k 比例常数计算器（正比例/反比例，表格检验）Constant of Proportionality Calculator (Direct or Inverse, Table Check)

使用说明与常见问题How-to & FAQ

「比例常数计算器（正比例/反比例，表格检验）」是什么？What is the Constant of Proportionality Calculator (Direct or Inverse, Table Check) tool?

由一对 x、y 求比例常数 k，或输入一组 x、y 数据，检验它们是否成正比例（y = kx）或反比例（y = k/x），并给出每一对的比值。也可以用 k 求另一个未知值。本地处理。Find the constant k from one x, y pair, or enter a table of x and y values to check whether they are directly (y = kx) or inversely (y = k/x) proportional, with the ratio for each pair. You can also use k to find a missing value. Processed locally.

如何使用「比例常数计算器（正比例/反比例，表格检验）」？How do I use the Constant of Proportionality Calculator (Direct or Inverse, Table Check) tool?

在「比例常数计算器（正比例/反比例，表格检验）」中，填写「比例类型」、「x 值（一个或多个）」、「y 值（一个或多个）」、「求 y 时的 x（可选）」等参数，结果会随输入实时计算并显示在下方。In the Constant of Proportionality Calculator (Direct or Inverse, Table Check): Fill in "Type", "x value(s)", "y value(s)", "x to find y for (optional)"; results are recalculated instantly as you type.

比例常数怎么求？How is k found?

正比例 y = kx 时 k = y ÷ x；反比例 y = k/x 时 k = x × y。多组数据时，k 必须对每一组都相同，才说明成比例。For direct proportion y = kx, k = y / x; for inverse proportion y = k/x, k = x × y. With several pairs, k must be the same for every pair for the values to be proportional.

y = 2x + 1 是正比例吗？Is y = 2x + 1 proportional?

不是。正比例的图像是过原点的直线，有常数项的一次函数不过原点，y/x 也不是常数。No. A direct proportion is a straight line through the origin; a linear function with a constant term misses the origin and y/x is not constant.

怎么用 k 求未知数？How do I use k to find a missing value?

在“求 y 时的 x”里填入 x，正比例时 y = kx，反比例时 y = k/x。Enter the x value and the page gives y = kx for direct or y = k/x for inverse proportion.

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

例如在「比例常数计算器（正比例/反比例，表格检验）」中填 比例类型 = 正比例 y = kx，x 值（一个或多个） = 1, 2, 3, 4，y 值（一个或多个） = 3, 6, 9, 12，求 y 时的 x（可选） = 10，结果区显示：比例常数 k：3；关系：y = 3x；x = 10 时 y：30For example, entering Type = Direct y = kx, x value(s) = 1, 2, 3, 4, y value(s) = 3, 6, 9, 12, x to find y for (optional) = 10 in the Constant of Proportionality Calculator (Direct or Inverse, Table Check) gives: Constant k: 3; Relation: y = 3x; y when x = 10: 30

哪些输入会被检查？Which inputs are validated?

「比例常数计算器（正比例/反比例，表格检验）」会检查这些输入——「求 y 时的 x（可选）」：可留空；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 Constant of Proportionality Calculator (Direct or Inverse, Table Check) checks its inputs — "x to find y for (optional)": optional; 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?

「比例常数计算器（正比例/反比例，表格检验）」的设置：「比例类型」可选 正比例 y = kx、反比例 y = k/x（默认 正比例 y = kx）；「x 值（一个或多个）」默认 1, 2, 3, 4；「y 值（一个或多个）」默认 3, 6, 9, 12；「求 y 时的 x（可选）」默认 10。每次生成结果都按当前设置处理。Settings in the Constant of Proportionality Calculator (Direct or Inverse, Table Check) — "Type": Direct y = kx, Inverse y = k/x (default Direct y = kx); "x value(s)" default 1, 2, 3, 4; "y value(s)" default 3, 6, 9, 12; "x to find y for (optional)" default 10. The result always uses the current settings.

计算精度如何？How precise are the results?

「比例常数计算器（正比例/反比例，表格检验）」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 Constant of Proportionality Calculator (Direct or Inverse, Table Check) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「比例常数计算器（正比例/反比例，表格检验）」免费吗？需要注册吗？Is the Constant of Proportionality Calculator (Direct or Inverse, Table Check) free? Do I need an account?

「比例常数计算器（正比例/反比例，表格检验）」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 Constant of Proportionality Calculator (Direct or Inverse, Table Check) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.