Area Calculator
An area calculator helps you find how much space is inside a two-dimensional shape or how much surface covers a three-dimensional object. Enter the measurements you know, choose the shape, and the calculator will apply the correct area formula automatically. You can calculate the area of a rectangle, square, circle, triangle, parallelogram, trapezoid, ellipse, rhombus, or circular sector, then convert the result into square feet, square inches, square yards, square metres, square centimetres, acres, or hectares.
Switch to Advanced Area & Surface Area when you need more than a basic geometry answer. The advanced mode includes a square foot calculator for rooms and rectangular spaces, feet-and-inches measurements, and surface area calculations for a cube, rectangular prism, sphere, cylinder, and cone. Results include the formula used, substituted values, converted units, and a clear final answer so you can check the calculation instead of only seeing a number.
Area Calculator
Calculate 2D area, square footage, and 3D surface area with unit conversions and formula breakdowns.
Calculate the area of common 2D shapes and convert the result into your preferred square unit.
Table of Contents
How to Use the Area Calculator
The calculator is divided into a simple mode and an advanced mode. Simple Area is the fastest choice when you already know the shape and its basic dimensions. Advanced Area & Surface Area adds a square feet calculator for measurements written in feet and inches, along with total surface area formulas for common three-dimensional shapes.
Simple Area
Choose Rectangle, Square, Circle, Triangle, Parallelogram, Trapezoid, Ellipse, Rhombus / Kite, or Circular Sector. The input fields change automatically so you only enter the measurements required by that shape. Select the measurement unit, choose the unit you want for the result, and click Calculate Area.
The answer includes the area formula, the measurements used, the substituted equation, and conversions to square metres, square feet, and square inches. This makes the tool useful both for quick area calculating and for checking a geometry problem step by step.
Advanced Area & Surface Area
Use the advanced mode when your measurements are in feet and inches or when the problem asks for surface area rather than ordinary 2D area. The room option converts feet and inches into decimal feet before multiplying length by width. The 3D options calculate the total exterior surface area of a cube, rectangular prism, sphere, cylinder, or cone.
If you need to perform a separate multiplication, division, or arithmetic check while working through an area formula, the simple math calculator can handle the basic arithmetic independently.
What Is Area?
Area measures the amount of two-dimensional space inside a boundary. A rectangle has an inside region enclosed by four sides, a circle has a region enclosed by its circumference, and a triangle has a region enclosed by three sides. Area describes the size of that region.
Because area is two-dimensional, the answer is written in square units. A rectangle measuring 10 feet by 8 feet has an area of 80 square feet, written as 80 ft². A square measuring 5 metres on each side has an area of 25 square metres, written as 25 m².
Area is different from perimeter. Perimeter measures the distance around the outside edge of a two-dimensional shape, while area measures the space inside it. It is also different from volume, which measures three-dimensional space. Surface area is related to area but adds together the areas of all exposed faces or curved surfaces of a three-dimensional object.
If your area problem uses percentages, such as adding a 10% waste allowance for flooring or tile, you can calculate the allowance separately with the percentage calculator.
Area Formulas
The correct area formula depends on the shape. Some formulas use length and width, some use a base and perpendicular height, and curved shapes often use π. The table below summarizes the formulas used by the calculator.
| Shape | Area Formula | Measurements Needed |
|---|---|---|
| Rectangle | A = L × W | Length and width |
| Square | A = s² | One side |
| Circle | A = πr² | Radius |
| Triangle | A = ½bh | Base and perpendicular height |
| Parallelogram | A = bh | Base and perpendicular height |
| Trapezoid | A = ½(b₁ + b₂)h | Two parallel bases and height |
| Ellipse | A = πab | Semi-major and semi-minor axes |
| Rhombus / Kite | A = ½d₁d₂ | Two diagonals |
| Circular Sector | A = (θ/360)πr² | Radius and central angle |
These formulas assume the measurements refer to the correct geometric dimensions. For example, the height in a triangle, trapezoid, or parallelogram is the perpendicular distance to the base. A slanted side is not automatically the height.
Rectangle Area Formula
The rectangle area formula is one of the most frequently used formulas in geometry:
If a rectangle is 14 feet long and 9 feet wide, multiply 14 by 9. The area is 126 square feet. The same formula works in any consistent unit. A rectangle that is 3 metres long and 2 metres wide has an area of 6 square metres.
When people search for the area of a rectangle, rectangle area formula, formula for area, how to find area, or how do you find the area of a rectangle, this multiplication is usually the calculation they need. The important part is keeping both linear measurements in the same unit before multiplying.
If one dimension is in feet and the other is in inches, convert first. The advanced room calculator does this automatically for feet-and-inches measurements. For other unit conversions, the online calculator is useful when you want to verify the arithmetic yourself.
How to Find the Area of a Square
A square has four equal sides, so its area formula is side × side, usually written as A = s². If the side length is 7 inches, the area is 7 × 7 = 49 square inches.
Because all sides are equal, only one measurement is required. Do not multiply the side by four; that would calculate the perimeter instead of the area. The square area formula squares the side length.
How to Find the Area of a Triangle
The area of a triangle is half the product of its base and perpendicular height:
For a triangle with a base of 12 centimetres and a perpendicular height of 8 centimetres, the calculation is ½ × 12 × 8 = 48 cm². This formula works because a triangle with the same base and height occupies half the area of a corresponding parallelogram.
The height must meet the base at a right angle. In some triangles the perpendicular height lies inside the triangle, while in others it may fall outside the visible side boundaries when the base line is extended.
Circle Area Calculator
The area of a circle is calculated from its radius using A = πr². The radius is the distance from the centre of the circle to its outer edge. If you are given the diameter instead, divide the diameter by 2 to get the radius.
For a circle with a radius of 5 feet, square the radius to get 25 and multiply by π. The area is approximately 78.54 square feet. If the diameter is 10 feet, the answer is the same because the radius is 5 feet.
The calculator uses the full mathematical value of π available in JavaScript rather than rounding π to 3.14 before the calculation. The displayed answer is then rounded to a practical number of decimal places.
Area of a Trapezoid
A trapezoid has one pair of parallel sides. To calculate its area, add the lengths of those two parallel bases, divide by 2, and multiply by the perpendicular height. The formula is A = ½(b₁ + b₂)h.
If the parallel sides are 10 metres and 6 metres and the height is 4 metres, the average base length is 8 metres. Multiply 8 by 4 to get an area of 32 m².
Area of a Parallelogram
The area of a parallelogram is base × perpendicular height. The slanted side does not replace the height unless it happens to be perpendicular to the selected base. If the base is 11 feet and the perpendicular height is 6 feet, the area is 66 ft².
You can visualize this formula by cutting a triangular section from one side of the parallelogram and moving it to the other side. The shape can be rearranged into a rectangle with the same base and height, so both shapes have the same area.
Area of an Ellipse
An ellipse uses the formula A = πab, where a and b are the semi-major and semi-minor axes. These are half of the full width and full height along the ellipse's principal axes.
If the full major axis is 12 metres and the full minor axis is 8 metres, the semi-axis values are 6 and 4. The area is π × 6 × 4, or approximately 75.40 m².
Area of a Rhombus or Kite
When the diagonals are known, the area of a rhombus or kite can be calculated using A = ½d₁d₂. A rhombus with diagonals of 10 inches and 8 inches has an area of 40 in².
This formula is useful when diagonal measurements are easier to obtain than a base and perpendicular height. As with every area calculation, both diagonal measurements should be expressed in the same unit before multiplying.
Area of a Circular Sector
A circular sector is a slice of a circle. Its area depends on the circle radius and the central angle. A 90-degree sector is one quarter of a full 360-degree circle, so its area is one quarter of πr².
The general formula is A = (θ ÷ 360) × πr² when the angle θ is measured in degrees. If the radius is 10 centimetres and the angle is 90 degrees, the sector area is approximately 78.54 cm².
Square Foot Calculator
Square footage is area measured in square feet. For a rectangular room, floor, wall, yard section, or other rectangular surface, multiply length in feet by width in feet. A 12-foot by 10-foot room has 120 square feet of floor area.
The advanced square foot calculator is designed for real measurements that include both feet and inches. If a room is 12 ft 6 in long and 10 ft 3 in wide, the calculator converts each measurement into decimal feet before multiplying.
Twelve feet six inches equals 12.5 feet. Ten feet three inches equals 10.25 feet. Multiplying 12.5 × 10.25 gives 128.125 square feet. This avoids the common mistake of treating 6 inches as 0.6 feet or 3 inches as 0.3 feet.
Feet and Inches Calculator for Area
There are 12 inches in one foot, so an inch measurement is converted to feet by dividing by 12. Six inches is 0.5 foot, three inches is 0.25 foot, and nine inches is 0.75 foot. Add the decimal portion to the whole-foot measurement before calculating the area.
If both measurements are entirely in inches, you can also calculate the area in square inches and then convert to square feet. There are 144 square inches in one square foot because 12 inches × 12 inches = 144 square inches.
How to Convert Inches to Square Feet
Linear inches cannot be converted directly to square feet without another dimension because inches measure length and square feet measure area. If you have an area already measured in square inches, divide by 144 to convert square inches to square feet.
For example, 1,440 square inches ÷ 144 = 10 square feet. If you instead have a rectangle measuring 40 inches by 36 inches, first multiply to get 1,440 square inches, then divide by 144 to get 10 ft².
Square Feet, Square Yards, Acres, and Square Metres
The calculator can return 2D area in several common units. This is useful because the same physical area may be described differently depending on the project. Flooring is commonly discussed in square feet or square metres, fabric and carpeting may use square yards, and land may be measured in acres or hectares.
| Conversion | Equivalent |
|---|---|
| 1 square foot | 144 square inches |
| 1 square yard | 9 square feet |
| 1 square metre | approximately 10.7639 square feet |
| 1 acre | 43,560 square feet |
| 1 hectare | 10,000 square metres |
| 1 hectare | approximately 2.47105 acres |
For land, an acre calculator is often just an area conversion once the land area has been established. If a rectangular parcel measures 330 feet by 264 feet, its area is 87,120 ft². Divide by 43,560 and the result is 2 acres.
What Is Surface Area?
Surface area measures the total area covering the outside of a three-dimensional object. Imagine unfolding the exterior of a cardboard box into flat pieces. The area of all those pieces added together is the box's total surface area.
Surface area is expressed in square units just like ordinary area because it measures two-dimensional surfaces, even though those surfaces belong to a three-dimensional object. Volume, by contrast, measures the space inside the object and is expressed in cubic units.
The advanced surface area calculator includes a cube, rectangular prism, sphere, cylinder, and cone. These formulas are useful in geometry as well as practical estimating problems involving wrapping, coating, painting, manufacturing, containers, and exterior materials.
Surface Area Formulas
| 3D Shape | Total Surface Area Formula |
|---|---|
| Cube | SA = 6s² |
| Rectangular Prism | SA = 2(lw + lh + wh) |
| Sphere | SA = 4πr² |
| Cylinder | SA = 2πr² + 2πrh |
| Cone | SA = πr² + πrl |
For a cone, l represents the slant height. When only the radius r and perpendicular height h are known, the calculator finds slant height using l = √(r² + h²). If you want to independently check square roots, powers, or π-based calculations, the scientific calculator can help.
Surface Area of a Cube
A cube has six identical square faces. If each side has length s, one face has area s². Since there are six faces, the total surface area is 6s².
A cube with 4-inch sides has a surface area of 6 × 4² = 6 × 16 = 96 square inches. This includes all six outside faces.
Surface Area of a Rectangular Prism
A rectangular prism has three pairs of matching rectangular faces. One pair has area length × width, one pair has area length × height, and one pair has area width × height. Doubling the sum gives the total surface area:
For a box measuring 8 inches long, 5 inches wide, and 3 inches high, the calculation is 2[(8×5) + (8×3) + (5×3)] = 2(40 + 24 + 15) = 158 in².
Surface Area of a Sphere
The surface area of a sphere uses the formula SA = 4πr². Only the radius is required. If you know the diameter, divide it by 2 before entering the radius.
For a sphere with a radius of 3 metres, the surface area is 4 × π × 3² = 36π, or approximately 113.10 m². A sphere's surface area is exactly four times the area of a circle with the same radius.
This distinction matters when a question asks for surface area of a sphere rather than the area of a circle. A circle is two-dimensional and uses πr². A sphere is three-dimensional and uses 4πr².
Surface Area of a Cylinder
The total surface area of a closed cylinder includes two circular ends and the curved side. The two circles contribute 2πr². The curved side can be imagined unrolled into a rectangle with width equal to the circle's circumference, 2πr, and height h, producing an area of 2πrh.
If a cylinder has a radius of 2 feet and a height of 5 feet, the total surface area is 2π(2)(2 + 5) = 28π, or approximately 87.96 ft².
Surface Area of a Cone
The total surface area of a cone includes its circular base and its curved lateral surface. The formula is SA = πr² + πrl, where r is radius and l is slant height.
If only the perpendicular height is known, the slant height can be calculated using the Pythagorean relationship l = √(r² + h²). The calculator does this automatically before calculating the final surface area.
Area Unit Conversions
Area conversions must account for the fact that both dimensions are being converted. This is why converting feet to inches uses a factor of 12, while converting square feet to square inches uses 144.
For example, a square measuring 1 foot by 1 foot is 12 inches by 12 inches. Its area is therefore 144 square inches. A 2-foot by 2-foot square has an area of 4 ft², which equals 576 in².
The same principle applies to metric conversions. One metre equals 100 centimetres, but one square metre equals 10,000 square centimetres because 100 × 100 = 10,000.
When converting an already-calculated area, use an area conversion factor rather than a linear conversion factor. This is one of the most common mistakes when moving between square feet, square inches, square metres, and similar units.
Area Calculator Examples
Example 1: Area of a Rectangle
A rectangle is 18 feet long and 11 feet wide. Use A = L × W. The area is 18 × 11 = 198 ft².
Example 2: Area of a Circle
A circle has a radius of 7 centimetres. Use A = πr². The area is π × 7² = 49π, or approximately 153.94 cm².
Example 3: Square Feet from Feet and Inches
A room measures 14 ft 6 in by 11 ft 9 in. Convert 6 inches to 0.5 foot and 9 inches to 0.75 foot. The decimal dimensions are 14.5 ft and 11.75 ft. Multiply them to get 170.375 ft².
Example 4: Surface Area of a Sphere
A sphere has a radius of 6 inches. Use SA = 4πr². The surface area is 4 × π × 36 = 144π, or approximately 452.39 in².
Example 5: Surface Area of a Cylinder
A cylinder has a radius of 4 centimetres and a height of 10 centimetres. Use SA = 2πr(r + h). The calculation is 2π × 4 × 14 = 112π, or approximately 351.86 cm².
How to Calculate Area for Irregular Spaces
An irregular floor, yard, patio, wall, or lot can often be divided into simpler shapes. Break the space into rectangles, triangles, circles, or other shapes that you can measure separately. Calculate each area and add the pieces together.
For example, an L-shaped room can usually be split into two rectangles. If one rectangle is 10 ft × 8 ft and another is 6 ft × 4 ft, their areas are 80 ft² and 24 ft². Add them to get 104 ft².
If the irregular shape includes a missing section, calculate the area of the larger enclosing shape and subtract the missing area. The exact approach depends on the geometry, but the general strategy is to turn one difficult shape into several simple calculations.
Using Area for Flooring, Tile, Paint, and Materials
Area is commonly used to estimate material quantities, but the mathematical area is only the starting point. Flooring, tile, roofing, wallpaper, and similar projects often need extra material for cuts, breakage, pattern matching, damaged pieces, or future repairs.
If a floor measures 500 ft² and you plan a 10% waste allowance, the extra amount is 50 ft², giving a purchase target of 550 ft². The appropriate allowance varies by material, layout, installation method, and project complexity, so use the recommendations for the specific product and project rather than assuming one percentage is universal.
Paint estimates may also require more than wall area. Doors, windows, multiple coats, surface texture, and paint coverage can change the actual quantity needed. For construction or purchasing decisions, use the calculator as a measurement tool rather than a replacement for project specifications.
Area vs. Surface Area vs. Volume
Area, surface area, and volume answer different questions. Area measures a flat region. Surface area measures all of the outside surfaces of a 3D object. Volume measures the space contained inside a 3D object.
| Measurement | What It Measures | Typical Units |
|---|---|---|
| Area | Space inside a 2D boundary | ft², m², in² |
| Surface Area | Total outside covering of a 3D object | ft², m², cm² |
| Volume | Space inside a 3D object | ft³, m³, cm³ |
A sphere therefore has surface area but no ordinary 2D area unless you are referring to a cross-section. A circle has area but not volume. A cylinder has both surface area and volume because it is a three-dimensional object.
Common Area Calculation Mistakes
One common mistake is mixing measurement units. Multiplying 10 feet by 24 inches directly does not produce a meaningful square-foot result until one dimension is converted. Convert both measurements to feet or both to inches first.
Another mistake is confusing diameter and radius in a circle. The radius is half the diameter. If a circle has a diameter of 10, its radius is 5. Using 10 as the radius would make the calculated area four times too large.
For triangles and parallelograms, using a slanted side in place of the perpendicular height can also produce the wrong answer. The height in these formulas is measured at a right angle to the base.
Surface-area problems have their own common error: forgetting one or more surfaces. A closed cylinder has two circular ends plus a curved side. A cube has six faces. Always check whether the problem asks for total surface area or only part of the surface.
Why Use an Online Area Calculator?
An online area calculator is useful when you want a fast answer without memorizing every formula or manually converting square units. It is also helpful as a checking tool after you solve the problem yourself.
- Calculate the area of common 2D shapes.
- Use the rectangle area formula without doing the multiplication manually.
- Find square feet from feet-and-inches room measurements.
- Convert square feet to square metres, square inches, acres, and other area units.
- Calculate the surface area of a sphere, cylinder, cube, cone, or rectangular prism.
- See the formula and substituted values used for the result.
- Check schoolwork, measurements, and planning calculations.
If you are working on school math and want to track your scores as well as your geometry calculations, the grade calculator can calculate test grades, weighted grades, final exam requirements, and GPA.
Area Calculator Frequently Asked Questions
How do you find area?
First identify the shape, then use the area formula for that shape. A rectangle uses length × width, a square uses side², a triangle uses ½ × base × height, and a circle uses πr². Enter the same measurements in the calculator above to check the result.
What is the formula for area?
There is no single area formula for every shape. The formula depends on the geometry. For a rectangle, A = L × W. For a square, A = s². For a circle, A = πr². For a triangle, A = ½bh.
What is the rectangle area formula?
The area of a rectangle is length multiplied by width: A = L × W. If a rectangle is 12 feet long and 8 feet wide, the area is 96 square feet.
How do you find the area of a square?
Multiply the side length by itself. The formula is A = s². A square with a 6-foot side has an area of 36 ft².
How do you calculate the area of a circle?
Use A = πr², where r is the radius. Square the radius and multiply by π. If you only know the diameter, divide it by 2 to get the radius first.
How does a square foot calculator work?
For a rectangular space, convert both dimensions to feet and multiply length by width. The advanced mode on this page accepts separate feet and inches, converts them to decimal feet, and returns the area in square feet.
How many square inches are in a square foot?
There are 144 square inches in 1 square foot because 1 foot equals 12 inches and 12 × 12 = 144.
How do you convert square inches to square feet?
Divide the number of square inches by 144. For example, 720 in² ÷ 144 = 5 ft².
Can you convert inches directly to square feet?
Not from one linear measurement alone. Inches measure length while square feet measure area. You need two dimensions, or you need an area already expressed in square inches. Once you have square inches, divide by 144 to get square feet.
How many square feet are in an acre?
One acre contains 43,560 square feet. To convert square feet to acres, divide the square-foot area by 43,560.
What is surface area?
Surface area is the total area covering the outside of a three-dimensional object. It is measured in square units such as square feet, square inches, or square metres.
What is total surface area?
Total surface area includes every exterior surface of the object. For a closed cylinder, that means both circular ends and the curved side. For a cube, it includes all six square faces.
What is the surface area of a sphere formula?
The total surface area of a sphere is SA = 4πr², where r is the sphere's radius.
How do you find the surface area of a cylinder?
For a closed cylinder, use SA = 2πr² + 2πrh, which can also be written as 2πr(r + h). The formula includes two circular bases and the curved lateral surface.
What is the difference between area and surface area?
Area usually describes the space inside a two-dimensional shape. Surface area describes the combined area of the outside surfaces of a three-dimensional object. Both are measured in square units.
What is the difference between surface area and volume?
Surface area measures the outside covering of a three-dimensional object and uses square units. Volume measures the space inside the object and uses cubic units.
How do you find the area of an irregular shape?
Divide the irregular shape into simpler shapes such as rectangles and triangles. Calculate each area separately, then add the areas together. If a section is missing, you can sometimes calculate a larger enclosing shape and subtract the missing area.
Do I need to add extra area for flooring or tile?
The mathematical area gives the measured surface, but real projects can require extra material for cuts, waste, breakage, or pattern matching. Use the product or installer's recommended allowance for the specific project.
Why are area units squared?
Area uses two dimensions. A square foot represents a region 1 foot long by 1 foot wide. Because the linear unit is multiplied by itself, the unit is written as ft². The same idea applies to m², in², cm², and other square units.
Can this calculator find acreage?
Yes. In Simple Area mode, calculate the area of the shape and choose Acres as the result unit. For rectangular land, enter the length and width in a supported unit and the calculator will convert the area to acres.
Final Thoughts
Area calculations become much easier once you identify the shape and the measurements that belong in its formula. A rectangle uses length and width, a square uses one side, a circle uses radius, and shapes such as triangles and trapezoids require a perpendicular height. The calculator handles the formula and unit conversion while still showing the math used for the answer.
For rooms, flooring, walls, and other rectangular spaces, use the square foot calculator in Advanced Area & Surface Area mode when your measurements contain both feet and inches. For three-dimensional geometry, use the surface area section to calculate a cube, rectangular prism, sphere, cylinder, or cone.
For related calculations involving fractions, the fraction calculator can help with fraction arithmetic and simplification while you work through measurements or geometry problems.
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