Missing Side Of A Right Triangle
Find the missing side of any right triangle using two known side lengths. This free Pythagorean theorem calculator computes the hypotenuse or a missing leg instantly.
Enter any two known side lengths. Leave the third blank.
About This Calculator
This free online missing side of a right triangle calculator uses the Pythagorean theorem (a\u00b2 + b\u00b2 = c\u00b2) to find any unknown side when at least two sides are known. Enter any two of the three sides (leg a, leg b, or hypotenuse c), leave the third blank, and the calculator instantly solves for the missing value. Unlike basic hypotenuse finders, this tool handles all three cases: finding the hypotenuse from two legs, finding a missing leg from the other leg and the hypotenuse, and verifying all three sides of a right triangle.
The formula behind the calculator is the Pythagorean theorem, one of the most fundamental relationships in Euclidean geometry. For a right triangle with legs a and b and hypotenuse c, the relationship is a\u00b2 + b\u00b2 = c\u00b2. To find the hypotenuse, the calculator computes c = \u221a(a\u00b2 + b\u00b2). To find a missing leg, it rearranges to a = \u221a(c\u00b2 - b\u00b2) or b = \u221a(c\u00b2 - a\u00b2). The calculator validates that the hypotenuse is the longest side and prevents impossible triangles where the hypotenuse is shorter than a leg.
Who should use this calculator? Students learning geometry, trigonometry, or the Pythagorean theorem for the first time -- it provides instant verification of homework problems. Carpenters and woodworkers calculating diagonal supports, rafter lengths, or squareness of frames. Architects and engineers designing ramps, staircases, roof trusses, or any structure involving right triangles. DIY enthusiasts measuring diagonal cuts, ladder placement, or fence bracing. Surveyors and landscapers calculating distances across rectangular plots.
Real-world applications: Find the base distance of a ladder leaning against a wall (enter ladder length as hypotenuse and wall height as leg). Calculate the diagonal of a rectangular TV screen (enter width and height as legs). Determine the correct TV or monitor diagonal to fit a given entertainment center (enter width and height openings). Measure rafter length for a roof (enter building width and desired roof pitch). Compute the shortest walking path across a rectangular field. Verify square corners in construction using the 3-4-5 triangle method -- a 3-4-5 right triangle always has a right angle and has been used by builders for millennia.
Regional notes: The Pythagorean theorem is universal and unit-agnostic. In the United States, common units include inches, feet, and yards for construction and DIY. In the UK, millimeters and meters are typical for architectural plans alongside imperial units for carpentry. In India, centimeters and meters are standard for construction and surveying, with feet still used in real estate listings. The calculator works with any consistent unit system -- simply enter all known values in the same unit.
Frequently Asked Questions
How do you find the missing side of a right triangle?
Use the Pythagorean theorem: a\u00b2 + b\u00b2 = c\u00b2. If you know two sides, you can find the third. For example, if a = 3 and b = 4, then c = \u221a(3\u00b2 + 4\u00b2) = 5. Enter any two side lengths into the calculator and it will compute the missing one.
Can I find a missing leg instead of the hypotenuse?
Yes, simply enter the other leg and the hypotenuse. The calculator rearranges the Pythagorean theorem to solve for the missing leg: a = \u221a(c\u00b2 - b\u00b2). For instance, if the hypotenuse is 10 and one leg is 6, the missing leg is \u221a(100 - 36) = 8.
What if I only know one side of a right triangle?
The Pythagorean theorem requires two known sides to find the third. If you only know one side, you need an angle as well. Use our Right Triangle Side Angle calculator which solves for missing sides from one side and one acute angle using trigonometric functions.
What units can I use with this calculator?
Any consistent unit works: inches, feet, centimeters, meters, yards, or miles. All three sides will be in the same unit you enter. Just make sure both known sides use the same unit.
What is the Pythagorean theorem formula?
The Pythagorean theorem states that in any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a\u00b2 + b\u00b2 = c\u00b2. This formula has been used for thousands of years in geometry, construction, navigation, and surveying.
How do I check if a triangle is right-angled?
A triangle is right-angled if the three sides satisfy the Pythagorean theorem: a\u00b2 + b\u00b2 = c\u00b2, where c is the longest side. Use our Is It A Right Triangle calculator to quickly verify any three side lengths.
Can I use this for a 45-45-90 triangle?
Yes. For a 45-45-90 (isosceles right) triangle, the two legs are equal and the hypotenuse equals leg \u00d7 \u221a2. Enter either leg as both Leg a and Leg b, or enter one leg and the hypotenuse to verify the other leg. Our Isosceles Right Triangle calculator handles this case specifically.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use with no registration or download required. Use it as many times as you need for homework, projects, or professional work.