Why do I need to enter at least one side, not just angles?

Three angles alone only fix a triangle's shape, not its size, since infinitely many triangles share the same three angles at different scales. At least one side is needed to pin down the actual dimensions.

What does it mean when the calculator says no such triangle exists?

It means the values entered cannot physically form a triangle, usually because two sides do not add up to more than the third side, or the angles already add up to 180 degrees or more.

Do angles need to be in degrees or radians?

Either is fine, just select the matching option in the Angle Unit dropdown before calculating and enter every angle in that same unit.

Free Online Triangle Calculator

Q: Can two sides and a non-included angle (SSA) give more than one answer?

Yes, this is known as the ambiguous case in trigonometry, where the same three values can sometimes describe two different valid triangles. This calculator returns one valid solution.

This triangle calculator is a full triangle solver — enter any 3 known values (as long as one of them is a side) and it works out every missing side and angle, plus area, perimeter, height, median, inradius and circumradius. It's built to show you how to find the angle of a triangle and every other measurement, whether you're checking homework or solving a real geometry problem.

Triangle Calculator

Fill in any 3 fields below — including at least one side — then click Calculate.

Side a

Side b

Side c

Angle A

Angle B

Angle C

Angle Unit

Which Values Can I Enter?

Any of these combinations of 3 known values will solve the triangle:

Case	What You Know
SSS	All 3 sides
SAS	2 sides + the angle between them
ASA / AAS	2 angles + any 1 side
SSA	2 sides + an angle not between them

Enter any 3 values (including one side) and your triangle's sides, angles, area and more will appear here.

How to Find the Angle of a Triangle

A triangle has three sides and three angles, and the moment you know any three of those six values (with at least one side in the mix), the other three are locked in — there's only one way to draw that triangle. Working them out by hand comes down to two classic tools: the Law of Cosines and the Law of Sines.

Side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.

Law of Cosines (when you know all 3 sides)

A = arccos( (b² + c² − a²) ÷ 2bc )

Once you have angle A, you can find B the same way, then get C by subtracting both from 180°.

Law of Sines (when you know an angle and its opposite side)

a ÷ sin(A) = b ÷ sin(B) = c ÷ sin(C)

This is the go-to formula whenever a full side/angle pair is known and you need to solve for another.

Worked Example

Given a = 8, b = 6, c = 10, find angle C:

C = arccos( (8² + 6² − 10²) ÷ (2 × 8 × 6) )
C = arccos( 0 ) = 90°

This confirms 8–6–10 is a right triangle — a scaled-up version of the classic 3-4-5.

Types of Triangles

Triangles are usually grouped two ways — by their sides and by their angles:

Equilateral: all 3 sides (and all 3 angles) are equal
Isosceles: exactly 2 sides are equal
Scalene: no sides are equal
Right: one angle is exactly 90°
Acute: every angle is less than 90°
Obtuse: one angle is greater than 90°

How to Find the Area of a Triangle

There's more than one way to get area, depending on what you already know:

Base & height: Area = ½ × base × height
Two sides & included angle: Area = ½ × a × b × sin(C)
Heron's formula: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c) ÷ 2

For the 8–6–10 triangle above, Heron's formula gives s = 12, so Area = √(12 × 4 × 6 × 2) = √576 = 24.

Frequently Asked Questions (FAQs)

Three angles alone only fix a triangle's shape, not its size — an infinite number of triangles share the same three angles but scale up or down. At least one side is needed to pin down the actual dimensions.

It means the values you entered can't physically form a triangle — usually because two sides don't add up to more than the third (the triangle inequality), or the angles you gave already add up to 180° or more.

A median runs from a vertex to the midpoint of the opposite side. The inradius is the radius of the largest circle that fits inside the triangle, touching all three sides. The circumradius is the radius of the circle that passes through all three vertices.

Yes — this is known as the "ambiguous case" in trigonometry, where the same three values can sometimes describe two different valid triangles. This calculator returns one valid solution; if you suspect a second one exists, it's worth double-checking with a sketch.

Either is fine — just pick the matching option in the "Angle Unit" dropdown before you calculate, and enter every angle in that same unit.

Disclaimer: This calculator rounds results for display and is intended for general learning and quick checks. For engineering, construction or other work where precision matters, verify critical measurements independently.

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