Three sides known
Ready to solve
Enter known values and click Calculate// solve any triangle — sides, angles, area, perimeter
Free online triangle calculator. Find missing sides, angles, area, and perimeter from any combination of known values using SSS, SAS, ASA, AAS, or SSA methods.
Ready to solve
Enter known values and click CalculateChoose SSS, SAS, ASA, AAS, or SSA based on what values you already know.
Fill in the side lengths and/or angles shown for that method. Leave unknowns blank.
All missing sides, angles, area, and perimeter are computed instantly.
A triangle calculator solves for unknown sides and angles using trigonometric laws. Given any combination of three known values (sides or angles), all remaining properties can be determined using the Law of Sines, Law of Cosines, or basic angle-sum rules.
SSS (Side-Side-Side) is used when all three sides are known. The Law of Cosines is applied to find each angle: cos(A) = (b² + c² − a²) / (2bc).
SAS (Side-Angle-Side) requires two sides and the angle between them. The Law of Cosines finds the third side, then the Law of Sines resolves the remaining angles.
SSA (Side-Side-Angle) gives two sides and an angle not between them. This is the "ambiguous case" — depending on the values, there may be 0, 1, or 2 valid triangles.
Angles are entered and displayed in degrees. Side lengths can be any consistent unit (cm, m, inches, etc.) — the calculator does not convert units, so use the same unit for all sides.
Area is computed using Heron's formula: Area = √(s(s−a)(s−b)(s−c)) where s is the semi-perimeter. Alternatively, Area = ½ · a · b · sin(C) when two sides and the included angle are known.
ASA requires two angles and the side between them. AAS requires two angles and a non-included side. Both use the angle-sum rule (A+B+C=180°) and the Law of Sines to find all unknowns.
The calculator identifies equilateral (all sides equal), isosceles (two sides equal), scalene (no equal sides), right (one 90° angle), acute (all angles under 90°), and obtuse (one angle over 90°) triangles.
If the values are geometrically impossible (e.g., one side longer than the sum of the other two, or angles not summing to 180°), the calculator will show a clear error message explaining the issue.
Whether you're a student working through geometry homework, an engineer laying out a design, or a developer computing collision polygons, our free triangle calculator handles every case. Enter any three known values — sides, angles, or a mix — and instantly get all missing measurements including area and perimeter.
💡 Looking for premium web development assets? MonsterONE offers unlimited downloads of templates, UI kits, and math/science educational assets — worth checking out.
Triangles have six properties: three sides (a, b, c) and three angles (A, B, C). Knowing any three — as long as at least one is a side — is enough to determine the rest. The five standard cases are:
The Law of Cosines generalizes the Pythagorean theorem to all triangles: a² = b² + c² − 2bc·cos(A). It's used for SSS and SAS cases. When A = 90°, it reduces to the familiar a² = b² + c².
The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C). This ratio equals the diameter of the triangle's circumscribed circle. It's the go-to formula for ASA, AAS, and the second step of SSA resolution.
Once all sides are known, perimeter is simply a + b + c. Area uses Heron's formula: first compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s · (s−a) · (s−b) · (s−c)). When two sides and an included angle are known, the equivalent formula Area = ½ · a · b · sin(C) is faster.
Triangles are classified by their sides and angles. By sides: equilateral (a = b = c, all angles 60°), isosceles (two equal sides), or scalene (no equal sides). By angles: acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°). Our calculator automatically identifies the type from the solved values.
SSA is the trickiest case. Given sides a and b and angle A (opposite to a), three scenarios arise. If a < b·sin(A), no triangle exists. If a = b·sin(A), exactly one right triangle exists. If a > b·sin(A) and a < b, two triangles exist (the second has angle B₂ = 180° − B₁). If a ≥ b, exactly one triangle exists. Our calculator detects all cases and reports both solutions when applicable.
Triangle calculations appear across many disciplines. In construction and architecture, roof pitch, truss angles, and land boundary surveys all rely on triangle geometry. In navigation, triangulation uses known distances between fixed points to determine position. In physics and engineering, force vector decomposition, structural load analysis, and optics problems reduce to triangle problems. In game development, polygon collision detection, raycasting, and pathfinding algorithms all use triangle math.
Use consistent units across all side inputs — mixing meters and centimeters will produce incorrect results. For angles, this tool accepts decimal degrees (e.g., 45.5° instead of 45° 30'). If you have degrees, minutes, and seconds, convert first: decimal degrees = degrees + minutes/60 + seconds/3600. For maximum precision, enter side values to at least 4 significant figures.