Spread love and kindness in your heart today.
WowCalculators

Triangle Calculator

Solve any triangle instantly. Enter your known sides and angles (SSS, SAS, ASA, AAS) to find the missing values and calculate the area.

Enter Knowns

Sides

Angles (Deg)

SSS Mode: Enter the known values based on your selection. The calculator will automatically solve for the rest using trigonometry.

Enter known values to solve the triangle

The Ultimate Triangle Calculator

Trigonometry is the mathematical foundation of engineering, architecture, and physics. Calculating the missing sides, angles, or area of a triangle manually requires complex memorization of algebraic laws (Sines and Cosines) that are highly prone to human error.

Our advanced Triangle Calculator removes the algebraic friction. By instantly processing standard geometric axioms, it solves any triangular equation the moment you input the required variables.

The Laws of Sines and Cosines

To mathematically solve a triangle that is not a right-angle triangle, the calculator uses two primary algorithms:

  1. The Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). This algorithm states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides of the triangle. It is heavily used for AAS (Angle-Angle-Side) and ASA calculations.
  2. The Law of Cosines: c² = a² + b² - 2ab*cos(C). This is essentially an advanced version of the Pythagorean theorem that works on any triangle. It is the core algorithm used for SSS (Side-Side-Side) and SAS calculations.

By utilizing our tool, you receive instant, flawlessly calculated geometric data for your academic or professional projects.

Frequently Asked Questions

What is the Pythagorean theorem?

The Pythagorean theorem (a² + b² = c²) is a mathematical algorithm used exclusively for right-angled triangles. It states that the square of the hypotenuse (the longest side) is exactly equal to the sum of the squares of the other two sides.

What do SSS, SAS, and ASA mean?

These are geometric acronyms indicating the variables you already know. SSS (Side-Side-Side) means you know all three sides. SAS (Side-Angle-Side) means you know two sides and the included angle. Knowing any of these three sets allows our calculator to solve the rest of the triangle using the Laws of Sines and Cosines.

Do the angles of a triangle always add up to 180 degrees?

Yes. In standard Euclidean geometry (which applies to flat planes), the three interior angles of any triangle will always mathematically sum to exactly 180 degrees, regardless of the triangle's shape or size.

Related Calculators