Hypotenuse Calculator
Calculate the hypotenuse of a right triangle given the two legs using c = √(a² + b²).
Results
Hypotenuse
5 units
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Hypotenuse Calculator. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.
Review your inputs
Double-check that all values are correct and match the units or format shown for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Hypotenuse Calculator computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
When to Use This Calculator
- •Use the Hypotenuse Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
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About Hypotenuse Calculator
The hypotenuse is the longest side of a right triangle, located opposite the 90-degree angle. The hypotenuse calculator uses the Pythagorean theorem to find this length: c = √(a² + b²). This is one of the most practical calculations in geometry, used constantly in construction, navigation, and engineering. When you need to find the straight-line distance between two points that differ in both horizontal and vertical position, you are computing a hypotenuse. Carpenters use the 3-4-5 triangle to check for right angles, surveyors use it to calculate distances, and pilots use it to determine ground speed from airspeed and wind components. This calculator provides the result instantly for any pair of leg lengths.
The Math Behind It
Formula Reference
Hypotenuse
c = √(a² + b²)
Variables: a, b = legs of the right triangle
Worked Examples
Example 1: TV screen diagonal
A TV screen is 48 inches wide and 27 inches tall.
c ≈ 55.07 inches (a 55-inch TV)
Common Mistakes & Tips
- !Forgetting to take the square root — a² + b² gives c², not c.
- !Using the formula when the triangle is not a right triangle.
- !Entering the hypotenuse as one of the legs when trying to find a missing leg.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
Can the hypotenuse be shorter than a leg?
No. The hypotenuse is always the longest side of a right triangle.
Is the diagonal of a rectangle the same as a hypotenuse?
Yes. The diagonal of a rectangle forms the hypotenuse of a right triangle with the length and width as legs.
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