Right Triangle Calculator
Find the missing side, area and perimeter using the Pythagorean theorem.
How to use this calculator
Choose whether you are finding the hypotenuse (the longest side, opposite the right angle) from the two shorter sides, or finding a missing shorter side from one leg and the hypotenuse. Enter the two values you know and press Calculate. The tool returns the missing side along with the triangle's area and perimeter, with the working shown. If you try to find a leg that is longer than the hypotenuse you enter, it flags the impossibility rather than returning an error.
The formula explained
Every right triangle obeys the Pythagorean theorem:
a² + b² = c² (c is the hypotenuse)
To find the hypotenuse, square the two legs, add them, and take the square root. To find a missing leg, subtract the known leg's square from the hypotenuse's square and take the square root. Because the right angle sits between the two legs, the area is simply half their product, and the perimeter is all three sides added together — both of which the calculator works out once it has the missing side.
A worked example
With legs 3 and 4: the hypotenuse is √(3² + 4²) = √(9 + 16) = √25 = 5. This famous 3-4-5 triangle has an area of ½ × 3 × 4 = 6 and a perimeter of 3 + 4 + 5 = 12. If instead you knew a leg of 3 and a hypotenuse of 5, the missing leg would be √(25 − 9) = √16 = 4.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, a² + b² = c² — the square of the hypotenuse equals the sum of the squares of the legs.
How do you find the hypotenuse?
Square the two legs, add them, and take the square root.
How do you find a missing leg?
Subtract the known leg's square from the hypotenuse's square, then take the square root.