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Right Triangle Calculator

Find the missing side of a right triangle with Pythagoras' theorem, plus both angles, the area and the perimeter.

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Longest side c (hypotenuse)

5

Angle opposite a
36.8699 °
Angle opposite b
53.1301 °
Area
6
Perimeter
12

A right triangle with sides 3 and 4 has a longest side of 5, and angles of 36.87° and 53.13° beside the right angle.

How it's worked out

  1. Pythagorasc = √(3² + 4²)5
  2. Angle opposite atan⁻¹(3 ÷ 4)36.8699°
  3. Area½ × 3 × 46

The formulas

c = √(a² + b²) · b = √(c² − a²) · angle = tan⁻¹(a ÷ b) · area = ½ab

Worked example

Sides of 3 and 4 give a longest side of √(9 + 16) = 5. The angles are 36.87° and 53.13°, the area is 6 and the perimeter is 12.

Questions people ask

What is Pythagoras' theorem?

In a right triangle, the square of the longest side equals the sum of the squares of the other two: a² + b² = c².

How do I find the hypotenuse?

Square the two shorter sides, add them, and take the square root. Sides 3 and 4 give √25 = 5.

How do builders check a right angle?

With the 3-4-5 rule: mark 3 units along one wall and 4 along the other. If the diagonal between the marks is exactly 5, the corner is square.

Formula and rules last checked 25 October 2026Written and tested by the CalcPenguin teamReport a problem