Side Calculations
Pythagorean Theorem Calculator
This calculator finds the hypotenuse (c) of a right triangle when you know both legs (a and b). Enter your two leg values and get the result instantly.
Pythagorean Theorem Calculator
This calculator finds Hypotenuse c using c = √(a² + b²).
Enter inputs to calculate Hypotenuse c.
Hypotenuse c
Result-
Solution Steps
Formula: c = √(a² + b²)
What This Tool Solves
Use this page when the two sides that meet at the 90° angle are known and the diagonal side is missing. The calculator focuses on the classic hypotenuse case, so the inputs stay simple and the result is easy to check.
Known values
Leg a and leg b
Finds
Hypotenuse c
Main formula
c = √a² + b²
Best for
Diagonals, ladders, ramps, screens, and geometry homework
Right Triangle Diagram: Finding the Hypotenuse
The diagram shows the exact side relationship used by the tool. The two legs are the known input values, and the slanted side c is the hypotenuse that the calculator finds.
Diagram Key
Leg a is one of the two sides that forms the right angle.
Leg b is the other side that forms the right angle.
Hypotenuse c is the longest side and sits opposite the 90° angle.
- a and b can be swapped; the hypotenuse result will be the same.
- Use the same unit for both legs before calculating.
- The answer c will always be greater than either leg in a valid right triangle.
Pythagorean Theorem Formula
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. To solve for the hypotenuse, take the square root of both sides.
In this formula, a and b are the two legs of the right triangle — the sides that form the right angle. c is the hypotenuse, the longest side, opposite the right angle. This formula only works for right triangles.
How to Use This Tool
- Identify the two legs of your right triangle. These are the sides that form the right angle.
- Enter leg a into the first input field.
- Enter leg b into the second input field.
- Click Calculate to find the hypotenuse.
- Read the result for c, along with the step-by-step solution.
Example: Find the Hypotenuse
Given: a = 6, b = 8. The hypotenuse of a right triangle with legs 6 and 8 is 10.
Where This Calculator Is Useful
The hypotenuse calculator is useful whenever two perpendicular distances combine into one diagonal distance. It is especially helpful when a drawing, floor plan, or homework problem gives the horizontal and vertical sides but leaves the diagonal side blank.
Because this page only solves for c, it avoids the confusion of switching between side modes. If your known values are the two legs, this is the focused Pythagorean theorem tool to use.
Common examples include:
- Finding the diagonal of a rectangle, screen, tile layout, or room.
- Calculating a ladder length from wall height and ground distance.
- Estimating the sloped length of a ramp from rise and run.
- Checking right triangle homework before submitting the final answer.
Input Tips for Better Results
Enter both leg lengths as positive numbers. Decimals are fine, and the calculator will keep enough precision to make the step-by-step work useful.
The two inputs must use the same unit. If a is measured in feet and b is measured in inches, convert one measurement first so the result is meaningful.
Before you calculate, check that:
- a and b are the sides that touch the 90° angle.
- Neither input is zero or negative.
- Both values are measured in the same unit.
- You are solving for the hypotenuse, not a missing leg.
How to Read the Answer
The output labeled Hypotenuse c is the side opposite the right angle. It is the diagonal side in the diagram and should be longer than both input legs.
If your result looks smaller than a or b, that is a sign that one of the inputs was mislabeled or that the triangle is not actually a right triangle.
A quick reasonableness check:
- c should be greater than a.
- c should be greater than b.
- c should be less than a + b.
- For common triples like 3-4-5 or 5-12-13, the result should match the known triple.
Common Mistakes
Most wrong hypotenuse answers come from using the right formula on the wrong sides. The legs must be the two sides that make the right angle; the hypotenuse is never an input on this page.
Another common issue is stopping at a² + b². That value is c², not c. The square root step is what turns the squared value back into the actual side length.
Avoid these mistakes:
- Using the formula on a triangle that does not have a 90° angle.
- Entering the diagonal side as a or b.
- Forgetting to take the square root at the end.
- Mixing units such as inches and feet in the same calculation.
Related Calculators
Frequently Asked Questions
Answers to the most common right-triangle solving questions.
01 What is the Pythagorean theorem? expand_more
The Pythagorean theorem is a formula that relates the three sides of a right triangle: a² + b² = c². It says that the square of the hypotenuse equals the sum of the squares of the two legs. It only applies to right triangles.
02 What does c mean in the formula? expand_more
In the formula c² = a² + b², c is the hypotenuse — the longest side of the right triangle. It’s the side directly across from the 90° angle.
03 Can I use this calculator for any triangle? expand_more
No. This calculator uses the Pythagorean theorem, which only works for right triangles. If your triangle doesn’t have a 90° angle, the formula won’t give a correct result.
04 How do I find the hypotenuse? expand_more
To find the hypotenuse, square both legs (a² and b²), add them together, and take the square root of the sum. The formula is c = √a² + b². Or just enter your values above and let the calculator do it.
05 What are a and b in a right triangle? expand_more
a and b are the two legs — the sides that form the right angle. They can be any positive length, and it doesn’t matter which one you call a or b. The hypotenuse (c) is always the remaining side.