This calculator computes the hypotenuse, area, and perimeter of a right triangle using the two shorter sides (legs).
The Right Triangle Calculator is a fast and accurate tool designed to help you solve all the sides and angles of a right-angled triangle. Whether you're a student, architect, or engineer, this calculator can instantly compute missing values based on any combination of inputs — including legs, hypotenuse, and angles. It simplifies trigonometry, geometry, and real-world applications by showing step-by-step solutions.
A right triangle (also called a right-angled triangle) is a triangle that has one of its angles exactly equal to 90°. The side opposite the right angle is called the hypotenuse, and the two sides adjacent to the right angle are called the legs or catheti.
The most fundamental equation for right triangles is:
c² = a² + b²
This allows you to solve for any missing side if the other two are known:
Trigonometric ratios are essential when you know one angle and one side. The calculator can use:
Inverse trigonometric functions are used to find unknown angles when sides are known:
Given: a = 3, b = 4
Find: c, angle A, angle B
Given: c = 10, angle A = 30°
Find: a, b, angle B
Area of a right triangle can be calculated using this formula:
Area = (1/2) × base × height = (1/2) × a × b
Perimeter = a + b + c
| Side a | Side b | Hypotenuse c | Angle A (°) | Angle B (°) |
|---|---|---|---|---|
| 3 | 4 | 5 | 36.87° | 53.13° |
| 6 | 8 | 10 | 36.87° | 53.13° |
| 5 | 12 | 13 | 22.62° | 67.38° |
Free Right Triangle Calculator to find missing angles, sides, area, and perimeter using Pythagorean Theorem and trigonometry. Accurate, fast, and easy to use.
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With the Right Triangle Calculator, you can instantly solve triangle problems without complex formulas or manual steps. It’s perfect for academic, professional, and everyday use — from trigonometry homework to home improvement projects. Try it out now and unlock the full power of triangle geometry!
Understanding right triangles builds a foundation for higher-level math and sciences. Here’s how students benefit from using this calculator:
This triangle has two equal angles and two equal legs. It’s an isosceles right triangle. Its side relationships are:
This triangle has angles of 30°, 60°, and 90°. Its side relationships are:
These triangle types appear frequently in standardized exams and geometry problems.
Land surveyors use right triangle trigonometry to measure distances and angles in difficult terrain using only a few known values.
Flight path optimization, line-of-sight distance, and altitude calculations all use right triangle concepts.
Motion physics, object angles, and camera tracking systems in games often use triangle-based calculations for 3D rendering and hitboxes.
Accurate layout of streets, stairs, and buildings depends on solving right triangles to ensure alignment and safety.
Problem 1: A ladder leans against a wall. The foot of the ladder is 6 ft from the wall, and the ladder reaches a height of 8 ft. What is the length of the ladder?
Solution: Use Pythagorean Theorem:
c = √(6² + 8²) = √(36 + 64) = √100 = 10 ft
Problem 2: You look up at a tree with an angle of elevation of 45°, and you're standing 20 meters away. How tall is the tree?
Solution: Use tangent: tan(θ) = height/base → tan(45°) = x / 20 → 1 = x / 20 → x = 20 m
Right triangles can also be placed on coordinate planes for solving geometry problems. The distance formula derived from the Pythagorean Theorem:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
This can be used to determine if a triangle drawn on a graph has a right angle by checking the slopes or applying the theorem between points.
All triangle angles must add up to 180°.
In a right triangle: A + B + 90° = 180° → A + B = 90°
This helps when solving for the second unknown angle after calculating the first.
Q: What if I only know the hypotenuse and one leg?
A: The calculator will use the Pythagorean Theorem to find the missing leg and apply trigonometry to calculate the angles.
Q: Can I use this to find triangle height?
A: Yes, if base and angle or base and hypotenuse are known.
Q: Is it accurate for decimals?
A: Yes, the calculator supports up to 10 decimal places for precise engineering and academic use.
Q: What if I enter invalid values?
A: The tool checks for invalid input, such as negative lengths or angles exceeding 90°.
The calculator is built to be fast, responsive, and compatible with all major browsers, including Chrome, Firefox, Safari, and Edge. It is also optimized for mobile devices, tablets, and desktops without requiring any downloads or installations.
Ready to solve right triangles the smart way? Use our Right Triangle Calculator to compute missing sides and angles instantly. Whether you're a student, engineer, or DIY enthusiast, this tool makes your triangle calculations accurate and easy!