Area of a Right Triangle Calculator
This calculator finds the area of a right triangle, plus its hypotenuse, perimeter and all three interior angles, from the two legs that meet at the right angle: the base and the height. Enter the base and height in the units of your choice, cm, m, mm, km, inches, feet or yards, and every result updates instantly. Area is worked out using the standard formula, half the base multiplied by the height, since a right triangle is exactly half of a rectangle with matching sides. The hypotenuse, the longest side, opposite the right angle, is calculated with the Pythagorean theorem: the square root of base squared plus height squared. From there you get the perimeter and both acute angles, worked out using arctan of the ratio between the two legs, with the right angle fixed at 90 degrees and all three angles summing to 180. A full breakdown, plus a worked example using the default values of base 6 and height 8, sits below the results so you can see how each figure was reached. This suits schoolwork, checking your own working, or practical jobs such as squaring up a wall, working out a roof pitch, or measuring rafter lengths. Make sure your base and height are entered in the same units before reading off the results, since the calculator does not convert between units.
1. Triangle Dimensions
2. Quick Reference
A right triangle has one angle of exactly 90°. The two shorter sides (legs) are called the base and height. The longest side, opposite the right angle, is the hypotenuse.
Formulae used:
Area = ½ × base × height
Hypotenuse = √(base² + height²)
Angle A = arctan(height ÷ base)
Angle B = arctan(base ÷ height)
Perimeter = base + height + hypotenuse
Full Measurements
All Angles
Worked Example (default values)
Given: base = 6 units, height = 8 units
Area = ½ × 6 × 8 = 24 units²
Hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10.00 units
Perimeter = 6 + 8 + 10 = 24.00 units
Angle A = arctan(8 ÷ 6) = arctan(1.3333) = 53.13°
Angle B = 90° − 53.13° = 36.87°