Area Calculator
Choose a shape, tell us what to solve for, enter your numbers, and see the full math.
Enter all dimensions using the same unit. Area results are shown in square units.
Your Area
Calculate the area and perimeter of rectangles, squares, triangles, circles, trapezoids, parallelograms, ellipses, sectors, rhombuses, and more. See the formula, your numbers substituted into it, unit conversions, diagrams, and step-by-step math.
Choose a shape, tell us what to solve for, enter your numbers, and see the full math.
Enter all dimensions using the same unit. Area results are shown in square units.
Area measures how much two-dimensional space is inside a flat shape. Imagine a rectangle drawn on a sheet of paper. Its boundary tells you where the shape begins and ends. Area answers a simple question: how much flat space is inside that boundary?
If a rectangle is 5 units long and 4 units wide, its area is 5 × 4 = 20 square units. You can imagine covering the rectangle with 20 little 1 × 1 squares. Each square represents one square unit. That is why area uses square units. Examples include cm², m², in², and ft². The ² means two dimensions are being multiplied.
Area appears in geometry, construction, flooring, painting, land measurement, gardening, fabric, home improvement, engineering, and many other everyday situations.
Area and perimeter describe different things. Area measures the space inside the shape. Perimeter measures the distance around the outside edge.
Suppose a rectangle is 10 feet long and 6 feet wide. Area: 10 × 6 = 60 ft². Perimeter: 10 + 6 + 10 + 6 = 32 ft. Notice the units: area is in square feet, perimeter is in feet. A flooring project may care about area. A fence around that same space may care about perimeter. The shape is the same. The question being asked is different.
Rectangle area is A = lw, length times width. Example: length 10 cm, width 6 cm. Substitute: A = 10 × 6. Calculate: A = 60. Final answer: 60 cm².
This formula works because the rectangle can be divided into rows and columns of equal unit squares. Ten squares across and six rows creates 10 × 6 = 60 squares.
A square is a special rectangle where all four sides are equal. If side length is s, then A = s². Example: side 8 meters. Area: 8² = 8 × 8 = 64 m². Perimeter: 4 × 8 = 32 m.
Triangle area is A = ½bh, where b = base and h = perpendicular height. Suppose base 10 cm, height 6 cm. A = ½ × 10 × 6. 10 × 6 = 60. Half: 30 cm².
Why one-half? Imagine making an identical copy of the triangle and fitting the two together. Together they can form a parallelogram or rectangle-like region with area base × height. One triangle occupies half. The important word is perpendicular. The height must meet the base at 90 degrees. A slanted side is not automatically the height.
You can use Heron's Formula. Suppose the side lengths are a, b, c. First find the semiperimeter: s = (a+b+c)/2. Then A = √[s(s-a)(s-b)(s-c)].
Example: sides 3, 4, 5. Semiperimeter: (3+4+5)/2 = 6. Area: √[6(6-3)(6-4)(6-5)] = √(6 × 3 × 2 × 1) = √36 = 6 square units. This agrees with the familiar 3-4-5 right triangle.
If you need a more complete triangle solution including missing angles or sides, use the Triangle Calculator.
Circle area is A = πr², where r is radius. Suppose radius 5 cm. Square the radius: 5² = 25. Then A = 25π. Using π: A ≈ 78.54 cm². The formula uses radius, not diameter. If diameter is 10, radius is 5.
Area describes a two-dimensional region. As radius grows, the circle expands both horizontally and vertically. That is why radius is squared. If radius doubles, r → 2r. Area: π(2r)² = 4πr². Therefore: double the radius, four times the area.
Circumference is the distance around a circle. Formula: C = 2πr. Area: πr². Circumference: 2πr. Do not confuse the two. If radius is 5: circumference 10π ≈ 31.42; area 25π ≈ 78.54. Circumference uses linear units. Area uses square units.
A sector is a portion of a circle, think of a slice of pizza. If the central angle is 90°, the sector contains 90/360 = 1/4 of the full circle. Formula: A = θ/360 × πr². Example: radius 8, angle 90°. Full circle area: π × 8² = 64π. Sector: 1/4 × 64π = 16π ≈ 50.27 square units.
A trapezoid has two parallel sides, call them a and b, with perpendicular height h. Formula: A = ½(a+b)h, also written A = [(a+b)/2] × h. That means find the average length of the two parallel sides and multiply by height.
Example: a = 10, b = 6, h = 4. Average parallel-side length: (10+6)/2 = 8. Then: 8 × 4 = 32 square units.
A parallelogram uses A = bh, base times perpendicular height. It may look like a slanted rectangle, but the slanted side is NOT automatically height. Imagine cutting the triangular section from one end and moving it to the other. The parallelogram becomes a rectangle with the same base, height, and area. That is why A = bh.
An ellipse looks like a stretched or compressed circle. Formula: A = πab, where a and b are the semi-axis lengths. If the full width is 10 and the full height is 6, then a = 5, b = 3. Area: π × 5 × 3 = 15π ≈ 47.12 square units. Be careful: full width and full height are NOT the same as a and b, they are twice the semi-axis measurements.
If the diagonals are known: A = ½d₁d₂. Example: diagonal 1 = 10, diagonal 2 = 8. Area: ½ × 10 × 8 = 40 square units.
A regular polygon has equal side lengths and equal angles. For n sides with side length s, one formula is A = ns² / [4 tan(π/n)]. This works by dividing the polygon into n congruent triangles meeting at the center. That same idea introduces the apothem, the perpendicular distance from the center to a side.
Sometimes you already know the area. Example: rectangle area 60 cm², width 6 cm, length unknown. Formula: A = lw. Substitute: 60 = l × 6. Divide: 60 ÷ 6 = 10. Length: 10 cm.
Notice: area uses cm², the missing length uses cm. The same idea works for triangle height, circle radius, parallelogram base, trapezoid height, and other dimensions. That is why this calculator includes a Missing Dimension mode.
Suppose a square measures 1 meter by 1 meter. Area: 1 m². Convert each side into centimeters: 1 meter = 100 centimeters. The same square measures 100 cm × 100 cm. Area: 100 × 100 = 10,000 cm². Therefore 1 m² = 10,000 cm². You cannot convert area units by applying the length conversion only once. This is one of the most common unit-conversion mistakes.
The same logic applies everywhere: 1 foot = 12 inches, but 1 square foot = 12 × 12 = 144 square inches.
Room floor area determines how much tile, carpet, wood, or laminate may be needed. If the main goal is measuring rooms or floors specifically in square feet, use the Square Footage Calculator.
Wall area helps estimate the surface to cover. Actual paint requirements also depend on coverage rates, number of coats, doors, windows, and surface conditions.
Property size may be measured in square feet, square meters, acres, hectares, or square miles.
Roof surfaces use area calculations, although slope and roofing-material requirements may require additional measurements.
Garden beds may require area calculations for soil, mulch, seed, or ground cover.
Area can help estimate material needed for flat surfaces.
Area appears throughout walls, floors, ceilings, panels, foundations, and layouts.
Area is two-dimensional. If the question asks how much space is inside a box, how much concrete fills a shape, how much a tank holds, or how much three-dimensional space a solid occupies, you need volume. Use the Volume Calculator. Area: square units. Volume: cubic units.
If you already know 250 ft² and only want to convert it into m², yd², or another measurement, use the Unit Converter. The Area Calculator above also shows several convenient conversions after calculating a shape.
A triangle does not use length × width the same way a rectangle does.
Triangle height must be perpendicular to the selected base.
Circle area uses r². If given diameter, divide by 2.
Circle area is πr², not πr.
Area measures inside. Perimeter measures around.
An answer of 60 feet is not the same as 60 square feet.
1 m² is not 100 cm². It is 10,000 cm².
Keep enough precision until the final result.
Rectangle? Triangle? Circle? Trapezoid? Another shape?
Determine what length, width, radius, base, height, angle, or sides are available.
Do this before multiplying numbers.
Put the actual measurements into the correct formula.
Follow the order of operations.
Area should end with cm², m², in², ft², or another appropriate square unit.
Helping With Math also breaks calculating area down by shape, walking through the same formula-substitute-calculate approach for rectangles, triangles, circles, and more. Their step-by-step area guide provides another useful educational explanation of this process.
Do not leave knowing only "my area is 60." Leave knowing: I understand what Area measures. I know why Area uses square units. I understand the difference between Area and Perimeter. I know how Rectangle and Square Area work. I understand why Triangle Area uses one-half. I know the Triangle Height must be perpendicular. I know how Heron's Formula can calculate Triangle Area from three sides. I understand Circle Area and Radius. I know the difference between Radius and Diameter. I understand how a Circular Sector represents part of a circle. I know how Trapezoid Area uses the average of the parallel sides. I understand why a Parallelogram uses perpendicular height. I know how Ellipse Area works. I understand how Regular Polygons can be broken into triangles. I know how to work backward to find a missing dimension. I understand why area conversions must square the conversion factor. I know when I need the Area Calculator instead of the Volume Calculator. And most importantly: I can see how the calculator arrived at my answer.
That is what the CalculateThisWay Area Calculator should help someone understand.
| Shape | Area Formula |
|---|---|
| Rectangle | A = lw |
| Square | A = s² |
| Triangle | A = ½bh |
| Triangle - 3 Sides | A = √[s(s-a)(s-b)(s-c)] |
| Circle | A = πr² |
| Semicircle | A = ½πr² |
| Sector - Degrees | A = θ/360 × πr² |
| Ellipse | A = πab |
| Trapezoid | A = ½(a+b)h |
| Parallelogram | A = bh |
| Rhombus / Kite | A = ½d₁d₂ |
| Regular Polygon | A = ns²/[4tan(π/n)] |
What is area?
Area measures the two-dimensional space inside a flat shape.
Why does area use square units?
Because area combines two dimensions.
What is the difference between area and perimeter?
Area measures the inside. Perimeter measures the boundary.
How do I calculate rectangle area?
Multiply length × width.
How do I calculate square area?
Square the side length.
How do I calculate triangle area?
Use one-half × base × perpendicular height.
Can any triangle side be the base?
Yes, but the height must be measured perpendicular to that chosen base.
How do I find triangle area without height?
If all three sides are known, Heron's Formula can be used.
How do I calculate circle area?
Use πr².
Is diameter the same as radius?
No. Diameter equals twice the radius.
How do I find radius from diameter?
Divide diameter by 2.
What is circumference?
The distance around a circle.
Is circumference the same as area?
No. Circumference is a length; area measures the region inside the circle.
How do I calculate a semicircle?
Use half the full-circle area.
Does semicircle perimeter include the diameter?
The full perimeter does. The curved arc alone does not.
How do I calculate sector area?
Multiply the full-circle area by the fraction of the circle represented by the central angle.
How do I calculate trapezoid area?
Average the two parallel sides and multiply by perpendicular height.
How do I calculate parallelogram area?
Base × perpendicular height.
Can I use the slanted side as parallelogram height?
Not unless it is actually perpendicular to the base.
How do I calculate ellipse area?
Multiply π by the two semi-axis lengths.
How do I calculate rhombus area from diagonals?
Use one-half × diagonal 1 × diagonal 2.
Can this calculate a missing dimension?
Yes, where enough information is available.
How do I find rectangle length from area?
Divide Area by Width.
How do I find circle radius from area?
Use √(A/π).
What is one square foot in square inches?
144 in².
How many square centimeters are in one square meter?
10,000 cm².
Is square footage the same as area?
Square footage is area expressed specifically in square feet.
What if I need cubic space?
Use the Volume Calculator.
Should I round π first?
No. Keep full precision and round the final result.
I need the two-dimensional space inside a shape.
You are hereI need missing triangle sides, angles, area, or a complete triangle solution.
Open Triangle Calculator →I need room, wall, floor, or property area specifically in square feet.
Open Square Footage Calculator →I already know an area or measurement and only need to convert units.
Open Unit Converter →I need a missing side of a right triangle.
Open Pythagorean Theorem Calculator →Every shape is validated before it is calculated: side lengths and angles must be positive and finite, three-side triangles must satisfy the triangle inequality, sector angles must fall between 0° and 360° (or 0 and 2π radians), and polygon side counts must be whole numbers of 3 or more. Perimeter is only calculated when enough independent information is known; this calculator never guesses a missing side length. The ellipse perimeter uses Ramanujan's well-known approximation and is always labeled as an approximation, since no simple exact elementary formula exists.