Triangle Calculator | Solve Sides, Angles, Area & Perimeter

The Triangle Solver — your complete triangle calculator — makes solving any triangle fast and accurate. Whether you need to find the area of a triangle, calculate missing sides and angles using the law of sines or law of cosines, verify the Pythagorean theorem in a right triangle, or explore triangle properties like inradius, circumradius, centroid, incenter or circumcenter, this free tool has you covered.

Perfect for students studying triangle formulas for board exams, engineers calculating rafter lengths, surveyors using triangulation, or anyone needing quick area of triangle results. Our triangle solver supports SSS, SAS, ASA, AAS, SSA (including the ambiguous case), computes Heron's formula using the semi-perimeter, and displays triangle area, incircle, circumcircle radius and more. No registration, mobile-friendly, offline-capable after first load, and completely ad-free. Start solving now on our Triangle Calculator page.

How to Solve Any Triangle Using Our Tool

Input Side Lengths and Angles – Works for All Triangle Types

Enter sides a, b, c (opposite angles A, B, C) and/or angles. The triangle calculator automatically detects SSS, SAS, ASA, AAS or SSA cases and solves using law of sines, law of cosines or Pythagorean theorem for right-angled triangles.

SAS – Two Sides and Included Angle

Classic case for roof pitch or vector problems. Uses law of cosines to find third side.

c² = a² + b² − 2ab cos C

SSS – Three Sides → Find All Angles & Area

Great for land surveying or checking triangle inequality. Tool computes angles, triangle area via Heron's formula (using semi-perimeter), inradius and circumradius.

Why at least one side is required

Pure angle input (AAA) only gives similar triangles. One side is needed to determine actual size and compute triangle area, circumradius, inradius, etc.

Essential Triangle Formulas & Properties

Heron's Formula – Area of Triangle

Area = √[s(s−a)(s−b)(s−c)] where semi-perimeter s = (a+b+c)/2

Area of triangle = √[s(s − a)(s − b)(s − c)]

Law of Sines

a / sin A = b / sin B = c / sin C = 2R

R = circumradius of the circumcircle

Law of Cosines

c² = a² + b² − 2ab cos C

Reduces to Pythagorean theorem when C = 90° in a right-angled triangle.

Inradius & Circumradius

Inradius r = Area / s
Circumradius R = abc / (4 × Area)

Triangle Properties – Acute, Obtuse, Right, Isosceles & Equilateral

Right-Angled Triangle & Pythagorean Theorem

In a right triangle (one angle = 90°), Pythagorean theorem applies: a² + b² = c² (c = hypotenuse).

Isosceles Triangle & Equilateral Triangle

Isosceles triangle: two equal sides → two equal base angles.
Equilateral triangle: all sides equal, all angles 60°, height = (√3/2) × side.

Acute, Right & Obtuse Triangle Classification

Largest angle opposite longest side:
• All angles < 90° → acute triangle
• One angle = 90° → right triangle
• One angle > 90° → obtuse triangle

Triangle Inequality & Troubleshooting

Triangle Inequality Theorem

For any triangle: sum of any two sides must be greater than the third side.

  • a + b > c
  • a + c > b
  • b + c > a

Example: sides 2, 3, 6 → 2 + 3 = 5 < 6 → cannot form a triangle.

Ambiguous Case (SSA)

Two sides + non-included angle may produce 0, 1 or 2 possible triangles. Our triangle solver detects and shows all valid solutions.

Practical Uses of the Triangle Calculator

  • Construction: roof pitch, rafter length, checking right triangle corners
  • Surveying & Navigation: triangulation with law of sines
  • School / College: area of triangle, Heron's formula, Pythagorean theorem problems
  • Physics: resolving forces, projectile angles

More Math Tools to Explore

Master every triangle property — from equilateral triangle symmetry to obtuse triangle calculations — with our free, accurate triangle solver. Bookmark this triangle calculator today and solve geometry problems faster in whole world or anywhere!

Frequently Asked Questions

Get instant answers to the most common questions. Can't find what you're looking for? Contact us

If you only know the lengths of all three sides (a, b, and c), you use Heron’s Formula. First, calculate the semi-perimeter $s = (a + b + c) / 2$. Then, the area is $\sqrt{s(s-a)(s-b)(s-c)}$. For a triangle with sides 3, 4, and 5, $s = 6$, and the area is $\sqrt{6(6-3)(6-4)(6-5)} = \sqrt{36} = 6$.

The Law of Sines states that $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$. You should use this in a triangle calculator when you know two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA). It allows you to find missing side lengths or angles proportionally.

The Law of Cosines is best for 'Side-Angle-Side' (SAS) scenarios. The formula is $c^2 = a^2 + b^2 - 2ab \cos(C)$. For example, if side $a=5$, $b=7$, and the included angle $C=60^\circ$, you would calculate $c^2 = 25 + 49 - 2(5)(7)(0.5)$, meaning $c = \sqrt{39} \approx 6.24$.

No, that is mathematically impossible in Euclidean geometry. The sum of all internal angles in a triangle must exactly equal 180°. Since a right angle is 90° and an obtuse angle is $>90°$, having two would either meet or exceed the 180° limit before the third angle is even added.

To calculate all sides and angles, you generally need at least three pieces of information, and at least one of them must be a side length. Common combinations include Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA). Knowing only three angles (AAA) will tell you the shape, but not the actual size.

A triangle can only exist if the sum of the two shortest sides is strictly greater than the longest side (the Triangle Inequality Theorem). For instance, sides of 2, 3, and 10 cannot form a triangle because $2 + 3$ is less than 10; the two shorter sides would never meet to close the shape.