Free online hypotenuse calculator using Pythagorean theorem. Enter two perpendicular sides of a right triangle to instantly calculate hypotenuse length.
The hypotenuse is the longest side of a right triangle, opposite to the right angle. This calculator allows you to determine the length of the hypotenuse when you know the lengths of the two perpendicular sides (legs) of a right triangle. Using the famous Pythagorean theorem, this tool provides instant, accurate calculations for any right triangle configuration.
The calculator performs all calculations client-side using JavaScript, providing immediate results without requiring any external APIs or databases.
The calculator performs the following checks on user inputs:
If invalid inputs are detected, helpful error messages will be displayed, and the calculation will not proceed until all inputs are corrected.
The hypotenuse length (c) is calculated using the Pythagorean theorem:
Where:
This fundamental mathematical relationship was discovered by the ancient Greek mathematician Pythagoras and forms the basis for countless geometric and trigonometric calculations.
The calculator uses the Pythagorean theorem to compute the hypotenuse length based on the user's input. Here's the step-by-step process:
The calculator performs these calculations using double-precision floating-point arithmetic to ensure accuracy across a wide range of input values.
The hypotenuse calculator has various applications across multiple fields:
Construction and Carpentry: Ensuring square corners and calculating diagonal braces, roof measurements, and foundation layouts.
Architecture and Engineering: Designing structural elements, calculating distances in blueprints, and verifying right angles in building plans.
Education and Mathematics: Teaching the Pythagorean theorem, solving geometry problems, and demonstrating mathematical relationships.
Navigation and Surveying: Calculating direct distances between two points when you know the horizontal and vertical distances.
Home Improvement: Measuring diagonal distances for tile installation, determining ladder placement angles, and planning room layouts.
Sports and Recreation: Calculating distances in baseball diamonds, soccer field diagonals, and court measurements.
While the Pythagorean theorem is the most direct method for calculating the hypotenuse, there are other related approaches:
Trigonometric Functions: Using sine, cosine, or tangent functions when you know one side and an angle.
Law of Cosines: A more general formula that works for any triangle, not just right triangles.
Distance Formula: In coordinate geometry, calculating the distance between two points using their coordinates.
Vector Mathematics: Using vector addition and magnitude calculations for more complex geometric problems.
The Pythagorean theorem has a rich mathematical history spanning over 2,500 years. While commonly attributed to the Greek mathematician Pythagoras (c. 570-495 BCE), evidence suggests that the relationship was known to ancient civilizations including the Babylonians, Indians, and Chinese centuries before Pythagoras.
The theorem gained prominence in ancient Greece through the work of Pythagoras and his followers, who provided one of the first formal proofs of the relationship. The Pythagorean school elevated this mathematical principle to a fundamental truth about the nature of geometric relationships.
Throughout history, mathematicians have discovered over 400 different proofs of the Pythagorean theorem, including contributions from notable figures such as Euclid, Leonardo da Vinci, and even U.S. President James Garfield. The theorem has been instrumental in the development of trigonometry, coordinate geometry, and modern mathematics.
In the modern era, the Pythagorean theorem remains one of the most recognizable and practically useful mathematical formulas, finding applications in fields ranging from computer graphics and GPS navigation to architectural design and scientific research.
Here are some code examples to calculate the hypotenuse using different programming languages:
1' Excel VBA Function for Hypotenuse Calculation
2Function CalculateHypotenuse(sideA As Double, sideB As Double) As Double
3 CalculateHypotenuse = Sqr(sideA ^ 2 + sideB ^ 2)
4End Function
5' Usage:
6' =CalculateHypotenuse(3, 4)
71import math
2
3def calculate_hypotenuse(side_a, side_b):
4 return math.sqrt(side_a**2 + side_b**2)
5
6# Example usage:
7side_a = 3.0 # length units
8side_b = 4.0 # length units
9hypotenuse = calculate_hypotenuse(side_a, side_b)
10print(f"Hypotenuse: {hypotenuse:.2f} units")
111function calculateHypotenuse(sideA, sideB) {
2 return Math.sqrt(Math.pow(sideA, 2) + Math.pow(sideB, 2));
3}
4
5// Example usage:
6const sideA = 5; // length units
7const sideB = 12; // length units
8const hypotenuse = calculateHypotenuse(sideA, sideB);
9console.log(`Hypotenuse: ${hypotenuse.toFixed(2)} units`);
101public class HypotenuseCalculator {
2 public static double calculateHypotenuse(double sideA, double sideB) {
3 return Math.sqrt(Math.pow(sideA, 2) + Math.pow(sideB, 2));
4 }
5
6 public static void main(String[] args) {
7 double sideA = 8.0; // length units
8 double sideB = 15.0; // length units
9
10 double hypotenuse = calculateHypotenuse(sideA, sideB);
11 System.out.printf("Hypotenuse: %.2f units%n", hypotenuse);
12 }
13}
14These examples demonstrate how to calculate the hypotenuse using various programming languages. You can adapt these functions to your specific needs or integrate them into larger mathematical calculation systems.
Classic 3-4-5 Triangle:
Construction Example:
Isosceles Right Triangle:
Decimal Example:
Large Scale Example:
Discover more tools that might be useful for your workflow