🥚 椭球体积计算器Volume of an Ellipsoid Calculator
输入椭球的三个半轴 a、b、c，按 V = 4/3·πabc 计算体积，并用 Knud Thomsen 公式估算表面积（误差不超过约 1.06%）；三个半轴相等时就是球。Enter the three semi-axes a, b and c of an ellipsoid to get its volume V = 4/3·πabc and an estimate of its surface area from Knud Thomsen's formula (within about 1.06%). Equal semi-axes give a sphere.
使用说明与常见问题How-to & FAQ
「椭球体积计算器」是什么？What is the Volume of an Ellipsoid Calculator tool?
输入椭球的三个半轴 a、b、c，按 V = 4/3·πabc 计算体积，并用 Knud Thomsen 公式估算表面积（误差不超过约 1.06%）；三个半轴相等时就是球。Enter the three semi-axes a, b and c of an ellipsoid to get its volume V = 4/3·πabc and an estimate of its surface area from Knud Thomsen's formula (within about 1.06%). Equal semi-axes give a sphere.
如何使用「椭球体积计算器」？How do I use the Volume of an Ellipsoid Calculator tool?
在「椭球体积计算器」中，填写「半轴 a」、「半轴 b」、「半轴 c」等参数，结果会随输入实时计算并显示在下方。In the Volume of an Ellipsoid Calculator: Fill in "Semi-axis a", "Semi-axis b", "Semi-axis c"; results are recalculated instantly as you type.
椭球体积公式是什么？What is the ellipsoid volume formula?
V = 4/3 × π × a × b × c，a、b、c 是三个半轴（中心到表面的距离，即轴长的一半）。a = b = c = r 时就是球的体积 4/3·πr³。V = 4/3 × π × a × b × c, where a, b and c are the semi-axes (half of each full axis). With a = b = c = r it becomes the sphere volume 4/3·πr³.
表面积为什么是近似值？Why is the surface area approximate?
一般椭球的表面积没有初等函数表示的公式，需要椭圆积分。这里用 Knud Thomsen 公式 S ≈ 4π((aᵖbᵖ + aᵖcᵖ + bᵖcᵖ)/3)^(1/p)，p = 1.6075，最大相对误差约 1.061%；球的情况给出精确值 4πr²。A general ellipsoid has no elementary closed form for its surface area (it needs elliptic integrals). Knud Thomsen's formula S ≈ 4π((aᵖbᵖ + aᵖcᵖ + bᵖcᵖ)/3)^(1/p) with p = 1.6075 is used, with a maximum relative error of about 1.061%; a sphere gets the exact 4πr².
默认值是什么？What are the defaults?
默认的半轴 3、2、1 只是示例。The default semi-axes 3, 2 and 1 are only an example.
计算精度如何？How precise are the results?
「椭球体积计算器」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 Volume of an Ellipsoid Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「椭球体积计算器」免费吗？需要注册吗？Is the Volume of an Ellipsoid Calculator free? Do I need an account?
「椭球体积计算器」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 Volume of an Ellipsoid 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.