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Triangle Calculator

Enter any 3 values (sides and angles) and get everything β€” all sides, angles, area, perimeter, heights, and a visual diagram

Opposite angle A
Opposite angle B
Opposite angle C
Opposite side a
Opposite side b
Opposite side c

About This Tool

Need to find a missing side, angle, or the area of a triangle? This calculator solves any triangle from just three known values. Enter any valid combination β€” three sides (SSS), two sides and an angle (SAS or SSA), two angles and a side (ASA or AAS) β€” and it computes everything else instantly. You get all three sides and angles, area, perimeter, all three heights, the inradius and circumradius, plus a scaled SVG diagram of your triangle. It automatically classifies the triangle type (right, acute, obtuse, equilateral, isosceles, scalene) and shows which formula was used for the solution. Works in degrees or radians. Handles the ambiguous case (SSA) and warns you when the triangle is impossible.

How to Use

1. Enter exactly 3 values in any combination of sides (a, b, c) and angles (A, B, C) 2. Angle A is opposite side a, angle B is opposite side b, angle C is opposite side c 3. The calculator auto-detects the case (SSS, SAS, ASA, etc.) 4. All missing values, area, and properties appear instantly 5. Toggle between degrees and radians 6. Click "Copy Link" to share your triangle

Frequently Asked Questions

How do I find the missing side of a triangle?
It depends on what you know. With two sides and the included angle (SAS), use the Law of Cosines: cΒ² = aΒ² + bΒ² βˆ’ 2abΒ·cos(C). With two angles and a side (AAS/ASA), use the Law of Sines: a/sin(A) = b/sin(B). With a right triangle, use the Pythagorean theorem: aΒ² + bΒ² = cΒ². This calculator handles all cases automatically.
How do I calculate the area of a triangle?
The most common formula is Area = Β½ Γ— base Γ— height. If you know all three sides, use Heron's formula: Area = √[s(sβˆ’a)(sβˆ’b)(sβˆ’c)] where s = (a+b+c)/2. If you know two sides and the included angle: Area = Β½Β·aΒ·bΒ·sin(C). This calculator uses whichever formula fits your inputs.
What is the Law of Cosines?
The Law of Cosines generalizes the Pythagorean theorem: cΒ² = aΒ² + bΒ² βˆ’ 2abΒ·cos(C). It's used to find a missing side when you know two sides and the included angle (SAS), or to find angles when you know all three sides (SSS).
What is the Law of Sines?
The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C). It's used to find missing sides or angles when you know a side-angle pair plus one more value (ASA, AAS, or SSA cases).
What is the ambiguous case (SSA)?
When you know two sides and a non-included angle, there may be zero, one, or two valid triangles. For example, if a = 8, b = 6, and A = 30Β°, there could be two different triangles that satisfy these conditions. This calculator detects and warns about the ambiguous case.
What are the inradius and circumradius?
The inradius (r) is the radius of the largest circle that fits inside the triangle (inscribed circle). The circumradius (R) is the radius of the circle that passes through all three vertices (circumscribed circle). Formulas: r = Area/s and R = a/(2Β·sin(A)), where s is the semi-perimeter.

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