Triangle Calculator — Sides, Angles, Area & Perimeter

Given Values

Side a

units

0.1500

Side b

units

0.1500

Side c

units

0.1500

Area

Scalene

14.7

Perimeter

Type

Scalene

Sides

Angles

A44.4°

B57.9°

C77.7°

A + B + C = 180° ✓

What is a Triangle?

The Triangle Calculator solves any triangle completely — finding all three sides, all three angles, area, and perimeter — from just three known values. Choose from three input modes: SSS (all three sides), SAS (two sides and the angle between them), or ASA (two angles and the side between them). The calculator applies the law of cosines and law of sines to derive every unknown, and automatically classifies the triangle as scalene, isosceles, equilateral, or right.

Unlike the Pythagorean Theorem Calculator which is restricted to right-angled triangles, this tool works for any triangle — acute, right, or obtuse. Triangles are the most fundamental polygon in geometry, and solving them is a skill with applications ranging from land surveying and structural engineering to trigonometry examination problems in Class 11 and competitive exams like JEE.

In Indian land records and construction, triangular parcels arise whenever roads meet at odd angles or when plots are bounded by natural features like rivers. Surveyors traditionally use the law of sines and cosines to compute areas and boundaries from measured angles and distances — this calculator automates that process.

For computing area alone (when base and height are known), the Area Calculator is simpler. But when you need angles, full side resolution, or the triangle classification, use the Triangle Calculator.

How to use this Triangle calculator

Select Known Values mode — click SSS if you know all three sides, SAS if you know two sides and the angle between them, or ASA if you know two angles and the side between them.
Enter Side inputs (SSS mode) — type values for Side a, Side b, and Side c using the sliders or direct input. Ensure the three sides satisfy the triangle inequality (sum of any two > third).
Enter Side and Angle inputs (SAS mode) — enter Side a and Side b, then set Included Angle C (the angle between those two sides) using the slider (1° to 178°).
Enter Angle and Side inputs (ASA mode) — set Angle A and Angle B (they must sum to less than 180°), then enter Included Side c (the side between those two angles). Angle C is computed automatically as 180°−A−B.
Read all outputs — the primary result card shows area and perimeter. The side-by-side panel below lists all three computed sides and all three angles. The triangle type badge (Equilateral / Isosceles / Right / Scalene) appears in the result header.
Verify A+B+C = 180° — the green confirmation line at the bottom of the angles panel confirms the result is consistent and no rounding error has accumulated beyond acceptable limits.

Formula & Methodology

Law of Cosines (SSS — finding angles):cos(A) = (b² + c² − a²) / (2bc)cos(B) = (a² + c² − b²) / (2ac)C = 180° − A − B

Law of Cosines (SAS — finding the third side):c = √(a² + b² − 2ab·cos C)

Law of Sines (ASA — finding unknown sides):a / sin(A) = b / sin(B) = c / sin(C)

Area formulae:SSS: s = (a+b+c)/2 ; Area = √(s(s−a)(s−b)(s−c))SAS: Area = ½ × a × b × sin(C)ASA: Area = ½ × a × b × sin(C) after sides resolved

Perimeter: P = a + b + c

Worked example — surveying a triangular plot in Bengaluru:

A plot of land has two measured sides of 18 m and 24 m with an included angle of 55° between them (SAS mode).

Step 1 — Third side (law of cosines):c = √(18² + 24² − 2 × 18 × 24 × cos 55°)c = √(324 + 576 − 864 × 0.5736)c = √(900 − 495.59) = √404.41 ≈ 20.11 m

Step 2 — Area:Area = ½ × 18 × 24 × sin 55° = ½ × 432 × 0.8192 ≈ 176.94 sq m

Step 3 — Perimeter:P = 18 + 24 + 20.11 = 62.11 m

Step 4 — Remaining angles (law of cosines):A ≈ 46.9°, B ≈ 78.1° (sum with C = 55° → 180° ✓)

Assumption: All calculations assume Euclidean plane geometry. Angles must be entered in degrees, not radians. For the ASA mode, the two known angles must be positive and sum to less than 180°; otherwise no valid triangle exists.

Frequently Asked Questions

What is a triangle calculator and what can it solve?

A triangle calculator computes all unknown sides, angles, area, and perimeter of a triangle when enough information is provided. Our Triangle Calculator supports three input methods: SSS (all three sides known), SAS (two sides and the included angle), and ASA (two angles and the included side). It applies the law of cosines and law of sines to find every remaining property, plus classifies the triangle type.

What is the SSS method for solving a triangle?

SSS (Side-Side-Side) means all three side lengths are known. Given sides a, b, and c, the angles are computed using the law of cosines: cos(A) = (b²+c²−a²)/(2bc). Once two angles are found, the third is 180°−A−B. The area is then computed via Heron's formula. SSS is the simplest triangle-solving case since it always has a unique solution provided the three sides satisfy the triangle inequality.

What is the SAS method for triangle calculation?

SAS (Side-Angle-Side) means two sides and the angle between them are known. The unknown third side is found via the law of cosines: c = √(a²+b²−2ab·cos C). The remaining angles are then found using the law of cosines again or the law of sines. SAS has a unique solution when the included angle is between 0° and 180° exclusive.

What is the ASA method for triangle calculation?

ASA (Angle-Side-Angle) means two angles and the side between them are known. The third angle is C = 180°−A−B, and the unknown sides are found via the law of sines: a/sin(A) = c/sin(C). ASA has a unique solution as long as the two known angles sum to less than 180°. It is commonly used in surveying and navigation where angles are measured directly.

What is the difference between equilateral, isosceles, scalene, and right triangles?

An equilateral triangle has all three sides equal and all angles equal to 60°. An isosceles triangle has two equal sides and two equal base angles. A scalene triangle has all sides and all angles different. A right triangle has one angle of exactly 90° and satisfies the Pythagorean theorem (c² = a²+b²). Our calculator automatically identifies and displays the triangle type based on your inputs.

What is Heron's formula for the area of a triangle?

Heron's formula computes area when all three sides are known, without needing the height. Let s = (a+b+c)/2 (the semi-perimeter). Then Area = √(s(s−a)(s−b)(s−c)). For a triangle with sides 5 m, 6 m, and 7 m: s = 9, Area = √(9×4×3×2) = √216 ≈ 14.70 sq m. This is the formula used in the SSS mode of our calculator.

What is the triangle inequality and why does it matter?

The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side: a+b > c, a+c > b, and b+c > a. If this condition is violated, no real triangle exists with those three side lengths. For example, sides of 3, 4, and 10 cannot form a triangle (3+4=7 < 10). Our calculator detects invalid inputs and will not produce a result for them.

How to find the area of a triangle without the height?

When the height is not known, use Heron's formula if all three sides are available, or use Area = ½×a×b×sin(C) if two sides and their included angle are known. The [Area Calculator](/area-calculator/) computes triangle area using base and height (the most common school formula), while the Triangle Calculator here uses the more general methods for any input combination.

Is the law of sines or law of cosines taught in CBSE?

The law of cosines is introduced at the Class 11 level in CBSE under 'Trigonometry' and is part of the Class 11 and Class 12 Mathematics syllabus. The law of sines is similarly covered in Class 11. These laws extend trigonometry beyond right triangles to all triangles. In Class 10, only the Pythagorean theorem and basic right-triangle trigonometry are covered — use the [Pythagorean Theorem Calculator](/pythagorean-theorem-calculator/) for Class 10 problems.

How do I calculate the perimeter of a triangle?

The perimeter of a triangle is simply the sum of all three sides: P = a + b + c. If a side is unknown, first solve for it using SSS, SAS, or ASA, then add all three sides. Our calculator always displays the perimeter alongside area once the triangle is fully solved. Perimeter is useful for fencing a triangular plot, framing a triangular structure, or measuring the boundary of a triangular region.

What is the angle sum property of a triangle?

The angle sum property states that the sum of all three interior angles of any triangle is always 180°. This is a fundamental geometric fact that our calculator uses to find the third angle once two are known (in ASA mode, the third angle = 180°−A−B). The calculator also displays the verification A+B+C = 180° in the output so you can confirm the result is consistent.

Can I solve an obtuse triangle with this calculator?

Yes — the Triangle Calculator handles acute, right, and obtuse triangles equally. Obtuse triangles (one angle greater than 90°) are fully solved by the law of cosines in SSS mode and by the same law in SAS and ASA modes. The law of sines can be ambiguous for obtuse triangles in some input configurations (the SSA ambiguous case), which is why we provide SSS, SAS, and ASA rather than SSA as an input mode.