Angles add up to 180 degrees
Every flat triangle has three angles that add up to exactly 180 degrees. With two of them, subtract both from 180 to get the third.
If the two angles you know already add up to 180 or more, there is no room for a third and the calculator refuses the input.
From three sides: the cosine rule
When you only have the sides, the cosine rule gives each angle: the cosine of an angle is the two sides beside it squared, minus the opposite side squared, all divided by twice the product of those two sides.
The calculator applies it three times, once per angle, and the three always add up to 180 degrees.
Worked example
Two angles of 50 and 60 degrees leave 180 - 50 - 60 = 70 degrees for the third, which makes a scalene, acute triangle.
A triangle with sides 6 cm, 8 cm and 10 cm has angles of 36.8699, 53.1301 and 90 degrees, so it is scalene and right-angled.
Units do not change the angles
Only the ratio between the sides matters, so measuring in centimetres or inches gives the same angles.
The unit choice is there so the sides read the way you measured them. It does not affect the answer.
Inputs for the triangle angle calculator
What do you know?
Choose two angles, or all three sides. The boxes below change to match.
Angle A and B
Two angles in degrees. Together they must leave room for a third, so they add up to less than 180.
Side a, b and c
The three sides, each opposite the angle with the same letter.
Sides measured in
The unit the sides are in. Any unit gives the same angles, because only their ratio matters.
CALCULATOR QUESTIONS
Triangle angle calculator questions
How do I find the third angle of a triangle?
Subtract the other two from 180. Angles of 50 and 60 degrees leave 70 degrees.
How do I find angles from three sides?
Use the cosine rule once per angle. For sides 6, 8 and 10 the angles are 36.8699, 53.1301 and 90 degrees.
What if the angles add up to more than 180?
Then they cannot belong to a flat triangle, so the calculator refuses them rather than returning a negative angle.
Does a right angle always show as exactly 90?
It shows as 90 to the decimal places displayed. Very slight differences come from rounding in your side measurements, not from the method.