🔺 三棱锥体积计算器（底面积、三边、正四面体）Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron)

使用说明与常见问题How-to & FAQ

「三棱锥体积计算器（底面积、三边、正四面体）」是什么？What is the Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) tool?

三棱锥（四面体）体积 V = 底面积 × 高 ÷ 3。底面可直接填面积、填三角形底和高、填三边（海伦公式），也可按正四面体只填棱长（V = a³ ÷ (6√2)）。本地处理。Triangular pyramid (tetrahedron) volume V = base area × height ÷ 3. Give the base as an area, as a triangle base and height, or as three sides (Heron's formula), or choose a regular tetrahedron and enter only the edge (V = a³ ÷ (6√2)). Processed locally.

如何使用「三棱锥体积计算器（底面积、三边、正四面体）」？How do I use the Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) tool?

在「三棱锥体积计算器（底面积、三边、正四面体）」中，填写「底面已知」、「底面积」、「三角形底边」、「三角形的高」、「边 a」等参数，结果会随输入实时计算并显示在下方。In the Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron): Fill in "Base given as", "Base area", "Triangle base", "Triangle height", "Side a"; results are recalculated instantly as you type.

为什么要除以 3？Why divide by 3?

任何锥体（棱锥、圆锥）的体积都是同底同高柱体的三分之一，这可以用积分或把三棱柱切成三个等体积的三棱锥来证明。Any pyramid or cone has one third of the volume of the prism or cylinder with the same base and height; this can be shown by integration or by cutting a triangular prism into three pyramids of equal volume.

能举个计算实例吗？Can you show a worked example?

例如在「三棱锥体积计算器（底面积、三边、正四面体）」中填 底面已知 = 三角形底和高，三角形底边 = 6，三角形的高 = 4，三棱锥的高 = 9，结果区显示：体积：36；底面积：12；高：9；ℹ V = 底面积 × 高 ÷ 3（高是顶点到底面的垂直距离）For example, entering Base given as = Triangle base and height, Triangle base = 6, Triangle height = 4, Pyramid height = 9 in the Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) gives: Volume: 36; Base area: 12; Height: 9; ℹ V = base area × height ÷ 3 (the height is the perpendicular distance from the apex to the base)

哪些输入会被检查？Which inputs are validated?

「三棱锥体积计算器（底面积、三边、正四面体）」会检查这些输入——「底面积」：须大于 0且不大于 1,000,000,000,000,000,000；「三角形底边」：须大于 0且不大于 1,000,000,000；「三角形的高」：须大于 0且不大于 1,000,000,000；「边 a」：须大于 0且不大于 1,000,000,000；「边 b」：须大于 0且不大于 1,000,000,000；「边 c」：须大于 0且不大于 1,000,000,000；「棱长」：须大于 0且不大于 1,000,000,000；「三棱锥的高」：须大于 0且不大于 1,000,000,000；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 Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) checks its inputs — "Base area": must be more than 0 and at most 1,000,000,000,000,000,000; "Triangle base": must be more than 0 and at most 1,000,000,000; "Triangle height": must be more than 0 and at most 1,000,000,000; "Side a": must be more than 0 and at most 1,000,000,000; "Side b": must be more than 0 and at most 1,000,000,000; "Side c": must be more than 0 and at most 1,000,000,000; "Edge length": must be more than 0 and at most 1,000,000,000; "Pyramid height": must be more than 0 and at most 1,000,000,000; 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?

「三棱锥体积计算器（底面积、三边、正四面体）」的设置：「底面已知」可选 底面积、三角形底和高、三边、正四面体棱长（默认 三角形底和高）；「底面积」默认 12；「三角形底边」默认 6；「三角形的高」默认 4；「边 a」默认 3；「边 b」默认 4；「边 c」默认 5；「棱长」默认 2；「三棱锥的高」默认 9。每次生成结果都按当前设置处理。Settings in the Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) — "Base given as": Base area, Triangle base and height, Three sides, Regular tetrahedron edge (default Triangle base and height); "Base area" default 12; "Triangle base" default 6; "Triangle height" default 4; "Side a" default 3; "Side b" default 4; "Side c" default 5; "Edge length" default 2; "Pyramid height" default 9. The result always uses the current settings.

计算精度如何？How precise are the results?

「三棱锥体积计算器（底面积、三边、正四面体）」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 Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「三棱锥体积计算器（底面积、三边、正四面体）」免费吗？需要注册吗？Is the Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) free? Do I need an account?

「三棱锥体积计算器（底面积、三边、正四面体）」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 Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.