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 — rectangles, triangles, trapezoids, circles, semi-circles, sectors, ellipses, and parallelograms — all in one place.
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. For a dedicated tool focused specifically on this shape, try our Area of a Rectangle Calculator.
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. You can also use our standalone Triangle Area Calculator or explore side and angle relationships with the Right Triangle Calculator.
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. For more options specific to this shape, see our Trapezoid Area Calculator.
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. Our dedicated Circle Area Calculator offers additional detail for circular calculations.
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. If you need to find just the arc length, our Arc Length Calculator is a helpful companion tool.
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. You can also use our specialized Area of a Parallelogram Calculator.
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). If you're working with three-dimensional objects instead, you may want to explore our Surface Area Calculator or Volume Calculator.
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. For problems involving non-right triangles, the Law of Cosines Calculator and Law of Sines Calculator can help you find missing sides or angles first.
- 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. For dedicated perimeter calculations, check out our Perimeter Calculator.
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
If you're working with construction or landscaping projects, our Square Footage Calculator and Cubic Yard Calculator can help you convert area measurements into the material quantities you actually need.
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. If you need to find the straight-line distance between two points, our Distance Calculator can help.
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. Related construction tools like our Tile Calculator, Carpet Calculator, Drywall Calculator, and Sod Calculator use area as their starting point to estimate materials. For more complex geometry problems involving shapes like hexagons or octagons, explore our Hexagon Calculator and Octagon Calculator. Understanding these basic formulas gives you the tools to solve real problems quickly and accurately.