Right Triangle Calculator
Quickly solve any right triangle using the Pythagorean theorem or trigonometric side-angle method. Get all side lengths, angles, area, and perimeter instantly.
About This Calculator
This free online right triangle calculator solves any right triangle using either the Pythagorean theorem (when you know two sides) or trigonometric ratios (when you know one side and one acute angle). It is designed for students, teachers, engineers, and anyone who needs to quickly compute missing dimensions of a right triangle for homework, design projects, construction layouts, or geometry problems.
The calculator uses a\u00b2 + b\u00b2 = c\u00b2 for the two-sides mode, allowing you to enter any two of the three sides (leg A, leg B, or hypotenuse) to find the third. For the side-angle mode, choose the side you know (leg A, leg B, or hypotenuse), enter its length and an acute angle in degrees, and the calculator uses sin, cos, and tan trigonometric functions to compute the remaining dimensions. Results include all three side lengths (leg A, leg B, hypotenuse), both acute angles (angle A and angle B), the area, and the perimeter. A visual bar chart compares the side lengths, and a doughnut chart displays the angle distribution.
How to use
Choose between "Two Sides" mode (enter any two of side A, side B, or hypotenuse) or "Side and Angle" mode (select which side you know, enter its value and an acute angle). Click Calculate to see all properties of the right triangle instantly. Share your results via the URL which automatically saves all your input values for easy bookmarking.
Key formulas
The fundamental relationship is the Pythagorean theorem: a\u00b2 + b\u00b2 = c\u00b2, where c is the hypotenuse (the longest side opposite the right angle) and a and b are the two legs. Trigonometric ratios extend this: sin(\u03b8) = opposite/hypotenuse, cos(\u03b8) = adjacent/hypotenuse, and tan(\u03b8) = opposite/adjacent. The area is calculated as \u00bd \u00d7 base \u00d7 height, and the perimeter is the sum of all three sides.
Frequently Asked Questions
How do you find the missing side of a right triangle?
Use the Pythagorean theorem: a\u00b2 + b\u00b2 = c\u00b2, where c is the hypotenuse and a and b are the legs. If you know two sides, you can find the third. For example, if a = 3 and b = 4, then c = \u221a(3\u00b2 + 4\u00b2) = 5.
What if I know one side and one angle?
Select the Side and Angle mode. Choose which side you know (leg A, leg B, or hypotenuse), enter its length and the acute angle in degrees. The calculator uses trigonometric ratios (sin, cos, tan) to find the remaining sides and angles automatically.
What is the area formula for a right triangle?
Area = \u00bd \u00d7 base \u00d7 height. In a right triangle, the two legs are perpendicular, so you can use them directly: Area = \u00bd \u00d7 leg\u2081 \u00d7 leg\u2082.
What are the angle measures in a right triangle?
A right triangle has one 90\u00b0 angle and two acute angles that sum to 90\u00b0. Angle A is opposite side a, Angle B is opposite side b. They are computed using inverse trigonometric functions: sin\u207b\u00b9(opposite/hypotenuse).
Can I calculate perimeter too?
Yes, the perimeter is simply the sum of all three sides: a + b + c. The calculator shows the perimeter automatically when all sides are known or computed.
What is a Pythagorean triple?
A Pythagorean triple is a set of three positive integers that satisfy a\u00b2 + b\u00b2 = c\u00b2, such as (3, 4, 5) or (5, 12, 13). These integer side lengths form perfect right triangles with no decimal values.
What are 30-60-90 and 45-45-90 special right triangles?
A 30-60-90 triangle has side ratios 1:\u221a3:2, and a 45-45-90 triangle has side ratios 1:1:\u221a2. These special right triangles appear frequently in geometry, trigonometry, and standardized tests due to their predictable side proportions.
How is a right triangle used in real life?
Right triangles are used in construction for roof pitch and stair calculations, in navigation for distance and bearing measurements, in engineering for structural analysis, and in everyday tasks like finding the height of a building using its shadow length.