△ Geometry

TRIANGLE CALCULATOR

Calculate area, perimeter, all sides and angles of any triangle. Choose your method — SSS, SAS, ASA, AAS, or right triangle.

Calculation method
SSS: Enter all 3 side lengths to find all angles, area and perimeter.
Units
△
Scalene Triangle
All sides and angles are different
📐 Area——
📏 Perimeter——
All sides & angles
Side a——
Side b——
Side c——
Angle A (opp a)—degrees
Angle B (opp b)—degrees
Angle C (opp c)—degrees
Height (h_a)——
Inradius (r)——
Circumradius (R)——

Triangle formulas explained

A triangle has three sides (a, b, c) and three angles (A, B, C). The angles always sum to 180°. Knowing any three pieces of information (with at least one side) is enough to determine the complete triangle.

Heron's Area: s=(a+b+c)/2; Area=√(s·(s-a)·(s-b)·(s-c))
Law of Cosines: c²=a²+b²−2ab·cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Inradius: r = Area / s  |  Circumradius: R = abc / (4·Area)
△ SSS (3 sides)

Given all three sides, use the law of cosines to find each angle: cos(A)=(b²+c²-a²)/(2bc). Then use Heron's formula for area.

△ SAS (2 sides + angle)

Given two sides and the included angle, use the law of cosines to find the third side, then the law of sines for remaining angles.

△ ASA / AAS (angles + side)

Third angle = 180°−A−B. Then use the law of sines to find missing sides: b = a·sin(B)/sin(A).

Right △

Pythagorean theorem: c²=a²+b². Angles: tan(A)=a/b. This calculator handles legs, hypotenuse, and any two known values.

Frequently asked questions

Area = ½ × base × height. If all three sides are known, use Heron's formula: s=(a+b+c)/2, Area=√(s(s-a)(s-b)(s-c)). If you know two sides and the included angle: Area = ½ab·sin(C). This calculator handles all cases automatically.
These describe which parts of the triangle you know: SSS=three sides, SAS=two sides and the angle between them, ASA=two angles and the side between them, AAS=two angles and a non-included side. Each uniquely determines the triangle except SSA (ambiguous case).
A right triangle has one 90° angle. The side opposite the right angle is the hypotenuse (the longest side). Pythagorean theorem: a²+b²=c². All trigonometric functions are based on right triangles.
Inradius (r) is the radius of the largest circle that fits inside the triangle. Circumradius (R) is the radius of the circle that passes through all three vertices. Inradius = Area/s where s is the semi-perimeter. Circumradius = abc/(4×Area).
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