Triangle Calculator

Length of Side a:
Length of Side b:
Length of Side c:
Angle A:
Angle B:
Angle C:

Area:
Perimeter:
Height of a:
Height of b:
Height of c:
Angle Bisector of a:
Angle Bisector of b:
Angle Bisector of c:
Median of a:
Median of b:
Median of c:
Inscribed Circle Radius:
Circumscribed Circle Radius:

Note: Calculation can be based on any 3 items above. If no results after click "Calculate" button, then the data provided is impossible to shape a triangle.

Calculation can be based on the coordinates of the three points of the triangle:
 
X
Y
A :
B :
C :



Note: If no results after filling in all coordinates, then the data provided is impossible to shape a triangle.


Triangle has three sides and three angles. The sum length of any two sides is longer than the length of the other side. All angles of a triangle always add up to 180 ̊C. Triangle has three types based on its three angles, including obtuse (1 angle > 90 ̊C), right (1 angle = 90 ̊C) and acute (no angle > 90 ̊C). It can be divided into three types based on three sides too, including scalene (no equal sides), equilateral (all sides equal) and isoscele (2 sides equal).



Triangle Formulas

• Law of Cosines
a2 = b2 + c2 - 2 × b × c × CosA;
b2 = a2 + c2 - 2 × a × c × CosB;
c2 = b2 + a2 - 2 × b × a × CosC;

• Area
a × b × Sin(C) / 2 or
c × b × Sin(A) / 2 or
a × c × Sin(B) / 2

• Angle Bisector of Side a
2 × b × c × Cos(A/2) / (b + c)

• Angle Bisector of Side b
2 × a × c × Cos(B/2) / (a + c)

• Angle Bisector of Side c
2 × a × b × Cos(C/2) / (a + b)

• Median of Side a ( ma )
ma2 = (2 * b2 + 2 * c2 - a2) / 4

• Median of Side b ( mb )
mb2 = (2 * a2 + 2 * c2 - b2) / 4

• Median of Side c ( mc )
mc2 = (2 * a2 + 2 * b2 - c2) / 4

• Circumscribed Circle Radius
a / ( 2 * sin (A)) or
b / ( 2 * sin (B)) or
c / ( 2 * sin (C))

• Inscribed Circle Radius
a × Sin(C/2) × Sin(B/2) / Cos (A/2) or
b × Sin(A/2) × Sin(C/2) / Cos (B/2) or
c × Sin(A/2) × Sin(B/2) / Cos (C/2)



Triangle Types

All three angles of a triangle always add up to 180 ̊C. Triangle has three types based on its three angles.
Obtuse Triangle
has an angle > 90 ̊C.
Right Triangle
has an angle = 90 ̊C.
Acute Triangle
all angles < 90 ̊C.

Triangle has three types based on the equality of its three sides.
Equilateral Triangle
all sides are equal, all angles are 60 ̊C.
Isosceles Triangle
two equal sides.
Scalene Triangle
no equal sides and angles.

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