Triangle Calculator | Solve Angles & Sides Instantly
Solve any triangle with our free online triangle calculator. Calculate missing angles, sides, area with SSS, SAS, ASA, AAS. Real-time visualization.
Quick Presets & Special Triangles
3-4-5Right
5-12-13Right
8-15-17Right
30-60-90Special
45-45-90Special
Equilateral10-10-10
Isosceles10-10-15
Equi (25)Equilateral
ScaleneObtuse
SAS Case10, 20, 90°
ASA Case45°, 45°, 10
SSA Case10, 15, 30°
Input Measurements
Sides
Angles (Degrees)
Diagram & Analysis
Enter dimensions to visualize and analyze your triangle live.
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Fundamental Triangle Rules
Master these core geometric principles used for all triangle calculations.
Angle Sum Property
The sum of all interior angles in any triangle always equals exactly 180 degrees.
∠A + ∠B + ∠C = 180°
Law of Sines
Used to find missing sides or angles when you have "opposite pairs" (Side/Angle matches).
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines
Used to find a side when two sides and the included angle are known (SAS), or to find angles when all sides are known (SSS).
c² = a² + b² - 2ab·cos(C)
Triangle Inequality
For any triangle, the sum of the lengths of any two sides must be strictly greater than the length of the third side.
a + b > c
Side-Angle Relationship
The longest side is always opposite the largest angle, and the shortest side is opposite the smallest angle.
Longest side ↔ Largest ∠
Exterior Angle Theorem
The measure of an exterior angle is equal to the sum of the two opposite interior angles. Total exterior angles sum to 360°.
Ext ∠A = ∠B + ∠C
Classification by Sides & Angles
Equilateral
All three sides are equal in length, and all interior angles are exactly 60°.
Isosceles
At least two sides are equal in length, and the angles opposite those sides are also equal.
Scalene
All three sides have different lengths, and all interior angles have different measures.
Right Angled
Contains one interior angle that is exactly 90°, following the Pythagorean theorem.
Acute
All three interior angles are less than 90°. Most equilateral triangles are acute.
Obtuse
Contains one interior angle that is greater than 90°. Only one such angle can exist.
Our **Advanced Triangle Studio** is an all-in-one geometry engine designed for students, engineers, and DIY enthusiasts. Whether you have three sides (SSS), two sides and an angle (SAS), or any valid combination, our tool provides instant solutions including all angles, side lengths, area, perimeter, and in-depth triangle classification. Featuring a real-time SVG diagram that updates as you type, it makes geometry intuitive and visual.
How to Use
- Enter at least three values, including at least one side length.
- Watch the triangle update in real-time in the visualization panel.
- Review the complete dataset including Area, Perimeter, and Triangle Type.
- Use the "Step-by-Step" section to understand the Laws of Sines and Cosines applied.
- Use the Power Search for rapid entry (e.g., "3 4 5 sides").
- Download or share your calculation result easily.
Features
- **Real-Time Computation**: No "Calculate" button needed—results update as you type.
- **SVG Visualization**: A dynamic diagram that accurately reflects your inputs.
- **Complete Solutions**: Handles SSS, SAS, SSA, ASA, and AAS scenarios.
- **Advanced Metrics**: Calculates Area, Perimeter, Heights, and Inradius/Circumradius.
- **Triangle Classification**: Identifies if the triangle is Scalene, Isosceles, Equilateral, Right, Acute, or Obtuse.
- **Formula Breakdown**: Shows the math behind the result (Laws of Sines/Cosines).
- **History Tape**: Keeps track of your recent triangle calculations.
- **NLP Power Search**: Enter side values naturally like "sides 5 12 13".
Common Use Cases
- **Education**: Verifying geometry homework and understanding triangle properties.
- **Construction & Roof Pitch**: Calculating lengths and angles for rafters and slopes.
- **Navigation & Land Surveying**: Solving navigational triangles and boundary measurements.
- **Graphic Design**: Determining precise coordinates for triangular elements in layouts.
- **DIY Projects**: Measuring material needs for triangular shelves or garden beds.
Tips & Best Practices
**Rule of Three**: You must provide at least three measurements, and at least one must be a side length.
**Angle Limit**: The sum of any two angles must be less than 180 degrees.
**Side Limit**: The sum of any two sides must be greater than the third side (Triangle Inequality).
**Precision**: We provide results up to 4 decimal places for professional accuracy.
**Right Triangles**: If one angle is 90°, you can also use the Pythagorean theorem (a² + b² = c²).
Geometry FAQ
What is the difference between Congruent and Similar triangles?
Law of Sines vs. Law of Cosines: When to use which?
