🔺 Triangle Calculator

Calculate triangle area, perimeter, side lengths, and interior angles

Enter Side Lengths (SSS)

Side a

Side b

Side c

How to Use the Triangle Calculator

Our online Triangle Calculator solves for the area, perimeter, side lengths, and interior angles of any triangle (right-angled, acute, obtuse, equilateral, isosceles, or scalene). By inputting three known parameters (such as three side lengths SSS, or two sides and an angle SAS), it applies geometric theorems instantly.

Key Geometric Formulas & Theorems

1. Pythagorean Theorem (Right Triangles): a² + b² = c²

2. Standard Area Formula: Area = ½ × Base × Height

3. Heron's Formula (All 3 Sides Known): Area = √[ s(s - a)(s - b)(s - c) ] where semi-perimeter s = (a + b + c) / 2

4. Law of Cosines: cos(A) = (b² + c² - a²) / (2bc)

5. Sum of Interior Angles: Angle A + Angle B + Angle C = 180°

Step-by-Step Example Calculation

Problem: Calculate the area and interior angles of a triangle with side lengths a = 5, b = 6, and c = 7:

Perimeter: 5 + 6 + 7 = 18 units.

Semi-perimeter (s): 18 / 2 = 9 units.

Heron's Area: √[ 9 × (9-5) × (9-6) × (9-7) ] = √[ 9 × 4 × 3 × 2 ] = √216 ≈ 14.70 square units.

Angle A (opposite side 5): cos(A) = (6² + 7² - 5²) / (2×6×7) = 60/84 = 0.7143 → A = 44.42°.

Angle B (opposite side 6): cos(B) = (5² + 7² - 6²) / (2×5×7) = 38/70 = 0.5429 → B = 57.12°.

Angle C (opposite side 7): 180° - 44.42° - 57.12° = 78.46°.

Types of Triangles Explained

Equilateral: All three sides are equal; all interior angles equal 60°.

Isosceles: Two sides are equal in length; two opposite angles are equal.

Scalene: All three sides and interior angles have different measurements.

Right-Angled: One interior angle measures exactly 90°.

Frequently Asked Questions (FAQ)

Q: What is the Triangle Inequality Theorem?
A: The Triangle Inequality Theorem states that for any valid triangle, the sum of the lengths of any two sides must be strictly greater than the length of the remaining side: a + b > c.

Q: How do you find triangle area without height?
A: Use Heron's formula if all three sides are known, or use the trigonometric formula Area = ½ × a × b × sin(C) if two sides and their included angle are known.