Triangle Angle Calculator
This calculator finds the third interior angle of a triangle when you know the other two, using the fundamental property that the three interior angles of any triangle in flat Euclidean geometry always sum to exactly 180 degrees. The formula could not be simpler: C equals 180 minus A minus B. Once all three angles are known, the calculator also classifies the triangle as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees) or obtuse (one angle greater than 90 degrees). A further check tells you whether the triangle is equilateral (all angles 60 degrees), isosceles (two angles equal), or scalene (all angles different). This is one of the most frequently used facts in geometry and underpins many other calculations involving triangles, including the law of sines, the law of cosines, and most problems in trigonometry. You enter angle A and angle B in degrees, and the calculator immediately shows angle C and the triangle classification. Both angles must be positive and their sum must be less than 180 degrees; otherwise no valid triangle exists. The tool is useful for students checking their geometry working, teachers setting or marking geometry problems, and anyone who needs a quick sanity check on angle values before proceeding to more involved calculations. The result is exact (no rounding error beyond floating-point precision) because the formula requires only a single subtraction.
Angle A and angle B must each be greater than 0 degrees and together less than 180 degrees.
How it works
The calculation is C = 180 − A − B. If A or B is zero or negative, or if A + B is 180 or more, the result is invalid and an error is shown. Triangle type is classified by comparing each angle to 90 degrees: if any angle equals 90 the triangle is right; if any angle exceeds 90 it is obtuse; otherwise it is acute. Shape is equilateral if all three angles equal 60, isosceles if any two angles are equal (within a rounding tolerance of 0.001 degrees), otherwise scalene.
Worked example
Enter A = 45 degrees and B = 60 degrees. C = 180 − 45 − 60 = 75 degrees. All three angles (45, 60, 75) are less than 90, so the triangle is acute. All three angles are different, so it is scalene. The angles sum to 180 degrees. These match the default values pre-filled above.
Related calculators
- Law of Sines Calculator: use the angles you just found to solve for triangle side lengths.
- Law of Cosines Calculator: find sides and angles using the cosine rule for SAS or SSS triangles.
- Sin Cos Tan Calculator: look up trig function values for each angle you have found.
- Percent Error Calculator: verify that your measured angles are close to the expected theoretical values.
Frequently asked questions
Why do the angles of a triangle always add up to 180 degrees?
In Euclidean (flat) geometry, the interior angles of any triangle sum to exactly 180 degrees. This can be shown by drawing a line through one vertex parallel to the opposite side: the alternate interior angles formed equal the two base angles, and the three angles along the straight line sum to 180 degrees. This holds for all triangles regardless of shape or size.
What is an acute triangle?
An acute triangle has all three interior angles strictly less than 90 degrees. An obtuse triangle has one angle greater than 90 degrees. A right triangle has exactly one angle equal to 90 degrees. An equilateral triangle is a special case of an acute triangle where all three angles are exactly 60 degrees.
Can a triangle have two obtuse angles?
No. Two obtuse angles would sum to more than 180 degrees, leaving no room for a positive third angle. A valid triangle must have three positive angles that sum to exactly 180 degrees, so it can contain at most one obtuse angle and at most one right angle.
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