Calculating the Length of a Triangle

Right-Angled Triangle Side Length Calculator

Enter any two known side lengths of a right-angled triangle, and the calculator will determine the third missing side using the Pythagorean theorem.

Side A Length: units
Side B Length: units
Hypotenuse Length: units

Understanding Right-Angled Triangles and the Pythagorean Theorem

A right-angled triangle is a special type of triangle where one of its angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and it is always the longest side. The other two sides are often referred to as legs or simply Side A and Side B.

The relationship between the sides of a right-angled triangle is described by the famous Pythagorean Theorem, named after the ancient Greek mathematician Pythagoras. The theorem states that 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

This theorem is fundamental in geometry and has countless applications in fields like construction, engineering, navigation, and even computer graphics.

How to Use the Calculator

Our Right-Angled Triangle Side Length Calculator simplifies the process of finding a missing side. Here's how it works:

Identify Known Sides: You need to know the lengths of any two sides of the right-angled triangle.
Enter Values: Input the known lengths into the corresponding fields: "Side A Length", "Side B Length", or "Hypotenuse Length".
Leave One Blank: Crucially, leave the field for the side you want to calculate completely empty. The calculator will automatically determine which side is missing.
Calculate: Click the "Calculate Missing Side" button.
View Result: The calculated length of the missing side will be displayed in the result area.

Calculation Examples

Example 1: Finding the Hypotenuse

Imagine you have a right-angled triangle where Side A is 3 units and Side B is 4 units. You want to find the length of the hypotenuse.

Enter "3" in "Side A Length".
Enter "4" in "Side B Length".
Leave "Hypotenuse Length" blank.
Click "Calculate".

The calculator will use the formula c = √(a² + b²), so c = √(3² + 4²) = √(9 + 16) = √25 = 5. The result will be "The missing Hypotenuse (c) is: 5.0000 units."

Example 2: Finding a Leg (Side A)

Suppose you know the hypotenuse is 10 units and Side B is 8 units. You need to find Side A.

Leave "Side A Length" blank.
Enter "8" in "Side B Length".
Enter "10" in "Hypotenuse Length".
Click "Calculate".

The calculator will use the formula a = √(c² - b²), so a = √(10² - 8²) = √(100 - 64) = √36 = 6. The result will be "The missing Side A (a) is: 6.0000 units."

Example 3: Finding a Leg (Side B)

If Side A is 5 units and the hypotenuse is 13 units, let's find Side B.

Enter "5" in "Side A Length".
Leave "Side B Length" blank.
Enter "13" in "Hypotenuse Length".
Click "Calculate".

The calculator will use the formula b = √(c² - a²), so b = √(13² - 5²) = √(169 - 25) = √144 = 12. The result will be "The missing Side B (b) is: 12.0000 units."

Important Considerations

Units: The calculator works with any consistent unit of length (e.g., centimeters, meters, inches, feet). Just ensure you use the same unit for all your inputs.
Positive Values: Side lengths must always be positive numbers.
Hypotenuse is Longest: When calculating a leg, the hypotenuse must always be strictly longer than the other known leg. If you enter a hypotenuse that is shorter than or equal to a leg, the calculation will result in an error (or an imaginary number), and the calculator will inform you.

/* Basic styling for the calculator */ .triangle-calculator { font-family: Arial, sans-serif; max-width: 600px; margin: 20px auto; padding: 20px; border: 1px solid #ccc; border-radius: 8px; background-color: #f9f9f9; } .triangle-calculator h2 { text-align: center; color: #333; margin-bottom: 20px; } .calculator-inputs label { display: inline-block; width: 150px; margin-bottom: 10px; font-weight: bold; } .calculator-inputs input[type="number"] { width: 150px; padding: 8px; margin-bottom: 10px; border: 1px solid #ddd; border-radius: 4px; } .calculator-inputs button { background-color: #007bff; color: white; padding: 10px 15px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; margin-right: 10px; margin-top: 10px; } .calculator-inputs button:hover { background-color: #0056b3; } .calculator-inputs button:last-of-type { background-color: #6c757d; } .calculator-inputs button:last-of-type:hover { background-color: #5a6268; } .calculator-result { margin-top: 20px; padding: 15px; border: 1px solid #e0e0e0; border-radius: 4px; background-color: #e9ecef; font-size: 1.1em; font-weight: bold; color: #333; min-height: 30px; /* Ensure space even when empty */ } .calculator-article { margin-top: 30px; line-height: 1.6; color: #555; } .calculator-article h3 { color: #333; margin-top: 25px; margin-bottom: 15px; } .calculator-article p, .calculator-article ul, .calculator-article ol { margin-bottom: 10px; } .calculator-article code { background-color: #eee; padding: 2px 4px; border-radius: 3px; font-family: 'Courier New', Courier, monospace; } .unit-label { margin-left: 5px; color: #666; } function calculateTriangleSide() { var sideAStr = document.getElementById("sideAInput").value; var sideBStr = document.getElementById("sideBInput").value; var hypotenuseStr = document.getElementById("hypotenuseInput").value; var resultDiv = document.getElementById("triangleResult"); resultDiv.innerHTML = ""; // Clear previous results var sideA = parseFloat(sideAStr); var sideB = parseFloat(sideBStr); var hypotenuse = parseFloat(hypotenuseStr); var filledCount = 0; if (sideAStr !== ") filledCount++; if (sideBStr !== ") filledCount++; if (hypotenuseStr !== ") filledCount++; if (filledCount 2) { resultDiv.innerHTML = "Please leave exactly one field blank to calculate the missing side."; return; } // Validate positive numbers and ensure they are valid numbers if entered if ((sideAStr !== " && (isNaN(sideA) || sideA <= 0)) || (sideBStr !== '' && (isNaN(sideB) || sideB <= 0)) || (hypotenuseStr !== '' && (isNaN(hypotenuse) || hypotenuse <= 0))) { resultDiv.innerHTML = "All entered side lengths must be positive numbers."; return; } var calculatedValue; var missingSideName = ""; if (sideAStr === '') { // Calculate Side A if (isNaN(sideB) || isNaN(hypotenuse)) { resultDiv.innerHTML = "Error: Missing valid numbers for Side B and Hypotenuse."; return; } if (hypotenuse <= sideB) { resultDiv.innerHTML = "Error: The hypotenuse must be strictly longer than Side B."; return; } calculatedValue = Math.sqrt(Math.pow(hypotenuse, 2) – Math.pow(sideB, 2)); missingSideName = "Side A (a)"; } else if (sideBStr === '') { // Calculate Side B if (isNaN(sideA) || isNaN(hypotenuse)) { resultDiv.innerHTML = "Error: Missing valid numbers for Side A and Hypotenuse."; return; } if (hypotenuse <= sideA) { resultDiv.innerHTML = "Error: The hypotenuse must be strictly longer than Side A."; return; } calculatedValue = Math.sqrt(Math.pow(hypotenuse, 2) – Math.pow(sideA, 2)); missingSideName = "Side B (b)"; } else if (hypotenuseStr === '') { // Calculate Hypotenuse if (isNaN(sideA) || isNaN(sideB)) { resultDiv.innerHTML = "Error: Missing valid numbers for Side A and Side B."; return; } calculatedValue = Math.sqrt(Math.pow(sideA, 2) + Math.pow(sideB, 2)); missingSideName = "Hypotenuse (c)"; } else { // This case should ideally not be reached due to filledCount check, but as a fallback resultDiv.innerHTML = "An unexpected error occurred. Please check your inputs."; return; } if (isNaN(calculatedValue) || !isFinite(calculatedValue)) { resultDiv.innerHTML = "Calculation error. Please check your input values (e.g., hypotenuse must be longest side)."; } else { resultDiv.innerHTML = "The missing " + missingSideName + " is: " + calculatedValue.toFixed(4) + " units."; } } function clearTriangleInputs() { document.getElementById("sideAInput").value = ""; document.getElementById("sideBInput").value = ""; document.getElementById("hypotenuseInput").value = ""; document.getElementById("triangleResult").innerHTML = ""; }