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Right Triangle Calculator

Calculate all properties of a right triangle including sides, angles, area, perimeter, and more. Enter any two known values and get complete triangle information with step-by-step solutions.

Triangle Properties

Sides

Angles

Note: Angle C is always 90° (π/2 radians) in a right triangle

Quick Examples:

Triangle Visualization

Enter at least two values to see the triangle

How to Use This Calculator

1
Enter Known Values
Input any two known values from sides (a, b, c) or angles (A, B). You need at least two values to solve the triangle.
2
Choose Units
Select your preferred units for length measurements and angles (degrees or radians).
3
View Results
The calculator will automatically compute all missing values and display the triangle with complete properties.
4
Use Quick Examples
Try the quick example buttons to see common right triangle configurations like 3-4-5 or 45-45-90 triangles.

Right Triangle Theory

What is a Right Triangle?

A right triangle is a triangle with one angle measuring exactly 90 degrees (π/2 radians). The side opposite to the right angle is called the hypotenuse and is always the longest side. The other two sides are called legs.

Key Properties

  • One angle is always 90°
  • The sum of the other two angles is 90°
  • The Pythagorean theorem applies: a² + b² = c²
  • The hypotenuse is always the longest side
  • The area equals (1/2) × leg₁ × leg₂

Special Right Triangles

45-45-90 Triangle:
Sides are in ratio 1 : 1 : √2
30-60-90 Triangle:
Sides are in ratio 1 : √3 : 2
Pythagorean Triples:
Common integer ratios like 3:4:5, 5:12:13, 8:15:17

Trigonometric Functions

sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent

Example Calculations

Example 1: Given Two Legs

Find all properties of a right triangle with legs a = 6 cm and b = 8 cm:

c = √(a² + b²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm
Area = (1/2) × a × b = (1/2) × 6 × 8 = 24 cm²
Angle A = arctan(a/b) = arctan(6/8) = 36.87°
Angle B = arctan(b/a) = arctan(8/6) = 53.13°

Example 2: Given Hypotenuse and One Leg

Find the missing leg when c = 13 m and a = 5 m:

b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12 m
Area = (1/2) × 5 × 12 = 30 m²
Perimeter = 5 + 12 + 13 = 30 m

Example 3: Given One Side and One Angle

Find all sides when a = 10 ft and angle A = 30°:

c = a / sin(A) = 10 / sin(30°) = 10 / 0.5 = 20 ft
b = a / tan(A) = 10 / tan(30°) = 10 / 0.577 = 17.32 ft
Angle B = 90° - 30° = 60°

Frequently Asked Questions

How many values do I need to solve a right triangle?

You need at least two values to solve a right triangle, but they can't be any two values. Valid combinations include: two sides, one side and one acute angle, or the hypotenuse and one other value.

What's the difference between legs and hypotenuse?

The legs are the two shorter sides that form the right angle, while the hypotenuse is the longest side opposite the right angle. In our calculator, sides A and B are legs, and side C is the hypotenuse.

Can I use this calculator for non-right triangles?

No, this calculator is specifically designed for right triangles (triangles with a 90° angle). For general triangles, you would need a different calculator that uses the law of cosines and law of sines.

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