What is a Triangle Calculator?

A Triangle Calculator is a tool that computes all unknown properties of a triangle — including sides, angles, area, perimeter, heights, medians, inradius, and circumradius — given at least 3 known values with at least one side.

How do I use the Triangle Calculator?

Enter at least 3 values into the side and angle fields, select your preferred angle unit (degrees or radians), then click Calculate. The tool will solve the triangle and display a full breakdown of all geometric properties.

What triangle configurations does the calculator support?

The calculator supports SSS (three sides), SAS (two sides and included angle), AAS (two angles and a side), ASA (two angles and included side), and SSA (two sides and non-included angle) configurations.

Why is my triangle showing as invalid?

A triangle is invalid if the angles do not sum to 180°, if a side or angle value is zero or negative, or if the given combination of values is geometrically impossible. Double-check your inputs for typos or inconsistencies.

Is the Triangle Calculator free to use?

Yes. The Triangle Calculator is completely free and instantly solves any triangle configuration, providing detailed results including area, perimeter, heights, medians, inradius, circumradius, and a visual diagram.

Triangle Calculator

A smart triangle calculator that solves any triangle configuration and displays detailed geometric results with visual charts.

Triangle Calculator

Get instant, accurate results

What is this?

A Triangle Calculator is a mathematical tool used to calculate the unknown sides, angles, area, perimeter, heights, medians, inradius, and circumradius of a triangle. It supports all triangle configurations including SSS, SAS, AAS, ASA, and SSA using the Law of Sines and Law of Cosines.

How to Use the Triangle Calculator

A triangle calculator helps you solve any triangle by computing unknown sides, angles, area,
perimeter, heights, medians, inradius, and circumradius. Triangles are fundamental shapes used
in mathematics, engineering, architecture, physics, and navigation.

The calculator processes your inputs using the Law of Sines and Law of Cosines and instantly
returns a complete geometric breakdown of the triangle along with a visual diagram and charts.

1. Enter at Least 3 Values

Input at least 3 known values into the side and angle fields. You must include at least
one side length. Accepted configurations include SSS, SAS, AAS, ASA, and SSA.

2. Select Your Angle Unit

Choose between degrees or radians depending on your use case. Degrees are standard for
everyday geometry while radians are preferred in scientific and engineering contexts.

3. Click Calculate

Submit the form to let the calculator solve the triangle. It will automatically detect
the configuration and compute all remaining sides, angles, and geometric properties.

4. Review the Results

Examine the full results including all sides, angles, area, perimeter, heights, medians,
inradius, circumradius, vertex coordinates, and visual bar charts for comparison.

Key Formulas Used in the Calculator

Law of Cosines

a² = b² + c² − 2bc·cos(A)

Used to find an unknown side when two sides and the included angle are known (SAS), or to find angles when all three sides are known (SSS). It generalizes the Pythagorean theorem.

Law of Sines

a / sin(A) = b / sin(B) = c / sin(C)

Used to find unknown sides or angles when two angles and a side are known (AAS or ASA), or when two sides and a non-included angle are known (SSA).

Triangle Area (Heron's Formula)

Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c) / 2

Computes the area of any triangle using all three side lengths without needing the height. The variable s is the semi-perimeter of the triangle.

Inradius

r = Area / s

The inradius is the radius of the largest circle that fits inside the triangle, touching all three sides. It is calculated by dividing the area by the semi-perimeter.

Circumradius

R = (a × b × c) / (4 × Area)

The circumradius is the radius of the circle that passes through all three vertices of the triangle. It is computed using all three sides and the triangle area.

Benefits

Solves all triangle types — equilateral, isosceles, scalene, right, obtuse, and acute
Supports SSS, SAS, AAS, ASA, and SSA configurations
Displays angles in both degrees and radians simultaneously
Computes area, perimeter, heights, medians, inradius, and circumradius
Shows vertex coordinates and circle center positions
Provides visual triangle diagram and comparison bar charts
Instantly detects and labels the triangle type

When & Where to Use

Solving geometry homework and exam problems
Calculating roof pitch and structural angles in construction
Determining distances and bearings in navigation and surveying
Designing architectural layouts and floor plans
Computing forces and vectors in physics and engineering
Creating 3D models and game development assets
Teaching and demonstrating triangle properties in classrooms

Who Should Use This Calculator

The Triangle Calculator is ideal for students studying geometry and trigonometry, engineers and architects working with structural designs, surveyors calculating land measurements, game developers building 2D and 3D environments, and teachers demonstrating triangle properties. Anyone who needs to quickly and accurately solve a triangle will benefit from this tool.

Tips to Get the Best Deal

Always include at least one side — angles alone cannot define a unique triangle size.

The three angles of any triangle must always sum to exactly 180°.

For right triangles, use the Pythagorean theorem as a quick verification check.

SSA (two sides and a non-included angle) may produce two solutions — the ambiguous case.

Switch to radian mode when working with calculus or trigonometric functions.

Heights, medians, and angle bisectors all coincide only in equilateral triangles.

Use vertex coordinates to plot or reconstruct the triangle on a coordinate plane.

Frequently Asked Questions (FAQs)

Helpful Resources

Pro Tips

Always provide at least one side length — the triangle cannot be solved with angles alone.
The sum of all three angles must equal 180°. The calculator will alert you if values are inconsistent.
If two sides and a non-included angle are given (SSA), there may be two possible triangles or none.
Use degree mode for everyday calculations and radian mode for scientific or engineering use.
Slope and side ratios of similar triangles remain constant — useful for scaling problems.