Right Triangle Calculator: Sides, Angles & Area
Solve a right triangle from two legs, one leg and the hypotenuse, or one leg and an acute angle. The calculator returns both legs, the hypotenuse, the two acute angles, area and perimeter. One angle is always 90 degrees.
Read How to Solve a Right Triangle: Sides, Angles, Area and Perimeter for worked examples and help choosing the correct side and angle labels.
Find the hypotenuse using two legs
The legs a and b meet at a right angle. The Pythagorean theorem gives c = square root of (a squared + b squared). For Leg a 3, Leg b 4 and Length unit Feet (ft), the hypotenuse is 5 ft.
The area is a x b / 2 = 6 ft², and the perimeter is a + b + c = 12 ft. Angle A is approximately 36.869898 degrees; angle B is approximately 53.130102 degrees.
Find a missing leg
If leg a and hypotenuse c are known, b = square root of (c squared - a squared). The hypotenuse must be longer than the known leg. Leg a 3 and Hypotenuse c 5 return Leg b 4.
Equal values would produce a zero-length leg, not a valid triangle. If c is shorter than a, the measurements cannot describe a right triangle with those labels.
Solve from a leg and an acute angle
In this tool, angle A is opposite the known leg a. Therefore c = a / sin(A) and b = a / tan(A). Enter angle A in degrees, strictly between 0 and 90. If your known angle is adjacent to leg a, it is angle B in this diagram; use A = 90 - B before entering it.
For Leg a 3 and Angle A 30 degrees, c = 6 and b is approximately 5.196152 in the selected length unit. Angle B is 60 degrees. This calculator does not use radians as an input.
Units, precision and practical limits
All sides use the same length unit. Area uses that unit squared, while perimeter uses the length unit. Changing the unit or input method clears measurements to prevent a hypotenuse from being reused as an angle or a foot value from becoming an inch value.
Input sides must be between 0.000001 and 1,000,000,000. Derived sides must remain between 0.000000000001 and 1,000,000,000,000. These are numerical limits, not construction tolerances. Near-zero angles and nearly equal leg/hypotenuse inputs can be sensitive to small measurement errors.
Right triangles are not structural designs
The formulas assume an exact right angle. They do not solve every possible triangle or account for tolerances, material thickness, loads, fasteners or building codes. A geometric hypotenuse is not automatically a stair-stringer cutting length or a structural specification.
For flat-shape areas, use the Area Calculator. For planning a flight's finished rise and going, use the Stair Calculator. Calculations run locally without saving or transmitting entries; the hosting website may have separate analytics and privacy practices.
Comments
Post a Comment