🌐 球面方程Sphere Equation Calculator
由球心 (a, b, c) 和半径 r 写出标准方程 (x - a)² + (y - b)² + (z - c)² = r² 与一般方程，并给出体积和表面积。本地处理。From centre (a, b, c) and radius r, write the standard equation (x - a)² + (y - b)² + (z - c)² = r² and the general form, plus volume and surface area. Processed locally.
使用说明与常见问题How-to & FAQ
「球面方程」是什么？What is the Sphere Equation Calculator tool?
由球心 (a, b, c) 和半径 r 写出标准方程 (x - a)² + (y - b)² + (z - c)² = r² 与一般方程，并给出体积和表面积。本地处理。From centre (a, b, c) and radius r, write the standard equation (x - a)² + (y - b)² + (z - c)² = r² and the general form, plus volume and surface area. Processed locally.
如何使用「球面方程」？How do I use the Sphere Equation Calculator tool?
在「球面方程」中，填写「球心 a」、「球心 b」、「球心 c」、「半径 r」等参数，结果会随输入实时计算并显示在下方。In the Sphere Equation Calculator: Fill in "Centre a", "Centre b", "Centre c", "Radius r"; results are recalculated instantly as you type.
由一般式求球心？From the general form?
x² + y² + z² + Dx + Ey + Fz + G = 0 的球心是 (-D/2, -E/2, -F/2)。For x² + y² + z² + Dx + Ey + Fz + G = 0 the centre is (-D/2, -E/2, -F/2).
能举个计算实例吗？Can you show a worked example?
例如在「球面方程」中填 球心 a = 1，球心 b = 2，球心 c = 3，半径 r = 4，结果区显示：标准方程：(x − 1)² + (y − 2)² + (z − 3)² = 16；一般方程：x² + y² + z² − 2x − 4y − 6z − 2 = 0；体积：268.082573；表面积：201.06193For example, entering Centre a = 1, Centre b = 2, Centre c = 3, Radius r = 4 in the Sphere Equation Calculator gives: Standard form: (x − 1)² + (y − 2)² + (z − 3)² = 16; General form: x² + y² + z² − 2x − 4y − 6z − 2 = 0; Volume: 268.082573; Surface area: 201.06193
哪些输入会被检查？Which inputs are validated?
「球面方程」会检查这些输入——「球心 a」、「球心 b」、「球心 c」：必须填写；「半径 r」：必须填写，须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Sphere Equation Calculator checks its inputs — "Centre a", "Centre b", "Centre c": required; "Radius r": required, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「球面方程」的设置：「球心 a」默认 1；「球心 b」默认 2；「球心 c」默认 3；「半径 r」默认 4。每次生成结果都按当前设置处理。Settings in the Sphere Equation Calculator — "Centre a" default 1; "Centre b" default 2; "Centre c" default 3; "Radius r" default 4. The result always uses the current settings.
计算精度如何？How precise are the results?
「球面方程」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Sphere Equation Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「球面方程」免费吗？需要注册吗？Is the Sphere Equation Calculator free? Do I need an account?
「球面方程」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Sphere Equation Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.