圓周長計算器
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.
什麼是周長？
圓的周長是其外緣的距離 — 即圓的邊界長度。這是幾何學最基本的測量之一，廣泛應用於工程、建築、製造和天文學等各個領域。對於任意圓形，其周長與直徑之比是數學常數 π（圓周率），約為 3.14159。
周長公式
C = 2πr （使用半徑）
C = πd （使用直徑）
兩個公式結果相同，因為直徑恰好是半徑的兩倍：d = 2r。
計算範例
半徑為 5 cm 的圓的周長為：
C = 2π × 5 = 10π ≈ 31.4159 cm
面積為：
A = π × 5² = 25π ≈ 78.5398 cm²
圓的四個量
| 量 | 符號 | 公式 |
|---|---|---|
| 半徑 | r | r = d ÷ 2 = C ÷ (2π) = √(A÷π) |
| 直徑 | d | d = 2r = C ÷ π |
| 周長 | C | C = 2πr = πd |
| 面積 | A | A = πr² = π(d÷2)² = C² ÷ (4π) |
如何使用本計算器
- 輸入四個值中的任一個：半徑、直徑、周長或面積。
- 選擇單位（mm、cm、m、in、ft 等）。
- 其他三個量會自動更新。
常見錯誤
- 混淆半徑與直徑。半徑從中心到邊緣；直徑是橫跨整個圓的距離。直徑永遠是半徑的兩倍。
- 忘記面積平方。面積使用 r²，不是 r — 半徑加倍代表面積變為原來的四倍。
- 混用一次與平方單位。周長以 cm 計，面積以 cm² 計。計算器以小 ² 標註面積單位。
- 把 π 當作精確 3.14。粗略估算可以，本計算器使用完整的 Math.PI 精度。
對於非圓形形狀（橢圓、卵形、不規則曲線），本計算器不適用。如需計算弧長，請使用弧長計算器。