OnlineAngleFinder

Triangle Angle Calculator

Calculate the missing angles and sides of any triangle by entering the known values. Perfect for geometry, trigonometry, and practical measurements.

Triangle Calculator

Enter any 3 values (including at least one side) to calculate the rest. Or enter 2 angles to get the 3rd.

How to Calculate Triangle Angles

Every triangle in Euclidean geometry obeys a fundamental mathematical rule: the sum of all three interior angles is always exactly 180 degrees (or π radians).

∠A + ∠B + ∠C = 180°

If you already know any two angles of a triangle, you can determine the missing third angle immediately by subtracting the two known angles from 180°:

Missing Angle = 180° - (∠Known1 + ∠Known2)

Trigonometry Formulas Used in This Calculator

When solving triangles where angles are unknown and only side lengths or combinations of sides and angles are available, our calculator applies classic trigonometric laws:

1. The Law of Sines

Relates the ratios of side lengths to the sines of their opposite angles. Best used for AAS (Angle-Angle-Side) and ASA (Angle-Side-Angle) problems:

a / sin(A) = b / sin(B) = c / sin(C)

2. The Law of Cosines

Generalizes the Pythagorean theorem for any arbitrary triangle. Essential when solving SSS (three sides known) or SAS (two sides and included angle):

c² = a² + b² - 2ab · cos(C)

Classifying Triangles by Angles and Sides

Right Triangle

Contains one exact 90° right angle. Solvable using the Pythagorean Theorem (a² + b² = c²).

Equilateral

All three sides are equal, and all three internal angles are exactly 60° (60° + 60° + 60° = 180°).

Isosceles

Has two sides of equal length and two matching base angles opposite those sides.

Scalene

All three sides have different lengths, and all three angles have completely distinct measurements.

Practical Real-World Uses

Roof Pitch & Construction Framing: Carpenters and roofers use triangle angle calculations to determine rafter lengths, plumb cuts, and pitch angles from rise-over-run specifications.

Woodworking & Joinery: When cutting complex miter joints, compound bevels, or polygonal tables, accurate triangle angle math prevents costly wood waste.

Surveying & Navigation (Triangulation): By establishing a known baseline between two observation points and measuring the angles to a remote target, surveyors can calculate the exact distance to unreachable landmarks.