Triangle Calculator
Fill in any three of the six boxes, with at least one side. The page works out the other three, the area, the perimeter and more, and shows which rule it used.
Side a is opposite angle A, side b is opposite angle B and side c is opposite angle C. Enter exactly three values.
Worked examples
Three sides
a = 3, b = 4, c = 5
Angles 36.87, 53.13 and 90 degrees, area 6
A right-angled triangle.
Two sides and the angle between
a = 5, b = 7, C = 49 degrees
c = 5.299, area 13.207
c² = 25 + 49 - 70 cos 49°.
About Triangle Calculator
A triangle has three sides and three angles, and any three of those six values, with at least one a side, are enough to find the rest. Three sides use the cosine rule. Two sides and the angle between them also use the cosine rule, to find the third side. Two angles and a side use the fact that angles add up to 180 degrees, then the sine rule. Two sides and an angle that is not between them use the sine rule, and can give two different triangles.
That last case is the ambiguous case. A shorter side swinging from the end of a longer one can meet the base in two places, making one triangle with an acute angle and another with an obtuse angle. When that happens, both are shown. For every triangle the page also works out the area, the perimeter, the three heights, the radii of the circles inside and around the triangle, and the type: scalene, isosceles or equilateral, and acute, right-angled or obtuse. The steps tell you which rule was used and why.
How to use Triangle Calculator
- Fill in any three of the six boxes: sides a, b, c and angles A, B, C. Side a is opposite angle A, and so on.
- Include at least one side. Three angles alone fit triangles of every size.
- Use the example buttons if you want to see the layout for each case.
- Read the sides, angles, area and the steps. If two triangles fit, both are shown.
Common uses
- Trigonometry homework using the sine and cosine rules
- Surveying and finding inaccessible distances
- Roof, frame and DIY cutting angles
- Checking the type and area of a triangular plot
Frequently asked questions
Which values can I enter?
Any three of the six, with at least one side: three sides, two sides and the included angle, two sides and another angle, or two angles and a side.
What is the cosine rule?
It is c² = a² + b² - 2ab cos C. It links three sides and one angle, and reduces to Pythagoras' theorem when the angle is 90 degrees.
What is the sine rule?
It says a / sin A = b / sin B = c / sin C. It links each side to the angle opposite it, so knowing one side and its opposite angle gives the others.
Why can there be two answers?
With two sides and an angle opposite one of them, the sine of the other angle has an acute and an obtuse solution. If both fit inside the triangle, there are two possible triangles.
Why does the page say no triangle fits?
Either the sides break the rule that each must be shorter than the other two combined, or the side opposite a known angle is too short to reach the other side.