📈 几何平均数计算器Geometric Mean Calculator

使用说明与常见问题How-to & FAQ

「几何平均数计算器」是什么？What is the Geometric Mean Calculator tool?

计算一组正数的几何平均数（n 个数乘积的 n 次方根），也可以输入每期增长率（%）求平均增长率；同时给出算术平均数作对比。Calculate the geometric mean of positive numbers (the n-th root of their product), or enter growth rates in percent to get the average growth rate, with the arithmetic mean for comparison.

如何使用「几何平均数计算器」？How do I use the Geometric Mean Calculator tool?

在「几何平均数计算器」中，填写「输入类型」等参数，结果会随输入实时计算并显示在下方。In the Geometric Mean Calculator: Fill in "Input type"; results are recalculated instantly as you type.

几何平均数怎么算？How is the geometric mean calculated?

G = (x₁ × x₂ × … × xₙ)^(1/n)。工具用对数求和计算，避免大量数据相乘时溢出。G = (x₁ × x₂ × … × xₙ)^(1/n). The tool sums logarithms so long lists do not overflow.

为什么平均增长率要用几何平均？Why use it for growth rates?

增长是相乘累积的：+10%、−5%、+20% 三年后为 1.1 × 0.95 × 1.2 = 1.254 倍，每年相当于 1.254^(1/3) − 1 ≈ 7.84%，而算术平均 8.33% 会高估。Growth compounds: +10%, −5% and +20% give 1.1 × 0.95 × 1.2 = 1.254 times after three years, which is 1.254^(1/3) − 1 ≈ 7.84% a year; the arithmetic mean of 8.33% overstates it.

可以有 0 或负数吗？Can the data contain 0 or negatives?

不能。几何平均只对正数有定义；增长率模式下每期须大于 −100%。No. It is only defined for positive numbers; in growth-rate mode each period must be above −100%.

计算精度如何？How precise are the results?

「几何平均数计算器」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 Geometric Mean Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「几何平均数计算器」免费吗？需要注册吗？Is the Geometric Mean Calculator free? Do I need an account?

「几何平均数计算器」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 Geometric Mean 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.