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Triangle Calculator

Solve triangles: find missing sides, angles, area and perimeter.

Given (solve mode)

Results

Triangle type
Scalene · Acute
Perimeter 18 · Area 14.6969
Side a
5
Side b
6
Side c
7
Angle A
44.4153°
Angle B
57.1217°
Angle C
78.463°
Perimeter
18
Area (Heron)
14.6969
Sum of angles
180°

Sketch

ABCabc

Sides are labelled with the letter opposite their vertex (side a is opposite angle A, etc.). Dashed arcs mark the interior angles.

What is the Triangle Calculator?

A triangle calculator is a free online tool that solves any triangle from three known parts — sides, angles, or a mix — and finds the missing sides, angles, area, perimeter, and type (right, acute, obtuse, equilateral, isosceles, or scalene). It supports SSS, SAS, ASA, and AAS input.

Triangle Calculator formula

SSS uses the Law of Cosines: A = arccos((b² + c² − a²) ÷ (2bc)), and similarly for B and C; angles sum to 180°. SAS uses the Law of Cosines to find the third side: a² = b² + c² − 2bc·cos(A). ASA/AAS use the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). Area is found with Heron's formula: s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)).

How to use the Triangle calculator

  1. 1Select the solve mode that matches what you know: SSS (three sides), SAS (two sides + included angle), ASA (two angles + included side), or AAS (two angles + non-included side).
  2. 2Enter the three known values in the input fields that appear.
  3. 3Read the solved triangle: all three sides, all three angles, perimeter, and area.
  4. 4Check the classification chip to see if the triangle is right, acute, or obtuse by angles and equilateral, isosceles, or scalene by sides.
  5. 5If your inputs are impossible (e.g., sides that violate the triangle inequality), the calculator shows a clear error rather than silent garbage.

Example calculation

Solve an SSS triangle with sides 3, 4, 5. Law of Cosines: A = arccos((4² + 5² − 3²)/(2·4·5)) = arccos(32/40) = 36.87°; B = arccos((3² + 5² − 4²)/(2·3·5)) = 53.13°; C = 180 − 36.87 − 53.13 = 90°. Heron: s = 6, area = √(6·3·2·1) = √36 = 6. Result: a 3-4-5 right triangle with area 6.

Frequently asked questions

How do I solve a right triangle?
If you know the two legs, use SSS after computing the hypotenuse with the Pythagorean theorem c = √(a² + b²), or use SAS with the included 90° angle. If you know one leg and the hypotenuse, use SSS or the Pythagorean theorem to get the other leg. The calculator handles right triangles just like any other — it also labels them 'Right' in the classification chip when one angle is exactly 90°.
What is the triangle inequality?
The sum of any two sides must be greater than the third (a + b > c, a + c > b, b + c > a). If your three sides violate this — for example 1, 2, 3 or 1, 2, 10 — no triangle exists, and the calculator returns 'Triangle inequality violated' instead of producing nonsensical angles.
How does the calculator find angles from three sides?
It uses the Law of Cosines: A = arccos((b² + c² − a²)/(2bc)). This is more numerically stable than the Law of Sines for SSS because it avoids the ambiguous 'SSA' case. The third angle is always 180° minus the other two, guaranteeing they sum to exactly 180°.
Does the calculator work in degrees or radians?
All angles are entered and displayed in degrees — the most natural unit for geometry and trigonometry homework. Internally, the conversion is handled by the standard π/180 factor; you do not need to switch modes.
What is Heron's formula for the area?
Given sides a, b, c, first compute the semiperimeter s = (a + b + c)/2, then the area is √(s(s − a)(s − b)(s − c)). For the 3-4-5 triangle: s = 6, so area = √(6·3·2·1) = √36 = 6. The calculator guards against tiny floating-point negative values inside the sqrt with Math.max(0, …).

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