How to Calculate the Hypotenuse of a Triangle

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Hypotenuse Calculator

The hypotenuse will appear here.
function calculateHypotenuse() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var resultDiv = document.getElementById('result'); if (isNaN(sideA) || isNaN(sideB) || sideA <= 0 || sideB <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for both sides."; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.borderColor = '#f5c6cb'; resultDiv.style.color = '#721c24'; return; } var hypotenuse = Math.sqrt(sideA * sideA + sideB * sideB); resultDiv.innerHTML = "The length of the Hypotenuse (Side C) is: " + hypotenuse.toFixed(4) + ""; resultDiv.style.backgroundColor = '#d4edda'; resultDiv.style.borderColor = '#c3e6cb'; resultDiv.style.color = '#155724'; }

Understanding the Hypotenuse of a Right-Angled Triangle

The hypotenuse is the longest side of a right-angled triangle. It is always the side opposite the right angle (the 90-degree angle). Calculating its length is a fundamental concept in geometry and is crucial for various applications in mathematics, engineering, and physics.

The Pythagorean Theorem

The calculation of the hypotenuse relies on the famous Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is expressed as:

a² + b² = c²

To find the length of the hypotenuse (c), you simply take the square root of the sum of the squares of the other two sides:

c = √(a² + b²)

How to Use the Hypotenuse Calculator

Our Hypotenuse Calculator simplifies this process for you. Follow these steps:

  1. Enter Side A Length: Input the length of one of the shorter sides of your right-angled triangle into the "Length of Side A" field.
  2. Enter Side B Length: Input the length of the other shorter side into the "Length of Side B" field.
  3. Click Calculate: Press the "Calculate Hypotenuse" button.
  4. View Result: The calculator will instantly display the length of the hypotenuse (Side C) in the result area.

Example Calculation

Let's say you have a right-angled triangle where:

  • Side A = 3 units
  • Side B = 4 units

Using the Pythagorean Theorem:

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5 units

So, the hypotenuse of this triangle is 5 units. You can test these values in the calculator above to see the result!

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