About the triangle calculator
The triangle calculator solves any triangle when you know three measurements, including at least one side. It works out the remaining sides and angles, the area and perimeter, the three heights and medians, and the inradius and circumradius, and draws the triangle.
It supports every standard case: three sides (SSS), two sides and the angle between them (SAS), two angles and a side (ASA or AAS) and two sides with a non-included angle (SSA), including the ambiguous case with two solutions.
Who should use the triangle calculator
- Students of geometry and trigonometry.
- Builders, surveyors and designers working out lengths and angles.
- Anyone who needs a missing side or angle fast.
How to use the triangle calculator: what each input means
- Sides a, b, c
- Side lengths in any one unit. Each side is opposite the angle with the same letter.
- Angles A, B, C
- In degrees, strictly between 0 and 180.
- How many to fill in
- Exactly three values, with at least one side. Leave the rest blank.
How the triangle calculator works: method and formula
Given three sides, the angles come from the law of cosines. Given two sides and the included angle, the third side comes from the law of cosines and the rest follow. Given two angles, the third is 180° minus their sum and the sides follow from the law of sines. For two sides and a non-included angle, the law of sines can produce zero, one or two valid triangles.
Area is found with Heron's formula: √(s(s − a)(s − b)(s − c)) where s is half the perimeter.
- Law of cosines
- c² = a² + b² − 2ab cos C
- Law of sines
- a ÷ sin A = b ÷ sin B = c ÷ sin C
- Heron's formula
- Area = √(s(s − a)(s − b)(s − c))
How to read your triangle calculator result
Angles always add to 180°. The triangle type (equilateral, isosceles, scalene; acute, right, obtuse) is reported. If two triangles fit your inputs, both are shown. If the numbers cannot form a triangle, for example sides 1, 2 and 10, the calculator says why.
Triangle Calculator worked example
Sides a = 3, b = 4 and c = 5; then sides 7 and 10 with a 50° included angle.
- For 3-4-5: s = 6, area = √(6 × 3 × 2 × 1) = 6.00.
- Angles: A = 36.87°, B = 53.13°, C = 90.00°. This is a scalene, right triangle.
- For two sides 7 and 10 with 50° between them: the third side is √(7² + 10² − 2 × 7 × 10 × cos 50°) = 7.682 and the area is 26.812.
3-4-5 gives area 6.00, angles 36.87°, 53.13° and 90.00°.
Practical uses of the triangle calculator
- Finding a rafter length or roof pitch.
- Land and plot measurements.
- Checking trigonometry homework.
Assumptions and limitations of this calculator
- Plane (flat) triangles only, not spherical ones.
- Angles alone do not fix the size, so at least one side is required.
- Results are floating-point and shown to about 10 significant digits.