📐

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.

✨

Measurement Parameters

Side Dimensions

cm
cm
cm

Angle Measures (Degrees)

°
°
°
Quick Presets & Special Triangles

Vector Blueprint

Enter at least 3 dimensions to solve and view the dynamic blueprint.

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.

Private Calculations: All data stays on your local browser.

Overview & Capabilities

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.

Tutorial

How to Use

01
Enter at least three values, including at least one side length.
02
Watch the triangle update in real-time in the visualization panel.
03
Review the complete dataset including Area, Perimeter, and Triangle Type.
04
Use the "Step-by-Step" section to understand the Laws of Sines and Cosines applied.
05
Use the Power Search for rapid entry (e.g., "3 4 5 sides").
06
Download or share your calculation result easily.
Capabilities

Key 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".
Applications

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.
Guidance

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).
Ecosystem

Related Tools

2D Area & Perimeter Calculator: Circle, Polygon & More

2D Area & Perimeter Calculator: Circle, Polygon & More

Fast, precise 2D shapes area and perimeter calculator. Supports circle, sector, triangle, polygon, kite & more with visual models and step-by-step math.

Professional Scientific Calculator Online

Professional Scientific Calculator Online

Free online scientific calculator. Solve complex math problems with sin, cos, tan, log, ln, roots, and more. Features NLP power search and shareable results.

🎓

GPA Calculator

Calculate your weighted, unweighted & cumulative GPA. Features multi-semester tracking, goal seeking, final grade calculation, and professional PDF reports.

Statistics Calculator

Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, and quartiles instantly. Features histogram, bell curve, CSV import, and expert report sharing.

Answers

Frequently Asked Questions

Q Can you solve a triangle with only 3 angles?

While we can determine the shape (ratios) of the triangle, we cannot determine its absolute size (side lengths) without at least one side value. In geometry, these are called "similar triangles".

Q What is the sum of angles in a triangle?

In Euclidean geometry, the sum of the three interior angles of a triangle is always exactly 180 degrees.

Q What is Heron's formula?

Heron's formula is used to find the area of a triangle when all three sides are known: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter (a+b+c)/2.

Q How do you know if a triangle exists?

For a triangle to be valid, the sum of the lengths of any two sides must be strictly greater than the length of the third side.

Q What is an Isosceles triangle?

An isosceles triangle is a triangle that has at least two sides of equal length and two equal angles opposite those sides.

Q When should I choose between the Law of Sines and the Law of Cosines?

Choose the Law of Cosines when you have an SSS (all three sides known) or SAS (two sides and their trapped included angle known) configuration. It provides a direct, unambiguous scalar path. For ASA, AAS, or SSA (where you have a matching pair of side and opposite angle), the Law of Sines is the correct choice to map relative ratios.