Triangle Angle Calculator

1. Choose what you know: three sides, two angles, or two sides of a right triangle.
2. Enter the values. Sides can be in any unit, as long as all of them use the same one. Angles are in degrees.
3. Read the missing angle or angles, then check the type, the sides, and the area in the cards below.
4. Press Copy report or Save to keep the result.

Side a always sits opposite angle A, side b opposite angle B, and side c opposite angle C.

Every flat triangle has three angles that add up to exactly 180 degrees. This is the fastest way to find a missing angle.

Example: Two angles are 50 and 60 degrees. They add up to 110, so the third angle is 180 - 110 = 70 degrees.

Because the total is fixed, two angles must add up to less than 180. Also, a triangle can have at most one right angle or one obtuse angle.

When you know all three sides but no angles, the law of cosines links each angle to the sides. It works for every triangle, not just right ones.

Worked Example: a 7-8-9 Triangle

1. Angle A: cos A = (8^2 + 9^2 - 7^2) / (2 x 8 x 9) = 96 / 144 = 0.6667. So A = arccos(0.6667) = 48.1897 degrees.
2. Angle B: cos B = (7^2 + 9^2 - 8^2) / (2 x 7 x 9) = 66 / 126 = 0.5238. So B = 58.4119 degrees.
3. Angle C: cos C = (7^2 + 8^2 - 9^2) / (2 x 7 x 8) = 32 / 112 = 0.2857. So C = 73.3985 degrees.

Check: 48.1897 + 58.4119 + 73.3985 = 180.0001. The tiny extra comes from rounding each angle to four decimals. All three angles are under 90, so this is an acute scalene triangle. Its area, from Heron's formula, is about 26.8328 square units.

In a right triangle, one angle is 90 degrees, so the other two must add up to 90. Two sides are enough to find both of them with inverse trig.

With legs 6 and 8, A = arctan(6 / 8) = 36.8699 degrees and B = 53.1301 degrees. The hypotenuse is the square root of 6^2 + 8^2, which is 10. The hypotenuse is always the longest side, so a leg can never be longer than it.

Need a refresher on which ratio to use? Our sine, cosine, and tangent guide covers the basics, and the sin cos tan calculator handles single trig values.

Triangles are named two ways: by their largest angle and by how many sides match. The calculator reports both.

From sides alone, compare the square of the longest side with the sum of the squares of the other two. Equal means right, bigger means obtuse, and smaller means acute.

1. Degrees vs Radians

Many calculators default to radians. The inverse cosine of 0.5 is 60 in degrees but about 1.047 in radians. If an angle looks far too small, check the mode. This tool always gives degrees.

2. An Invalid Triangle

Not every set of lengths closes into a triangle. The two shorter sides must add up to more than the longest one. Sides of 1, 2, and 10 fail, and so do two angles that already reach 180.

3. Rounding Too Early

If you round each angle before adding, the total can drift to 179.9999 or 180.0001. Keep full precision in the middle steps and round only the final answer.

4. Mixing Up Labels

Each side must be opposite its matching angle. Swapping them in the law of cosines gives the wrong angle, even though the math looks fine.

Add the two angles you know and subtract the total from 180 degrees. For example, if two angles are 50 and 60 degrees, the third angle is 180 - 110 = 70 degrees.

Use the law of cosines. For angle C, compute (a^2 + b^2 - c^2) divided by 2ab, then take the inverse cosine. Repeat for the other angles, or subtract the first two from 180.

A 3-4-5 triangle is a right triangle. Its angles are about 36.87 degrees, 53.13 degrees, and exactly 90 degrees, with the right angle opposite the side of length 5.

It is most likely set to radians instead of degrees. An inverse cosine of 0.5 is 60 in degree mode but about 1.047 in radian mode. This calculator always reports degrees.

No. The two shorter sides must add up to more than the longest side. Lengths of 1, 2 and 10 fail this triangle inequality, so they cannot form a triangle.

Square each side. If the square of the longest side equals the sum of the other two squares, the triangle is right. If it is bigger, the triangle is obtuse. If it is smaller, the triangle is acute.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Weisstein, E. W. Law of Cosines. MathWorld, Wolfram Research (law of cosines and its angle form).
• OpenStax. Algebra and Trigonometry 2e (right triangle trigonometry, law of cosines, Heron's formula).
• NIST Digital Library of Mathematical Functions, section 4.14 (definitions of the trigonometric functions).