area
Find area from two legs
If you know both legs of a right triangle, multiply them and divide by 2 to get area.
Area = (a × b) / 2
Pythagorean Theorem Solver & Calculator
Solve a² + b² = c² and find any side of a right triangle in seconds.
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Enter Side Lengths
Enter any two values and click the button to calculate the third.
Result
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Calculation Summary
?² + ?² = ?²
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Right Triangle Formulas This Solver Handles
Use the calculator as an a² + b² = c² solver for side length, area, perimeter, altitude, and missing-leg checks. These compact formulas cover the most common right triangle searches.
perimeter
Find perimeter quickly
After computing the missing side, add all three sides to get the full boundary length.
Perimeter = a + b + c
altitude
Altitude to the hypotenuse
The altitude from the right angle to the hypotenuse is useful for area and similarity problems.
h = (a × b) / c
a² + b² = c²
Solve for a missing leg
When the hypotenuse and one leg are known, subtract squares and take a square root.
a = √(c² - b²), b = √(c² - a²)
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FAQ
Can I solve for any side?
Yes. Enter any two sides and the calculator finds the third.
Does it work for non-right triangles?
No, the formula applies only to right triangles.
Why is c the hypotenuse?
c is opposite the 90° angle and is always the longest side.
What is the Pythagorean Theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
a² + b² = c²
Derived Calculations: Angles, Ratios, and Scaled Triangles
You can extend Pythagorean theorem results into angle estimation and triangle scaling for practical tasks in design, drafting, and measurement.
Find an acute angle with tangent
If both legs are known, use inverse tangent to estimate one acute angle.
θ = arctan(a / b)
Find an angle with sine
If one leg and the hypotenuse are known, use inverse sine for angle solving.
θ = arcsin(a / c)
Scale any known right triangle
If (a, b, c) forms a right triangle, multiplying by the same factor keeps the triangle similar.
(ka)² + (kb)² = (kc)²
Explore related guides: Pythagorean theorem formula · How to find the hypotenuse · Pythagorean examples