面积计算器
计算矩形、圆形、三角形等各种形状的面积，支持多种单位换算。
What is an Area Calculator?
An Area Calculator is a geometry tool that measures the area of a shape, which is the amount of flat space inside its boundaries. Area is used in many real-world tasks—like estimating how much paint you need for a wall, how much flooring or carpet to buy, how large a garden bed is, or how much material is required to cover a surface.
Different shapes have different area formulas. For example, rectangles use length × width, triangles use (base × height) ÷ 2, and circles use πr². An area calculator lets you choose the shape, enter the required dimensions, and instantly compute the area—without worrying about formula mistakes.
Area is always expressed in square units, such as square inches (in²), square feet (ft²), square meters (m²), or square centimeters (cm²). If your inputs are in feet, your output will be in square feet; if your inputs are in meters, your output will be in square meters.
Supported Shapes in This Calculator:
- Rectangle -- length and width
- Circle -- radius
- Triangle -- base and height
- Square -- side length
How to Use This Area Calculator
- Select the shape -- choose from Rectangle, Circle, Triangle, or Square using the tabs above
- Enter the required measurements -- such as length/width, radius, base/height, or side length
- Choose units if applicable -- use consistent units for all inputs (in, ft, cm, m)
- Click "Calculate" -- to compute the area
- Review the result -- confirm it's displayed in square units
Tips:
- Use consistent units for all inputs (don't mix inches and feet unless you convert first)
- If the calculator asks for radius, don't enter the diameter by mistake (diameter = 2 × radius)
- If you're estimating materials, consider adding a small extra percentage for waste (cutting, trimming, mistakes)
Area Formulas
Below are the most common area formulas used in geometry.
Rectangle
A = l × w
Where l = length and w = width
Square
A = s²
Where s = side length
Triangle
A = (b × h) ÷ 2
Where b = base and h = height
Circle
A = πr²
Where r = radius and π ≈ 3.14159
Parallelogram
A = b × h
Where b = base and h = perpendicular height
Trapezoid
A = ((a + b) ÷ 2) × h
Where a and b are the parallel sides, h is the height
Ellipse
A = πab
Where a and b are the semi-major and semi-minor axes
Example Calculations
Example 1: Rectangle Area
Length: 12 ft, Width: 8 ft
Calculation: A = 12 × 8 = 96
Result: 96 ft²
Example 2: Triangle Area
Base: 10 cm, Height: 6 cm
Calculation: A = (10 × 6) ÷ 2 = 60 ÷ 2 = 30
Result: 30 cm²
Example 3: Circle Area
Radius: 7 m
Calculation: A = π × 7² = π × 49 ≈ 153.94
Result: Area ≈ 153.94 m²
Example 4: Trapezoid Area
Parallel sides: a = 6 in, b = 10 in, Height: 4 in
Calculation: A = ((6 + 10) ÷ 2) × 4 = (16 ÷ 2) × 4 = 8 × 4 = 32
Result: 32 in²
Frequently Asked Questions
What is area measured in?
Area is measured in square units, such as in², ft², cm², or m². The "square" part comes from multiplying two lengths (like length × width).
What's the difference between area and perimeter?
Area is the space inside a shape. Perimeter is the distance around the outside of a shape. Area is in square units; perimeter is in regular units.
How do I know if I should use radius or diameter for a circle?
The area formula uses radius (r). If you have the diameter (d), convert it by using r = d ÷ 2.
Why do I get different results when I change units?
The number changes because the unit size changes (1 ft is bigger than 1 in). If you convert inputs correctly, the area will be consistent. For example, 1 ft² equals 144 in².
How do I estimate material needs using area?
Calculate the area of the surface, then compare it to the coverage of your material (paint coverage per gallon, tile area per box, etc.). It's common to add 5–15% extra for waste or cuts.
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什么是面积？
面积是二维平面图形所占区域的大小，用平方单位（如 m²、ft²、cm²）表示。不同形状有各自的面积公式，本计算器涵盖最常用的 8 种几何形状。
面积计算在日常生活中极为常见——装修买地板、铺地砖、规划花园、计算土地面积，都需要精确计算面积。掌握基本公式，可以快速完成这些任务。
如何使用本计算器
- 1选择形状：矩形、正方形、圆形、三角形、梯形等。
- 2输入所需尺寸（长、宽、半径、高等）。
- 3点击「计算」，立即获得面积和周长结果。
- 4切换单位，查看不同单位制下的换算结果。
各形状面积公式
矩形：A = 长 × 宽
正方形：A = 边长²
圆形：A = π × r²（r 为半径）
三角形：A = ½ × 底 × 高
梯形：A = ½ × (上底 + 下底) × 高
椭圆：A = π × a × b（a、b 为半轴长）
平行四边形：A = 底 × 高
正六边形：A = (3√3 / 2) × 边长²π ≈ 3.14159；高指底边到对边（或对角）的垂直距离，不是斜边长。
计算示例
客厅铺地板 — 矩形
客厅长 6 m、宽 4.5 m。面积 = 6 × 4.5 = 27 m²。购买地板时建议多加 10% 损耗，即约需 29.7 m²。
圆形花园 — 圆形
圆形花坛半径 4 m。面积 = π × 4² = 50.27 m²。购买覆盖物或草籽时，以此为参考用量。
三角形地块 — 三角形
三角形土地底边 30 ft、高 25 ft。面积 = ½ × 30 × 25 = 375 ft²。适合计算不规则边角地块的绿化面积。