Triangle Calculator
Please provide 3 values including at least one side to calculate the remaining triangle properties. When radians are selected as the angle unit, you can enter values such as pi/2, pi/4, etc.
Enter Triangle Values
Results
Sides
Side a: –
Side b: –
Side c: –
Angles
Angle A: –
Angle B: –
Angle C: –
Properties
Area: –
Perimeter: –
Semi-perimeter: –
Inradius: –
Circumradius: –
Triangle Classification
By sides: –
By angles: –
Triangle Properties
What is a triangle?
A triangle is a polygon with three vertices and three sides. The three vertices are points where the sides meet, and they are typically labeled as A, B, and C. The sides opposite to these vertices are labeled as a, b, and c respectively.
Triangle Classifications
By Sides:
- Equilateral Triangle: All three sides have equal lengths and all three angles are equal (60°).
- Isosceles Triangle: Two sides have equal lengths, and the angles opposite those sides are equal.
- Scalene Triangle: All three sides have different lengths and all three angles are different.
By Angles:
- Acute Triangle: All three angles are less than 90°.
- Right Triangle: One angle is exactly 90° (a right angle).
- Obtuse Triangle: One angle is greater than 90°.
Important Triangle Formulas
Area Formulas:
Basic formula with base and height: \(A = \frac{1}{2} \times b \times h\)
Heron’s formula: \(A = \sqrt{s(s-a)(s-b)(s-c)}\) where \(s = \frac{a+b+c}{2}\)
Using two sides and included angle: \(A = \frac{1}{2} \times a \times b \times \sin(C)\)
Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
Law of Cosines:
\(a^2 = b^2 + c^2 – 2bc\cos(A)\)
\(b^2 = a^2 + c^2 – 2ac\cos(B)\)
\(c^2 = a^2 + b^2 – 2ab\cos(C)\)
Angle Calculation:
\(A = \arccos\left(\frac{b^2 + c^2 – a^2}{2bc}\right)\)
\(B = \arccos\left(\frac{a^2 + c^2 – b^2}{2ac}\right)\)
\(C = \arccos\left(\frac{a^2 + b^2 – c^2}{2ab}\right)\)
Inradius:
\(r = \frac{\text{Area}}{s}\) where \(s\) is the semi-perimeter
Circumradius:
\(R = \frac{abc}{4 \times \text{Area}}\)
Triangle Facts
- The sum of all angles in a triangle is always 180° (or π radians).
- The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
- The Pythagorean theorem (a² + b² = c²) applies only to right triangles.
- The area of a triangle can be calculated using multiple formulas depending on the known values.
- Every triangle has a circumscribed circle passing through all three vertices.
- Every triangle has an inscribed circle tangent to all three sides.