Pythagorean Theorem Calculator
Calculate the missing side of a right triangle instantly with our free Pythagorean theorem calculator. Perfect for geometry homework, construction projects, and engineering calculations. Get step-by-step solutions and verify your results with common Pythagorean triples.
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What is Pythagorean Theorem Calculator?
Enter any two sides of a right triangle and this calculator finds the third side using the Pythagorean theorem. It solves for the hypotenuse when you know both legs, or for a missing leg when you know the hypotenuse and one leg. Results are instant and include the formula used for verification.
How does Pythagorean Theorem Calculator work?
An online geometry tool that applies the Pythagorean theorem to find unknown side lengths in right triangles. The theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides. Enter known values and the calculator computes the missing side, whether it is the hypotenuse or one of the legs.
Key Features
- Finds the hypotenuse from two known legs
- Finds a missing leg from the hypotenuse and one leg
- Shows the formula and calculation steps
- Supports decimal and fractional input
- Works with any unit of measurement
- Verifies the result by checking a2 plus b2 equals c2
- Instant results with no page reload
Common Use Cases
Geometry Homework
Verify your Pythagorean theorem calculations and check your work on right triangle problems assigned in math class.
Construction and Carpentry
Calculate diagonal bracing lengths, rafter spans, or ladder reach distances using right triangle measurements on the job site.
Navigation and Surveying
Find straight-line distances when you have horizontal and vertical displacement components measured separately.
CAD and Design Work
Compute diagonal distances for layout planning, panel sizing, and fitting materials at right angles.
How to Use This Tool
Identify the Known Sides
Determine which two sides of the right triangle you know. These can be the two legs, or one leg and the hypotenuse.
Enter the Values
Type the lengths of the two known sides into the input fields. Use any consistent unit of measurement.
Read the Missing Side
The calculator computes and displays the third side length along with the step-by-step calculation.
Pro Tips
- 1
The hypotenuse is always the longest side and is always opposite the 90-degree angle in a right triangle.
- 2
Common Pythagorean triples like 3-4-5, 5-12-13, and 8-15-17 are useful to memorize for quick mental checks.
- 3
Square both leg lengths, add them, and take the square root to find the hypotenuse without a calculator for simple values.
- 4
Double-check that your triangle is actually a right triangle before applying the theorem, as it only works for 90-degree angles.
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Written as a formula, a squared plus b squared equals c squared, where c is the hypotenuse and a and b are the legs.
Can I use this for non-right triangles?
No, the Pythagorean theorem only applies to right triangles with a 90-degree angle. For non-right triangles, you would need to use the law of cosines or law of sines depending on what information you have.
What are Pythagorean triples?
Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem. The most common examples are 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Any multiple of these numbers also forms a valid triple.
How do I find a missing leg instead of the hypotenuse?
Rearrange the formula to solve for the unknown leg. If you know the hypotenuse c and leg a, then b equals the square root of c squared minus a squared. This calculator handles the rearrangement automatically.
What units does this calculator support?
The calculator works with any unit of measurement including inches, feet, centimeters, meters, and more. Just enter the numbers and apply the same unit to the result. The math is unit-agnostic and applies equally to all measurement systems.
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