Pythagorean Theorem Calculator
Solve right-triangle side lengths using the Pythagorean theorem. Enter any two valid sides and choose whether the missing value is leg a, leg b or hypotenuse c. The calculator also reports triangle area and perimeter.
How to use the Pythagorean Theorem Calculator
- Choose which side of the right triangle is unknown.
- Enter the other two positive side lengths.
- When the hypotenuse is unknown, the calculator evaluates the square root of a²+b².
- When a leg is unknown, the known leg squared is subtracted from the hypotenuse squared before taking the square root.
- The completed side lengths are used to calculate area and perimeter.
Examples
3-4-5 triangle
For legs 3 and 4, the hypotenuse is 5 because 3²+4²=5².
Find a missing leg
If c=13 and b=5, then a=sqrt(13²−5²)=12.
Area
The area of a right triangle equals one-half times the product of its two legs.
Frequently asked questions
What is the Pythagorean theorem?
For a right triangle, a²+b²=c², where c is the hypotenuse.
Which side is the hypotenuse?
The hypotenuse is the side opposite the 90-degree angle and is the longest side.
Can the theorem be used for any triangle?
The Pythagorean theorem in this form applies specifically to right triangles.
How do I find a missing leg?
Subtract the square of the known leg from the square of the hypotenuse and take the square root.
More math tools
Area Calculator
PopularCalculate area for rectangles, squares, triangles, circles, trapezoids, parallelograms, ellipses and sectors.
Open tool →Slope Calculator
PopularCalculate slope from two points plus line equation, angle, grade and point distance.
Open tool →Quadratic Formula Calculator
PopularSolve quadratic equations and find real or complex roots.
Open tool →Scientific Calculator
PopularAdvanced calculator for trig, logs, roots, powers, factorials and more.
Open tool →Percentage Calculator
PopularCalculate percentages, increases and decreases.
Open tool →Ratio Calculator
PopularSimplify ratios and find equivalent ratios.
Open tool →