Solve any triangle from its three sides. This free triangle calculator finds all angles, the area, perimeter and type (scalene, isosceles, equilateral; acute, right, obtuse) instantly.
Three sides
Enter the three side lengths and the calculator finds all three angles, the area, the perimeter and the triangle type. Sides must satisfy the triangle inequality.
Area
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Enter all three sides
Angle A (opp. a)
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Angle B (opp. b)
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Angle C (opp. c)
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Perimeter
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Type (sides)
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Type (angles)
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Angles are found with the law of cosines and the area with Heron’s formula. The three angles always add up to 180°.
Use this free triangle calculator to solve a triangle from its three sides. Enter sides a, b and c to find all three angles, the area, the perimeter and the triangle type.
What this triangle calculator shows you
A triangle calculator solves a triangle when you know its three sides (the SSS case). It returns every angle, the area and perimeter, and classifies the triangle by both its sides and its angles.
How the triangle is solved
Angle A = arccos((b² + c² − a²) ÷ 2bc) (law of cosines)
Area = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 (Heron)
A 3-4-5 triangle is a right triangle: angles of 90°, 53.13° and 36.87°, an area of 6 and a perimeter of 12.
Triangle types
By sides
By angles
Equilateral — all sides equal
Acute — all angles < 90°
Isosceles — two sides equal
Right — one angle = 90°
Scalene — all sides different
Obtuse — one angle > 90°
The triangle inequality
A valid triangle needs each side shorter than the sum of the other two. If a + b ≤ c (or any equivalent), the sides can’t form a triangle, and the calculator will let you know.
How to use the triangle calculator
Enter side a, side b and side c.
Read the area and all three angles.
Check the perimeter and type.
Triangle Calculator FAQ
How do I find a triangle's angles from its sides?
Use the law of cosines: each angle equals the arccosine of (sum of the other two sides squared, minus the opposite side squared, divided by twice their product). This calculator does it for all three.
How do I find a triangle's area from three sides?
Use Heron's formula: with s as half the perimeter, area = √(s(s−a)(s−b)(s−c)). A 3-4-5 triangle has an area of 6.
What makes three lengths a valid triangle?
The triangle inequality: each side must be shorter than the sum of the other two. If not, the lengths can't form a triangle.
What are the types of triangle?
By sides: equilateral, isosceles or scalene. By angles: acute (all under 90°), right (one 90°) or obtuse (one over 90°). The calculator labels both.
Do the angles always add to 180°?
Yes. In any flat (Euclidean) triangle, the three interior angles always sum to exactly 180 degrees.
Is the triangle calculator free?
Yes, this triangle calculator is completely free, needs no sign-up, and gives instant results in your browser.
