, or circumradius.

Internally, this page uses a numerically stable rearrangement of Heron's formula, described in William Kahan's triangle-area notes. It reduces roundoff problems for very thin triangles and avoids multiplying four large or tiny side-length factors before taking a square root. It cannot recover precision missing from the original measurements.

Circle and circular sector area

A circle's area equals pi times the radius squared. Circumference equals two times pi times the radius. A circular sector is a fraction of a complete circle, so its area and arc length are proportional to the central angle divided by 360 degrees.

circle area = pi x radius²
sector area = angle / 360 x pi x radius²
sector arc length = angle / 360 x 2 x pi x radius

A 90-degree sector is one quarter of a full circle. For angles below 360 degrees, the perimeter includes the curved arc plus two radii. Exactly 360 degrees forms a complete disk: its outer boundary is the circumference alone, with no radial cut edges. For radius 6 feet, the full-circle area is about 113.0973 square feet and the boundary is about 37.6991 feet, not 49.6991 feet. Cutting that disk along a radius would be a different boundary model.

Ellipse area

An ellipse uses two radii: the semi-major axis from the center to the farthest edge and the semi-minor axis from the center to the nearest edge. Multiply the two semi-axis lengths by pi.

ellipse area = pi x semi-major axis x semi-minor axis

The ellipse perimeter has no simple elementary formula. This calculator uses Ramanujan's widely used approximation for the supporting perimeter result, while the area calculation itself is direct.

Parallelogram and trapezoid area

A parallelogram has the same area as a rectangle with the same base and perpendicular height. A trapezoid's area is its height multiplied by the average of the two parallel base lengths.

parallelogram area = base x perpendicular height
trapezoid area = (base a + base b) x height / 2

The calculator does not report a trapezoid perimeter because the two nonparallel side lengths are not provided. Likewise, base and height do not uniquely determine the slanted side lengths of a parallelogram.

Convert square units correctly

Linear conversion factors must be squared for area. One foot is exactly 0.3048 meter, so one square foot is 0.3048² = 0.09290304 square meter. Multiplying square feet by only 0.3048 would be incorrect. This calculator converts the computed area to square inches, square feet, square yards, square millimeters, square centimeters, square meters, square kilometers, acres, and hectares through square meters.

One acre is exactly 43,560 square feet under the international-foot relationship used here, and one hectare is 10,000 square meters. Use the square feet to acres calculator when you need lot dimensions and one-acre comparisons.

Choosing measurements and rounding

Use measurements taken in the same linear unit. If one dimension is in feet and another is in inches, convert one before calculating. The selected input unit applies to every length field on this page. The result is converted to the chosen area unit after the geometric formula is applied. Keep more precision during intermediate calculations and round only the final value to the accuracy supported by the original measurements.

Keep each room section's original dimensions, units and addition or deduction separately from the final converted area. A 280-square-foot outline minus a 48-square-foot cutout gives 232 square feet, but those three numbers alone cannot show whether the cutout measurements or placement were correct. Verify the underlying outline and avoid overlapping sections or subtracting the same opening twice.

Formula and unit references

The rectangle, square, triangle, circle, and trapezoid formulas match the OpenStax geometric formulas reference. The SI unit of area is the square meter, as described by the National Institute of Standards and Technology. NIST conversion tables provide the relationships used for US customary and metric area units. Construction estimates should still include waste, openings, material coverage, and local project requirements; use the square footage calculator for material overage and cost planning.

For a measured walkthrough of L-shaped and other irregular rooms, including a worked square-footage example and ordering checks, read how to calculate square footage for an irregular room.

Frequently asked questions

Is area the same as square footage?

Square footage is area expressed specifically in square feet. Area can be expressed in any square unit.

Can I calculate an irregular room?

Split it into supported shapes that do not overlap, then use Add current shape to room total for each piece. For a cutout, leave the missing section out of the sum or subtract its area separately. Confirm that every dimension uses the same scale.

Why is triangle perimeter unavailable in base-height mode?

Many different triangles can share the same base and height. The other side lengths are required for a unique perimeter.

Does the calculator include material waste?

No. It calculates geometric area. Flooring, tile, roofing, paint, and concrete projects require product-specific coverage and waste allowances.