CIRCLE
Circle perimeter & area, all from one radius.
Fill the radius (or diameter) and get the perimeter and area instantly; add a central angle for arc length and sector area; switch to sphere mode for volume and surface area. Radius and diameter are linked — change one and the other follows.
Everything runs locally in your browser
How to use
Pick the object, then fill the radius or diameter (they are linked) and, where relevant, the central angle: circle mode gives perimeter and area; the sector mode adds arc length and sector area; sphere mode gives volume and surface area. Results keep two decimals and the working shows every substitution, with the value of π noted below.
Common questions
Perimeter and area — which formula is which?
The perimeter is the distance around the circle, 2πr; the area is how much fits inside, πr². The classic mistake is using 2πr when the problem asks for area, or πr² when it asks for the perimeter. Remember: perimeter goes "once around" with r to the first power; area covers a "disk" with r squared.
How are arc length and sector area computed?
Both use the fraction of the full circle the angle covers: arc = (θ/360) × 2πr, sector area = (θ/360) × πr². With θ = 90° that is exactly a quarter: a quarter of the perimeter and a quarter of the area.
What is the difference between a circle and a sphere?
A circle is a flat shape (perimeter and area only); a sphere is a solid, so besides its surface area it has a volume. The sphere surface area S = 4πr² is exactly four times the circle area πr² — you can picture the sphere as four large discs. The volume is V = (4/3)πr³.
Is any data uploaded?
No. All computing runs locally in the browser.
示例与注意事项Example & notes
一个例子A worked example
已知半径 3：得到周长 18.85、面积 28.27；把圆心角填 90° 再算，弧长 4.71、扇形面积 7.07，正好是全圆的 1/4。With radius 3: perimeter 18.85, area 28.27; add a 90° central angle and the arc is 4.71 with sector area 7.07 — exactly a quarter of the circle.
注意事项Things to watch
- 半径与直径双向联动：改其中一个，另一个自动换算（填直径 10 时半径自动变 5）。Radius and diameter are linked: change either and the other follows (diameter 10 gives radius 5).
- 结果保留两位小数；π 取 3.14159265358979，题目要求精确值时按 π 保留到题目给定的位数。Results keep two decimals; π is taken as 3.14159265358979, so keep as many digits as the problem asks for.
- 球模式给的是球（立体）的体积与表面积，不要与圆面积 πr² 混淆：球表面积恰是圆面积的 4 倍。Sphere mode gives the volume and surface area of the solid — do not confuse it with the circle area πr²; the sphere surface area is exactly four times that.
相关问答More Q&A
周长和面积总是分不清怎么办？I keep mixing up perimeter and area
记两个特征：周长是「绕一圈多长」，用 2πr，r 的一次方；面积是「铺满里面多大」，用 πr²，r 的平方。做题时先问自己：题目要的是长度还是「能装多少」。Anchor on two cues: perimeter is "how far around" — 2πr with r to the first power; area is "how much fits inside" — πr² with r squared. Ask whether the question asks for a length or for "how much fits".
弧长为什么用 θ/360 这样的比例？Why is the arc computed with θ/360?
因为弧长与扇形面积都随圆心角成正比：θ=360° 时是整圆（弧长=周长、扇形=全圆），θ=90° 时就是四分之一，θ=60° 时是六分之一。比例式能自动覆盖所有情形。Arc length and sector area are both proportional to the central angle: 360° gives the full circle (arc = perimeter, sector = whole area), 90° gives a quarter, 60° a sixth. The ratio handles every case at once.