➗ 调和平均数计算器Harmonic Mean Calculator

使用说明与常见问题How-to & FAQ

「调和平均数计算器」是什么？What is the Harmonic Mean Calculator tool?

计算一组正数的调和平均数 n ÷ Σ(1/x)，适合求平均速度、平均单价等「比率」的平均；可选填权重求加权调和平均，并给出算术、几何平均作对比。Calculate the harmonic mean n ÷ Σ(1/x) of positive numbers — the right average for rates such as speeds or unit prices — with optional weights, and the arithmetic and geometric means for comparison.

如何使用「调和平均数计算器」？How do I use the Harmonic Mean Calculator tool?

在「调和平均数计算器」中，填写上方字段等参数，结果会随输入实时计算并显示在下方。In the Harmonic Mean Calculator: Fill in the fields above; results are recalculated instantly as you type.

调和平均数怎么算？How is the harmonic mean calculated?

H = n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ)；加权时 H = Σw ÷ Σ(w/x)。H = n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ); weighted, H = Σw ÷ Σ(w/x).

为什么平均速度要用调和平均？Why is it right for average speed?

去程 60 km/h、回程 40 km/h（路程相同），总时间按路程算，平均速度是 2 ÷ (1/60 + 1/40) = 48 km/h，不是 50。若每段路程不同，把各段路程作为权重。Out at 60 km/h and back at 40 km/h over the same distance gives 2 ÷ (1/60 + 1/40) = 48 km/h, not 50, because time depends on distance. If the legs differ in length, use each leg's distance as its weight.

三种平均数的关系？How do the three means compare?

对正数总有 调和 ≤ 几何 ≤ 算术，数据全部相等时三者相同。For positive numbers, harmonic ≤ geometric ≤ arithmetic, with equality only when all values are the same.

计算精度如何？How precise are the results?

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

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

「调和平均数计算器」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 Harmonic 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.