圆周长计算器
圆周长计算器
FAQs
- What is the circumference of a circle?
- The circumference is the distance around the outside of a circle — its perimeter. For a circle with radius r, the circumference equals 2πr.
- What is the formula for circumference?
- C = 2πr (using radius) or C = πd (using diameter). Both give the same result because diameter is exactly twice the radius.
- How do I find the circumference if I know the area?
- First derive the radius from the area: r = √(A/π). Then plug into C = 2πr. This calculator does both steps for you.
- Why does π appear in every formula?
- π is defined as the ratio of any circle's circumference to its diameter — about 3.14159. Because every circle scales the same way, π shows up whenever you connect a circle's radius/diameter to its perimeter or area.
- Can I enter the diameter instead of the radius?
- Yes — pick any one of the four quantities (radius, diameter, circumference, area) and the other three update automatically.
- What's the difference between circumference and area?
- Circumference is a length (the boundary), measured in linear units like centimetres. Area is a surface, measured in square units like cm². For a circle of radius r, C = 2πr and A = πr².
什么是周长？
圆的周长是其外边缘的距离 — 即圆的边界长度。这是几何学最基本的测量之一，广泛应用于工程、建筑、制造和天文学等各个领域。对于任意圆形，其周长与直径之比是数学常数 π（圆周率），约为 3.14159。
周长公式
C = 2πr （使用半径）
C = πd （使用直径）
两个公式结果相同，因为直径恰好是半径的两倍：d = 2r。
计算示例
半径为 5 cm 的圆的周长为：
C = 2π × 5 = 10π ≈ 31.4159 cm
面积为：
A = π × 5² = 25π ≈ 78.5398 cm²
圆的四个量
| 量 | 符号 | 公式 |
|---|---|---|
| 半径 | r | r = d ÷ 2 = C ÷ (2π) = √(A÷π) |
| 直径 | d | d = 2r = C ÷ π |
| 周长 | C | C = 2πr = πd |
| 面积 | A | A = πr² = π(d÷2)² = C² ÷ (4π) |
如何使用本计算器
- 输入四个值中的任意一个：半径、直径、周长或面积。
- 选择单位（mm、cm、m、in、ft 等）。
- 其他三个量会自动更新。
常见错误
- 混淆半径和直径。半径是从中心到边缘；直径是横跨整个圆的距离。直径始终是半径的两倍。
- 忘记面积平方。面积使用 r²，不是 r — 半径加倍意味着面积变为原来的四倍。
- 混用一次与二次单位。周长以 cm 计，面积以 cm² 计。计算器会用小 ² 标注面积单位。
- 把 π 当作精确 3.14。粗略估算可以，本计算器使用完整的 Math.PI 精度。
对于非圆形形状（椭圆、卵形、不规则曲线），本计算器不适用。如需计算弧长，请使用弧长计算器。