Triangle Calculator

Q: What is the difference between degrees, radians, and gradians?

These are three ways to measure angles. Degrees split a full circle into 360 parts. Radians split it into 2π parts (about 6.283). Gradians split it into 400 parts. A straight line is 180°, π radians, or 200 gradians. Pick the unit you are working with before entering angle values.

Q: Which side is opposite which angle?

Side a is always opposite angle A . Side b is opposite angle B . Side c is opposite angle C . You can click the labels on the triangle diagram to jump to the matching input field.

Q: What does the computed tag mean next to a field?

A field marked computed means the calculator figured out that value from your other inputs. These fields are highlighted with a light purple background so you can easily tell which values you entered and which ones were calculated.

Q: What are the heights shown in the results?

A height (or altitude) is the shortest distance from a vertex straight down to the opposite side at a 90° angle. The calculator shows three heights: from vertex A down to side a, from B down to side b, and from C down to side c. Each height equals 2 × area ÷ the base side length.

Q: What is the inradius and circumradius?

The inradius is the radius of the largest circle that fits perfectly inside the triangle, touching all three sides. The circumradius is the radius of the circle that passes through all three corners of the triangle. Both are calculated automatically once the triangle is solved.

Q: What are medians?

A median is a line drawn from one corner of the triangle to the exact middle of the opposite side. Every triangle has three medians. They all cross at a single point called the centroid. The calculator shows the length of each median.

Q: Why do my three angles not add up correctly?

In any triangle, the three angles must add up to exactly 180° (or π radians, or 200 gradians). If you enter all three angles and their sum is off, the calculator will show an error. Check your values or enter only two angles and let the calculator find the third.

Q: What do the charts show?

The Angle Distribution chart is a donut chart that shows how the three angles compare in size. The Side Lengths Comparison chart is a bar chart that compares the three side lengths. Both charts update based on Solution 1.

Triangle Calculator

Updated Sep 1, 2026 By Jehan Wadia

Introduction

A triangle has six main parts: three sides and three angles. If you know at least three of these parts (with at least one side), you can find the rest. This triangle calculator does that work for you. Enter any three known values, and it will solve the triangle in full. You get all missing sides, angles, area, perimeter, heights, medians, inradius, and circumradius. It handles every case: SSS, SAS, ASA, AAS, and even the tricky SSA ambiguous case where two valid triangles can exist. You can work in degrees, radians, or gradians. Results update instantly with a diagram and charts so you can see the triangle you just solved.

How to Use Our Triangle Calculator

Enter any 3 known values of a triangle (at least 1 must be a side), and the calculator will find all missing sides, angles, area, perimeter, and more.

Angle Unit: Pick degrees, radians, or gradians. This sets how angle values are read and shown.

Angle A: Enter the angle at vertex A. This is the angle across from side a.

Angle B: Enter the angle at vertex B. This is the angle across from side b.

Angle C: Enter the angle at vertex C. This is the angle across from side c.

Side a: Enter the length of side a. This is the side across from angle A.

Side b: Enter the length of side b. This is the side across from angle B.

Side c: Enter the length of side c. This is the side across from angle C.

Calculate: Click this button to solve the triangle. All missing values will be computed and highlighted.

Reset: Click this button to clear your inputs and start over with the default example.

Triangle Calculator – Solve Any Triangle

A triangle is a shape with three straight sides and three angles. The three angles of any triangle always add up to 180 degrees. Each side of a triangle is opposite to one angle. The side across from angle A is called side a, the side across from angle B is called side b, and the side across from angle C is called side c.

How to Solve a Triangle

To fully solve a triangle means to find all three sides and all three angles. You need to know at least three values to do this, and at least one of them must be a side. Three angles alone tell you the shape but not the size. The most common ways to solve a triangle are:

SSS (Side-Side-Side): All three sides are known. The angles are found using the law of cosines.
SAS (Side-Angle-Side): Two sides and the angle between them are known.
ASA or AAS (Angle-Angle-Side): Two angles and one side are known. The third angle is found by subtracting from 180°.
SSA (Side-Side-Angle): Two sides and an angle not between them are known. This can sometimes give two valid answers, called the ambiguous case.

Key Formulas Used

The law of sines says that a/sin(A) = b/sin(B) = c/sin(C). This links each side to the angle across from it. The law of cosines says that c² = a² + b² − 2ab·cos(C). It works like an extended version of the Pythagorean theorem for all triangles, not just right triangles.

Triangle Properties

Once all sides and angles are known, you can find many other useful values. The area is found using ½·a·b·sin(C). The perimeter is the sum of all three sides. The inradius is the radius of the largest circle that fits inside the triangle. The circumradius is the radius of the circle that passes through all three corners. Medians are lines from each corner to the middle of the opposite side. You can find the midpoint of any side to locate where a median meets that side. Heights (or altitudes) are lines from each corner straight down to the opposite side at a right angle.

Types of Triangles

Triangles are grouped by their angles and sides. An acute triangle has all angles less than 90°. A right triangle has one angle equal to 90°. An obtuse triangle has one angle greater than 90°. A scalene triangle has all sides of different lengths. An isosceles triangle has two equal sides. An equilateral triangle has all three sides equal and all angles equal to 60°.

Formulas used

Law of Cosines (find side)

c = \sqrt{a^2 + b^2 - 2ab\cos C}

Law of Cosines (find angle)

A = \arccos\!\left(\frac{b^2 + c^2 - a^2}{2bc}\right)

Law of Sines

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Area

\text{Area} = \frac{1}{2}\,a\,b\,\sin C

Inradius

r = \frac{\text{Area}}{s}, \quad s = \frac{a+b+c}{2}

Circumradius

R = \frac{a}{2\sin A}

Median

m_a = \frac{1}{2}\sqrt{2b^2 + 2c^2 - a^2}

Height (Altitude)

h_a = \frac{2\,\text{Area}}{a}

Frequently asked questions

What does the ambiguous case mean?

The ambiguous case happens when you enter two sides and an angle that is not between them (SSA). With these inputs, there can be two different valid triangles that match your numbers. The calculator finds both and shows them as Solution 1 and Solution 2 so you can pick the one you need.

What is the difference between degrees, radians, and gradians?

These are three ways to measure angles. Degrees split a full circle into 360 parts. Radians split it into 2π parts (about 6.283). Gradians split it into 400 parts. A straight line is 180°, π radians, or 200 gradians. Pick the unit you are working with before entering angle values.

Which side is opposite which angle?

Side a is always opposite angle A. Side b is opposite angle B. Side c is opposite angle C. You can click the labels on the triangle diagram to jump to the matching input field.

What does the computed tag mean next to a field?

A field marked computed means the calculator figured out that value from your other inputs. These fields are highlighted with a light purple background so you can easily tell which values you entered and which ones were calculated.

What are the heights shown in the results?

A height (or altitude) is the shortest distance from a vertex straight down to the opposite side at a 90° angle. The calculator shows three heights: from vertex A down to side a, from B down to side b, and from C down to side c. Each height equals 2 × area ÷ the base side length.

What is the inradius and circumradius?

The inradius is the radius of the largest circle that fits perfectly inside the triangle, touching all three sides. The circumradius is the radius of the circle that passes through all three corners of the triangle. Both are calculated automatically once the triangle is solved.

What are medians?

A median is a line drawn from one corner of the triangle to the exact middle of the opposite side. Every triangle has three medians. They all cross at a single point called the centroid. The calculator shows the length of each median.

Why do my three angles not add up correctly?

In any triangle, the three angles must add up to exactly 180° (or π radians, or 200 gradians). If you enter all three angles and their sum is off, the calculator will show an error. Check your values or enter only two angles and let the calculator find the third.

What do the charts show?

The Angle Distribution chart is a donut chart that shows how the three angles compare in size. The Side Lengths Comparison chart is a bar chart that compares the three side lengths. Both charts update based on Solution 1.

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