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- Solves any triangle from three sides (SSS), two sides and the angle between (SAS), or two angles and a side (ASA, AAS).
- Gives every side and angle, the area and the perimeter.
- Tells you if the triangle is equilateral, isosceles or scalene, and acute, right or obtuse.
- Also shows the height, inradius and circumradius, with the laws used.
How to use the triangle calculator
Choose what you know
Three sides, two sides and an angle, or two angles and a side.
Enter the values
Side a is opposite angle A, side b opposite B, and side c opposite C. Angles are in degrees.
Read the solved triangle
See all sides, angles, area, perimeter and type.
How a triangle is solved
Any triangle can be solved when you know three of its parts, as long as at least one is a side. The calculator uses the law of cosines when it knows sides and the angle between them, and the law of sines when it knows two angles. The three angles always add up to 180°.
Triangle formulas
Law of cosines: c² = a² + b² − 2ab cos C
Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C
Area = ½ab sin C, or Heron: √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
Example 1: sides 5, 6 and 7 (SSS)
A scalene acute triangle.
- Angles 44.42°, 57.12°, 78.46°
- Area 14.6969
- Perimeter 18
Example 2: sides 3 and 4 with a 90° angle (SAS)
The classic right triangle.
- Third side 5
- Angles 36.87°, 53.13°, 90°
- Area 6
Example 3: angles 30° and 60°, side a = 5 (AAS)
Using the law of sines.
- Third angle 90°
- Sides 5, 8.6603, 10
- Area 21.6506
Where the triangle calculator helps
Trigonometry homework
Check answers that use the laws of sines and cosines.
Construction and DIY
Find angles and lengths for frames and roofs.
Land and surveying
Work out the area of a triangular plot.
Design
Plan triangular shapes with exact angles.
For right triangles, use the right triangle calculator or the Pythagorean theorem calculator. Find sine, cosine and tangent with the trig calculator.
Triangle calculator FAQ
How do you find the area of a triangle with three sides?
Use Heron’s formula. For sides 5, 6 and 7, s = 9 and the area is √(9 × 4 × 3 × 2) ≈ 14.70.
What do the angles of a triangle add up to?
Always 180°.
When do you use the law of cosines?
When you know three sides, or two sides and the angle between them.
When do you use the law of sines?
When you know two angles and any side.
Can any three lengths make a triangle?
No. Any two sides must add up to more than the third side. 1, 2 and 5 cannot form a triangle.
What is the difference between scalene, isosceles and equilateral?
A scalene triangle has no equal sides, an isosceles triangle has two, and an equilateral triangle has all three.