Triangle Angle Calculator

About the Triangle Angle Calculator

Every triangle has three interior angles that always add up to exactly 180 degrees. This fundamental property lets you find any missing angle if you know the other two. But what if you only know one angle, or none at all? When you know all three side lengths instead, the Law of Cosines unlocks every angle: cos A = (b² + c² − a²) / (2bc).

This triangle angle calculator supports multiple solving modes. In "Angles" mode you enter one or two known angles and the calculator fills in the rest automatically. In "Sides (SSS)" mode you enter three side lengths and the calculator computes all three angles using the Law of Cosines, then classifies the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene.

Beyond the raw numbers, the calculator shows angle proportion bars so you can visualize how the three angles relate, a reference table of common triangle types with their angle measures, and preset buttons for right triangles, equilateral triangles, 30-60-90, 45-45-90, and more. Whether you are checking homework, designing a roof truss, or exploring trigonometry concepts, the page gives you the solved angles with supporting context.

When This Page Helps

Triangle angle problems are easy to state but surprisingly easy to mis-handle once you switch between angle-sum logic and side-based solving. This calculator is useful because it supports both workflows together: you can fill in missing interior angles from partial angle data or compute all three angles from side lengths using the Law of Cosines. The added classification and angle-comparison bars make it practical for classroom checks, trigonometry review, drafting, and any geometry task where you need both the values and the shape category.

How to Use the Inputs

1. Select the solving mode — "Angles" if you know angle values, or "Sides (SSS)" if you know all three sides.
2. In Angles mode enter one or two known angles in degrees. The calculator finds the missing angle(s).
3. In Sides mode enter all three side lengths. The calculator uses the Law of Cosines to compute each angle.
4. Review the classification (acute/right/obtuse, equilateral/isosceles/scalene).
5. Check the angle proportion bars for a visual comparison.
6. Use preset buttons to load well-known triangle types.
7. Consult the reference table below for common angle combinations.

Example Calculation

Tips & Best Practices

• The three interior angles must always sum to 180°. If they don't, recheck your inputs.
• In Sides mode, the longest side is always opposite the largest angle.
• A right triangle has one 90° angle; an obtuse triangle has one angle greater than 90°.
• For very flat triangles (one angle near 0° or 180°), rounding can introduce small errors.
• Use the degree/radian toggle if your coursework requires radians.

Solving Missing Angles From The 180 Degree Rule

The fastest triangle-angle problems rely on one fact: interior angles always sum to 180 degrees. If two angles are known, the third is just 180 - A - B. This is the core of classroom geometry problems, but it also matters in practice whenever a drawing gives partial angular information and you need to recover the remaining corner before building a layout, truss, or panel cut.

When Side Lengths Are All You Know

If no angles are given but all three sides are known, the triangle can still be solved with the Law of Cosines. That is exactly what the calculator does in SSS mode. Each side determines the angle opposite it, and the longest side must pair with the largest angle. This method is useful in surveying, CAD work, and any measurement workflow where distances are easier to obtain than direct angle readings.

Classifying The Triangle Once The Angles Are Known

After the angles are found, the triangle can be classified immediately. A right triangle contains one 90 degree angle, an obtuse triangle contains one angle greater than 90 degrees, and an acute triangle keeps all three below 90 degrees. Looking at the angle pattern also helps identify equilateral and isosceles cases. The calculator surfaces those labels automatically so you can move from raw numbers to a geometric interpretation without doing a second round of analysis.

Frequently Asked Questions

• How many angles do I need to know to solve a triangle?

  You need at least two angles (the third follows from 180° − A − B) or all three side lengths to compute every angle.

• What if my two angles add up to more than 180°?

  That is not a valid triangle. Every pair of angles must sum to less than 180° so the third angle is positive.

• Can I enter sides instead of angles?

  Yes. Switch to "Sides (SSS)" mode, enter all three side lengths, and the calculator uses the Law of Cosines to find every angle.

• What is the Law of Cosines?

  It generalizes the Pythagorean theorem: a² = b² + c² − 2bc cos A. It works for any triangle, not just right triangles.

• How does the calculator classify the triangle?

  By angle: acute (all < 90°), right (one = 90°), obtuse (one > 90°). By side: equilateral (all equal), isosceles (two equal), scalene (all different).

• Are the results in degrees or radians?

  Results are displayed in degrees by default. Use the unit selector to switch to radians if needed.