Triangle Calculator
Solve any triangle from any combination of sides and angles — SSS, SAS, ASA, AAS, or SSA. Uses the Law of Sines and Law of Cosines to find all unknown sides and angles, plus area, perimeter, inradius, circumradius, and triangle type. Handles the SSA ambiguous case with both solutions. Free, private, and 100% client-side. No signup required.
Select the known combination of sides and angles, enter the values, and click Solve. Supports SSS, SAS, ASA, AAS, and SSA (ambiguous case). Computes all sides, angles, area, perimeter, inradius, and circumradius with a step-by-step solution and diagram.
- Law of Cosines: c² = a² + b² − 2ab·cos(C)
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- Area (Heron): √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2
- Inradius: r = Area / s
- Circumradius: R = abc / (4 × Area)
The most complete triangle calculator online — solves all five triangle cases with full derived properties, a visual diagram, and step-by-step solutions.
All Five Triangle Cases
Solves SSS, SAS, ASA, AAS, and SSA (ambiguous case) using the Law of Sines and Law of Cosines. The triangle calculator automatically detects and displays both solutions for the SSA ambiguous case.
Complete Triangle Properties
Computes all three sides, all three angles, area (Heron's formula), perimeter, inradius, and circumradius — plus triangle type classification (scalene, isosceles, equilateral, right, acute, obtuse).
Secure Triangle Calculator Online
Every calculation runs entirely in your browser using client-side JavaScript. Your inputs never leave your device — complete privacy, zero server uploads, no tracking.
100% Free — No Signup Required
The triangle calculator is completely free with no account, no ads, and no usage limits. Solve as many triangles as you need, any time, on any device.
See how students, engineers, surveyors, and designers use the triangle calculator in their daily work.
Geometry Homework & Exams
Students use the triangle calculator to verify homework answers and understand the step-by-step application of the Law of Sines and Law of Cosines. The solution breakdown shows every formula substitution.
Architecture & Construction
Architects and builders use the triangle calculator to find unknown dimensions in roof trusses, rafter lengths, and structural bracing. Enter two sides and the included angle (SAS) to find the third side instantly.
Engineering & Technical Drawing
Mechanical engineers use the triangle calculator to solve force triangles, vector decomposition, and geometric constraints in CAD drawings. The circumradius and inradius are useful for fitting circles to triangular components.
Surveying & Navigation
Surveyors use the triangle calculator to compute distances and bearings using triangulation. Enter two angles and the baseline distance (ASA) to find the distances to a remote point.
Trigonometry & Pre-Calculus
Teachers and students use the triangle calculator to explore the SSA ambiguous case — the only triangle configuration that can produce zero, one, or two valid solutions. The calculator shows both solutions when they exist.
Game Development & Computer Graphics
Game developers and 3D artists use the triangle calculator to compute angles and distances for collision detection, mesh generation, and procedural geometry. The inradius and circumradius are useful for bounding circle calculations.
A complete reference guide to the five triangle cases, the laws used to solve them, and the derived properties computed by the triangle calculator.
What is Triangle Solving?
Triangle solving is the process of finding all unknown sides and angles of a triangle from a given set of known values. A triangle has six elements — three sides (a, b, c) and three angles (A, B, C) — and any three of these (with at least one being a side) are sufficient to determine the triangle uniquely, except in the SSA ambiguous case which may produce two valid solutions. The triangle calculator uses the Law of Cosines for SSS and SAS cases, and the Law of Sines for ASA, AAS, and SSA cases.
How Our Triangle Calculator Works
- 1Select your case: Choose the combination of known values — SSS, SAS, ASA, AAS, or SSA. The input fields update automatically to match the selected case.
- 2Enter your values: Type the known sides (any positive number) and angles (0°–180°). All calculations run locally in your browser — your inputs never leave your device.
- 3Read the full solution: The triangle calculator shows all sides, angles, area, perimeter, inradius, circumradius, triangle type, a visual diagram, and a step-by-step solution.
What Gets Computed
- Area (Heron's Formula): Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2 is the semi-perimeter.
- Inradius (r): The radius of the inscribed circle: r = Area / s. The incircle touches all three sides.
- Circumradius (R): The radius of the circumscribed circle: R = abc / (4 × Area). The circumcircle passes through all three vertices.
- Triangle Type: Classified by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse).
SSS & SAS (Law of Cosines)
SSS: three sides → find angles using c² = a² + b² − 2ab·cos(C). SAS: two sides and included angle → find the third side, then use Law of Sines for the remaining angles.
ASA & AAS (Law of Sines)
ASA: two angles and included side → find the third angle (C = 180°−A−B), then use a/sin(A) = c/sin(C). AAS: two angles and non-included side → same approach.
SSA (Ambiguous Case)
Two sides and a non-included angle may produce 0, 1, or 2 valid triangles. The triangle calculator checks sin(B) = b·sin(A)/a and shows both solutions when they exist.
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A triangle calculator is a tool that solves a triangle — finding all unknown sides and angles — from any valid combination of known values. Our triangle calculator supports SSS, SAS, ASA, AAS, and SSA cases using the Law of Sines and Law of Cosines, and also computes area, perimeter, inradius, and circumradius. It runs entirely in your browser with no signup required.
SSS = three sides known. SAS = two sides and the included angle. ASA = two angles and the included side. AAS = two angles and a non-included side. SSA = two sides and a non-included angle (ambiguous case). Any of these combinations uniquely determines a triangle, except SSA which may produce two solutions.
The SSA case (two sides and a non-included angle) is called ambiguous because it can produce zero, one, or two valid triangles. When sin(B) = b·sin(A)/a is between 0 and 1, there are two possible values for angle B (B and 180°−B), each potentially giving a valid triangle. The triangle calculator checks both and displays all valid solutions.
The Law of Cosines states: c² = a² + b² − 2ab·cos(C). It generalizes the Pythagorean theorem to any triangle. It is used to find the third side when two sides and the included angle are known (SAS), or to find angles when all three sides are known (SSS).
The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C). It relates each side to the sine of its opposite angle. It is used to find unknown sides and angles in ASA, AAS, and SSA cases.
The inradius (r) is the radius of the largest circle that fits inside the triangle, touching all three sides. Formula: r = Area / s, where s is the semi-perimeter. The circumradius (R) is the radius of the circle that passes through all three vertices. Formula: R = abc / (4 × Area).
The triangle calculator uses Heron's formula: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2 is the semi-perimeter. This formula works for any triangle given all three sides, and is numerically stable for all triangle shapes.
Yes, completely. All calculations are performed locally in your web browser using client-side JavaScript. No inputs, results, or steps are ever sent to any server. Your data stays entirely on your device.
Yes. The triangle calculator is 100% free with no account registration, no payment, and no usage limits. Solve as many triangles as you need, any time, on any device.