Methodology
How this calculator works
The calculator rearranges a² + b² = c² for the selected unknown side. It then uses right-triangle trigonometry and standard area relationships for the supporting measurements.
Formula testedGeometry & Coordinate Math
Pythagorean Theorem Calculator
Solve a missing leg or hypotenuse and get the angles, area, perimeter, inradius and altitude of the complete right triangle.
Geometry & coordinate math
Solve a right triangle
Choose the missing side, enter the other two lengths and review sides, angles, area, perimeter, inradius and altitude.
Your entries stay in this browser and are used only for this calculation.
Right-triangle result
Enter your values
The missing side and full right-triangle breakdown will appear here.
Worked example
Reading the result
With legs 3 and 4, c = √(3² + 4²) = √25 = 5. The area is 6, the perimeter is 12 and the acute angles are about 36.87° and 53.13°.
Choose the unknown correctly
The hypotenuse is opposite the right angle
Select c only when solving for the longest side. When solving a leg, enter the other leg first and the longer hypotenuse second; the calculator validates that geometry before taking a square root.
Reference method
Right-triangle formula and distance
OpenStax derives the missing-side calculation and shows how the same theorem leads to the coordinate distance formula.
OpenStax: right-triangle trigonometryRelated geometry tools
Continue solving
Common questions
Frequently asked questions
What is the Pythagorean theorem?+
For a right triangle with legs a and b and hypotenuse c, the relationship is a² + b² = c².
How do I calculate the hypotenuse?+
Square both legs, add the results, and take the positive square root.
How do I find a missing leg?+
Subtract the square of the known leg from the square of the hypotenuse, then take the positive square root.
Why must the hypotenuse be the longest side?+
It lies opposite the 90° angle and its square equals the sum of both positive leg squares, so it must exceed either leg.
Does this calculator work for non-right triangles?+
No. Use the Triangle Calculator, which supports the laws of sines and cosines for general triangles.
Can the answer be negative?+
No. Side length uses the positive square root because geometric lengths cannot be negative.
Important scope
This theorem applies only when the angle between legs a and b is exactly 90°. Measurements with rounding or field error can produce a slightly different practical result. This calculator is for planning and education, not personal financial advice.