Triangle Calculator
Solve any triangle from three of its sides and angles: every side, angle, area, perimeter, height, median, inradius, circumradius and the triangle's centres, with both answers in the ambiguous case.
Change the values and press Calculate to work out your own figures.
Enter any three of the six values, including at least one side.
Show the working
- Three sides: each angle from the law of cosines, cos A = (b² + c² − a²) ÷ 2bc
- Area = √(s(s − a)(s − b)(s − c)) = 72.61843774
How to use it
Enter any three of the six values, including at least one side.
Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.
Key facts
a ÷ sin A = b ÷ sin B = c ÷ sin C; c² = a² + b² − 2ab cos C; A = √(s(s − a)(s − b)(s − c))
The ambiguous case
Given two sides and an angle that is not between them, there can be two different triangles, one or none. With a = 5, b = 7 and A = 40°, angle B can be 64.1° or 115.9°.
Questions
Which three values do I need?
Any three, as long as at least one is a side: three angles fix the shape but not the size.
What does the triangle's type mean?
Acute, right or obtuse by its largest angle; equilateral, isosceles or scalene by its sides.
Formulas
a ÷ sin A = b ÷ sin B = c ÷ sin C; c² = a² + b² − 2ab cos C; A = √(s(s − a)(s − b)(s − c))
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).