📍 线性插值计算器Linear Interpolation Calculator
已知两点 (x₁, y₁)、(x₂, y₂)，用直线插值求任意 x 对应的 y（可一次输入多个 x），或由 y 反求 x；超出两点范围时会提示属于外推。Given two points (x₁, y₁) and (x₂, y₂), find y for any x on the straight line between them (several x values at once), or solve x from y — with a note when a value is outside the two points (extrapolation).
使用说明与常见问题How-to & FAQ
「线性插值计算器」是什么？What is the Linear Interpolation Calculator tool?
已知两点 (x₁, y₁)、(x₂, y₂)，用直线插值求任意 x 对应的 y（可一次输入多个 x），或由 y 反求 x；超出两点范围时会提示属于外推。Given two points (x₁, y₁) and (x₂, y₂), find y for any x on the straight line between them (several x values at once), or solve x from y — with a note when a value is outside the two points (extrapolation).
如何使用「线性插值计算器」？How do I use the Linear Interpolation Calculator tool?
在「线性插值计算器」中，填写「求」、「x₁」、「y₁」、「x₂」、「y₂」等参数，结果会随输入实时计算并显示在下方。In the Linear Interpolation Calculator: Fill in "Find", "x₁", "y₁", "x₂", "y₂"; results are recalculated instantly as you type.
线性插值公式？What is the formula?
y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁)。它假设两点之间按直线变化，常用于查表时估算表中没有的值。y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁). It assumes a straight line between the points and is often used to estimate values between entries in a table.
插值和外推有什么区别？How is interpolation different from extrapolation?
x 在 x₁ 和 x₂ 之间是插值；超出这个范围是外推。外推假设直线关系在范围外依然成立，误差可能很大。Between x₁ and x₂ it is interpolation; outside, extrapolation, which assumes the line keeps going and can be far off.
计算精度如何？How precise are the results?
「线性插值计算器」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 Linear Interpolation Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「线性插值计算器」免费吗？需要注册吗？Is the Linear Interpolation Calculator free? Do I need an account?
「线性插值计算器」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 Linear Interpolation 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.