在此页

• 句法
• 描述
• Polyfill
• 范例
• 规范
• 浏览器兼容性
• 另请参阅
• 相关话题

Math.hypot() function returns the square root of the sum of squares of its arguments, that is:

$$\mathtt{\operatorname{Math.hypot}(v_1, v_2, \dots, v_n)} = \sqrt{\sum_{i=1}^n v_i^2} = \sqrt{v_1^2 + v_2^2 + \dots + v_n^2}$$

The source for this interactive example is stored in a GitHub repository. If you'd like to contribute to the interactive examples project, please clone https://github.com/mdn/interactive-examples and send us a pull request.

句法

Math.hypot([value1[, value2[, ...]]])
					

参数

value1, value2, ...

Numbers.

返回值

The square root of the sum of squares of the given arguments. If at least one of the arguments cannot be converted to a number, NaN 被返回。

描述

Calculating the hypotenuse of a right triangle, or the magnitude of a complex number, uses the formula Math.sqrt(v1*v1 + v2*v2) , where v1 and v2 are the lengths of the triangle's legs, or the complex number's real and complex components.  The corresponding distance in 2 or more dimensions can be calculated by adding more squares under the square root: Math.sqrt(v1*v1 + v2*v2 + v3*v3 + v4*v4) .

This function makes this calculation easier and faster; you simply call Math.hypot(v1, v2) ，或 Math.hypot(v1, v2, v3, v4, ...) .

Math.hypot also avoids overflow/underflow problems if the magnitude of your numbers is very large. The largest number you can represent in JS is Number.MAX_VALUE , which is around 10 ³⁰⁸ . If your numbers are larger than about 10 ¹⁵⁴ , taking the square of them will result in Infinity. For example, Math.sqrt(1e200*1e200 + 1e200*1e200) = Infinity .  If you use hypot() instead, you get better answer: Math.hypot(1e200, 1e200) = 1.4142...e+200 . This is also true with very small numbers. Math.sqrt(1e-200*1e-200 + 1e-200*1e-200) = 0 , but Math.hypot(1e-200, 1e-200) = 1.4142...e-200 .

因为 hypot() is a static method of Math , you always use it as Math.hypot() , rather than as a method of a Math object you created ( Math is not a constructor).

If no arguments are given, the result is +0. If any of the arguments is ±Infinity, the result is Infinity. If any of the arguments is NaN (unless another argument is ±Infinity), the result is NaN. If at least one of the arguments cannot be converted to a number, the result is NaN .

With one argument, Math.hypot() 相当于 Math.abs() .

Polyfill

A naive approach that does not handle overflow/underflow issues:

if (!Math.hypot) Math.hypot = function() {
  var y = 0, i = arguments.length, containsInfinity = false;
  while (i--) {
    var arg = arguments[i];
    if (arg === Infinity || arg === -Infinity)
      containsInfinity = true
    y += arg * arg
  }
  return containsInfinity ? Infinity : Math.sqrt(y)
}
					

A polyfill that avoids underflows and overflows:

if (!Math.hypot) Math.hypot = function () {
  var max = 0;
  var s = 0;
  var containsInfinity = false;
  for (var i = 0; i < arguments.length; ++i) {
    var arg = Math.abs(Number(arguments[i]));
    if (arg === Infinity)
      containsInfinity = true
    if (arg > max) {
      s *= (max / arg) * (max / arg);
      max = arg;
    }
    s += arg === 0 && max === 0 ? 0 : (arg / max) * (arg / max);
  }
  return containsInfinity ? Infinity : (max === 1 / 0 ? 1 / 0 : max * Math.sqrt(s));
};
					

范例

使用 Math.hypot()

Math.hypot(3, 4);          // 5
Math.hypot(3, 4, 5);       // 7.0710678118654755
Math.hypot();              // 0
Math.hypot(NaN);           // NaN
Math.hypot(NaN, Infinity); // Infinity
Math.hypot(3, 4, 'foo');   // NaN, since +'foo' => NaN
Math.hypot(3, 4, '5');     // 7.0710678118654755, +'5' => 5
Math.hypot(-3);            // 3, the same as Math.abs(-3)
					

规范

规范
ECMAScript (ECMA-262) The definition of 'Math.hypot' in that specification.

浏览器兼容性

The compatibility table in this page is generated from structured data. If you'd like to contribute to the data, please check out https://github.com/mdn/browser-compat-data and send us a pull request.

更新 GitHub 上的兼容性数据

	Desktop						Mobile						Server
	Chrome	Edge	Firefox	Internet Explorer	Opera	Safari	Android webview	Chrome for Android	Firefox for Android	Opera for Android	Safari on iOS	Samsung Internet	Node.js
hypot	Chrome 38	Edge 12	Firefox 27	IE No	Opera 25	Safari 8	WebView Android 38	Chrome Android 38	Firefox Android 27	Opera Android 25	Safari iOS 8	Samsung Internet Android 3.0	nodejs 0.12

图例

完整支持

完整支持

不支持

不支持

另请参阅

• Math.abs()
• Math.pow()
• Math.sqrt()

元数据

• 最后修改： Aug 23, 2020

相关话题

1. 标准内置对象
2. Math
3. 特性
   1. Math.E
   2. Math.LN10
   3. Math.LN2
   4. Math.LOG10E
   5. Math.LOG2E
   6. Math.PI
   7. Math.SQRT1_2
   8. Math.SQRT2
4. 方法
   1. Math.abs()
   2. Math.acos()
   3. Math.acosh()
   4. Math.asin()
   5. Math.asinh()
   6. Math.atan()
   7. Math.atan2()
   8. Math.atanh()
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   12. Math.cos()
   13. Math.cosh()
   14. Math.exp()
   15. Math.expm1()
   16. Math.floor()
   17. Math.fround()
   18. Math.hypot()
   19. Math.imul()
   20. Math.log()
   21. Math.log10()
   22. Math.log1p()
   23. Math.log2()
   24. Math.max()
   25. Math.min()
   26. Math.pow()
   27. Math.random()
   28. Math.round()
   29. Math.sign()
   30. Math.sin()
   31. Math.sinh()
   32. Math.sqrt()
   33. Math.tan()
   34. Math.tanh()
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5. 继承：
6. Object
7. 特性
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8. 方法
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   2. Object.prototype.__defineSetter__()
   3. Object.prototype.__lookupGetter__()
   4. Object.prototype.__lookupSetter__()
   5. Object.prototype.hasOwnProperty()
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