Math calculators

Area Calculator

Updated Sep 1, 2026 By Infinity Calculator
Rate Formulas
Rectangle
l (length) w (width)
Enter a positive number
Enter a positive number
Area
50.00 sq ft
Perimeter
30.00 ft
Common Conversions
Triangle
a b c h
Enter a positive number
Enter a positive number
Enter a positive number
These sides cannot form a valid triangle
Area
14.70 sq ft
Perimeter
18.00 ft
Common Conversions
Trapezoid
b₁ b₂ h
Enter a positive number
Enter a positive number
Enter a positive number
Area
50.00 sq ft
Perimeter (bases + sides est.)
—
Common Conversions
Circle
r
Enter a positive number
Area
78.54 sq ft
Circumference
31.42 ft
Common Conversions
Semi-circle
r
Enter a positive number
Area
39.27 sq ft
Perimeter
25.71 ft
Common Conversions
Sector
r θ
Enter a positive number
Enter a positive angle
Area
19.63 sq ft
Arc Length + Radii
17.85 ft
Common Conversions
Ellipse
a b
Enter a positive number
Enter a positive number
Area
75.40 sq ft
Circumference (approx)
31.73 ft
Common Conversions
Parallelogram
b (base) h
Enter a positive number
Enter a positive number
Area
60.00 sq ft
Perimeter (2 × (b + side))
—
Common Conversions
Area Comparison Across Shapes
Interactive Map Area Calculator

Click on the map to place points and draw a polygon. The area and perimeter are calculated in real-time using the Haversine formula. Double-click to close the polygon. Use the buttons below to manage your polygon.

Loading map...
Requires Leaflet CDN. If unavailable, a canvas fallback will render.
Area
0.00 sq m
Perimeter
0.00 m
Points
0
Common Conversions

Introduction

Area is the amount of space inside a flat shape. Whether you need to measure a room, plan a garden, or solve a homework problem, knowing how to calculate area is an important skill. This free area calculator lets you find the area of eight common shapes, all in one place: rectangles, triangles, trapezoids, circles, semi-circles, sectors, ellipses, and parallelograms.

Just enter your measurements, pick your units, and click "Calculate." The tool gives you the area, perimeter, and instant unit conversions so you can switch between square feet, square meters, acres, hectares, and more. You can also compare the areas of all eight shapes side by side using the built-in bar chart. If you need to measure an irregular area on a real map, switch to the Map Area Calculator tab, click points to draw a polygon, and get the area and perimeter calculated automatically using real-world coordinates.

How to Use Our Area Calculator

Enter the measurements for any shape below, and the calculator will give you the area, perimeter, and common unit conversions. You can also switch to the Map Area Calculator tab to draw a shape on a real map and find its area.

Rectangle: Enter the length and width of your rectangle. Pick the unit for each side (such as feet, meters, or inches) and choose your desired output unit. The calculator will return the area and perimeter.

Triangle: Choose one of two methods. With Heron's method, enter all three side lengths (a, b, and c). With Base × Height, enter the base and the height. Select your units for each value and the output unit to get the area and perimeter.

Trapezoid: Enter the two parallel bases (b₁ and b₂) and the height between them. Choose the unit for each measurement and your output unit. The calculator will return the area.

Circle: Enter the radius of the circle and select its unit. Choose your output unit, and the calculator will give you the area and circumference.

Semi-circle: Enter the radius and select its unit. Pick your output unit to get the area and perimeter of the half-circle.

Sector: Enter the radius and the angle of the sector. The angle can be in degrees or radians. Select your output unit to get the area and the total length of the arc plus the two straight sides.

Ellipse: Enter the semi-major axis (a) and the semi-minor axis (b), which are the longer and shorter distances from the center to the edge. Choose your units and the output unit to get the area and an approximate circumference.

Parallelogram: Enter the base and the height (the straight-line distance between the top and bottom sides). Select your units and output unit to get the area.

Output Unit: For every shape, use the output unit dropdown to see your results in square feet, square meters, acres, hectares, or other common area units. A conversions table is also shown with each result.

Map Area Calculator: Switch to the Map Area Calculator tab, then click on the map to place points and draw a polygon over any land area. Double-click or press "Close Polygon" to finish your shape. The calculator uses the Haversine formula to find the real-world area and perimeter. Use the area display unit dropdown to change between square meters, acres, hectares, and more.

What Is Area?

Area is the amount of space inside a flat (two-dimensional) shape. Think of it as how much paint you would need to cover a surface, or how much carpet you would need to cover a floor. Area is always measured in square units, such as square feet (sq ft), square meters (sq m), or square inches (sq in).

Area Formulas for Common Shapes

Every shape has its own formula for calculating area. Here are the most common ones:

  • Rectangle: Area = length × width. A rectangle with a length of 10 ft and a width of 5 ft has an area of 50 sq ft.
  • Triangle: Area = ½ × base × height. You can also use Heron's formula if you know all three side lengths. Heron's formula uses the semi-perimeter (half the perimeter) to find the area without needing the height.
  • Trapezoid: Area = ½ × (base₁ + base₂) × height. A trapezoid has two parallel sides of different lengths, and you average them before multiplying by the height.
  • Circle: Area = π × r², where r is the radius. Pi (π) is approximately 3.14159.
  • Semi-circle: Area = ½ × π × r². It is exactly half the area of a full circle.
  • Sector: Area = ½ × r² × θ, where θ is the angle in radians. A sector is a "slice" of a circle, like a piece of pie.
  • Ellipse: Area = π × a × b, where a is the semi-major axis (the longer radius) and b is the semi-minor axis (the shorter radius).
  • Parallelogram: Area = base × height. The height must be measured straight up from the base, not along the slanted side.

Understanding Perimeter vs. Area

Perimeter and area measure two different things. Perimeter is the total distance around the outside edge of a shape, measured in regular units like feet or meters. Area is the space enclosed inside the shape, measured in square units. Two shapes can have the same perimeter but very different areas, and vice versa.

Converting Between Area Units

Because area uses square units, conversions are not the same as simple length conversions. For example, 1 foot = 12 inches, but 1 square foot = 144 square inches (12 × 12). Here are some helpful area conversions:

  • 1 sq ft = 144 sq in
  • 1 sq yd = 9 sq ft
  • 1 acre = 43,560 sq ft
  • 1 sq m ≈ 10.764 sq ft
  • 1 hectare = 10,000 sq m
  • 1 sq mi = 640 acres

Measuring Area on a Map

You can also measure the area of real-world land by plotting points on a map. This method uses GPS coordinates and the Haversine formula, which accounts for the curvature of the Earth, to calculate distances between points. By connecting those points into a polygon, you can find the area of a plot of land, a park, a property, or any region on Earth's surface. This is useful for real estate, farming, landscaping, and construction projects.

Practical Uses of Area Calculations

Knowing how to calculate area helps with many everyday tasks. You need area to figure out how much flooring to buy for a room, how much fertilizer to spread on a lawn, how much fabric to cut for a project, or how much paint to purchase for a wall. Builders, farmers, architects, and engineers all rely on area calculations daily. Understanding these basic formulas gives you the tools to solve real problems quickly and accurately.

Formulas used

Rectangle Area
A = l \times w
Triangle Area (Heron's Formula)
A = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \frac{a+b+c}{2}
Triangle Area (Base × Height)
A = \frac{1}{2} b \times h
Trapezoid Area
A = \frac{1}{2}(b_1 + b_2) \times h
Circle Area
A = \pi r^2
Sector Area
A = \frac{1}{2} r^2 \theta
Ellipse Area
A = \pi a b
Parallelogram Area
A = b \times h

Frequently asked questions

What is the difference between area and square footage?

There is no real difference. Square footage is just area measured in square feet. Area can be measured in any square unit like square meters, square inches, or acres. Square footage is the term people use most often in the United States when talking about rooms, homes, or land.

Can I use different units for each measurement?

Yes. Each input field has its own unit dropdown. You can enter the length in feet and the width in meters, for example. The calculator converts everything to a common unit before doing the math, so your answer will be correct no matter which units you mix.

How do I find the area of an irregular shape?

Use the Map Area Calculator tab. Click on the map to place points around your shape, then close the polygon. The tool calculates the area automatically. For shapes that are not on a map, you can break them into smaller regular shapes (like rectangles and triangles), find each area, and add them together.

What is Heron's formula and when should I use it?

Heron's formula finds the area of a triangle when you know all three side lengths but not the height. It uses the semi-perimeter (half the perimeter) in the calculation: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2. Use it when measuring the height of a triangle is hard or impossible.

Why does the trapezoid not show a perimeter?

The trapezoid section only asks for the two bases and the height. To find the perimeter, you also need the lengths of the two slanted sides. Since the calculator does not have those values, it shows a dash instead of a perimeter.

How do I convert acres to square feet?

One acre equals 43,560 square feet. Multiply the number of acres by 43,560 to get square feet. You can also just change the output unit dropdown in the calculator, and it will convert for you automatically.

What is the semi-major and semi-minor axis of an ellipse?

An ellipse is like a stretched circle. The semi-major axis (a) is the longer distance from the center to the edge. The semi-minor axis (b) is the shorter distance from the center to the edge. If both are equal, the ellipse becomes a circle.

Why is the height of a parallelogram not the same as the side length?

The height of a parallelogram is the straight-up distance between the top and bottom sides, measured at a right angle. The slanted side is usually longer than the height. If you use the side length instead of the true height, your area answer will be wrong.

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