$Triangle Calculator$

Triangle Calculator

Solve a triangle from SSS, SAS, ASA, AAS or SSA: law of sines and law of cosines, all angles, heights, medians, bisectors, radii and an existence check.

What is known:

Three sides (SSS)

Two sides and the included angle (SAS)

Side and two adjacent angles (ASA)

Side, opposite angle and another angle (AAS)

Two sides and an angle opposite one of them (SSA)

Side a

Side b

Side c

Units:

Side a is opposite angle α, b is opposite β, c is opposite γ. Angles are in degrees.

Test yourself

The triangle calculator solves a triangle from three known elements: three sides (SSS), two sides and the included angle (SAS), a side and two angles (ASA, AAS), or two sides and an angle opposite one of them (SSA). It finds all sides and angles, the perimeter, area, heights, medians, angle bisectors, inradius and circumradius, determines the type of the triangle and checks whether it exists.

Law of cosines

a² = b² + c² − 2bc · cos α

It finds the third side from two sides and the included angle, and the angles from three sides: cos α = (b² + c² − a²) / (2bc).

Law of sines

a / sin α = b / sin β = c / sin γ = 2R

It finds the sides when a side and two angles are known. With two sides and an angle opposite one of them (the ambiguous case), there may be two solutions, one or none — the calculator finds all of them.

Elements of a triangle

Element	Formula
Height	h_a = 2S / a
Median	m_a = ½√(2b² + 2c² − a²)
Angle bisector	l_a = 2bc · cos(α/2) / (b + c)
Circumradius	R = a / (2 sin α) = abc / (4S)
Inradius	r = S / p

Example. Sides 3, 4 and 5.
cos γ = (9 + 16 − 25) / 24 = 0 ⇒ γ = 90°, the triangle is right.
S = 6, R = 2.5, r = 6 / 6 = 1.

Types of triangles

By angles: acute (all angles less than 90°), right (one angle is 90°), obtuse (one angle greater than 90°). By sides: equilateral, isosceles, scalene.