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Triangle Calculator

Enter any three measurements that pin down a triangle — three sides, two sides and the angle between them, or two angles and a side — and get every side, every angle, the area and the perimeter. Combinations that cannot form a triangle return a blank result.

Quick examples

Side a is opposite angle A.

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Area6 ft²
Perimeter
12 ft
Side a
3 ft
Side b
4 ft
Side c
5 ft
Angle A
36.87 °
Angle B
53.13 °
Angle C
90 °
Type of triangle
Right, scalene

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      Formula

      Angles add up: A + B + C = 180°
      Law of cosines: c² = a² + b² − 2ab × cos(C)
      Law of sines: a ÷ sin(A) = b ÷ sin(B) = c ÷ sin(C)
      Area (Heron): √(s(s − a)(s − b)(s − c)), where s is half the perimeter

      How to use it

      1. Choose what you know: SSS, SAS, ASA or AAS.
      2. Enter the values. Side a is opposite angle A, side b opposite B, and side c opposite C.
      3. Read the missing sides and angles, the area, the perimeter and the type of triangle.

      Worked examples

      Sides of 3 m, 4 m and 5 m (SSS)

      Angle A
      36.87 °
      Angle B
      53.13 °
      Angle C
      90 °
      Area
      6 m²
      Perimeter
      12 m
      Type of triangle
      Right, scalene

      Sides of 5 m and 7 m with 60° between them (SAS)

      Side c
      6.24 m
      Angle A
      43.9 °
      Angle B
      76.1 °
      Area
      15.16 m²
      Type of triangle
      Acute, scalene

      Angles of 45° and 60° either side of a 10 m side (ASA)

      Angle C
      75 °
      Side a
      7.32 m
      Side b
      8.97 m
      Area
      31.7 m²

      Angles A = 30° and B = 100° with side a = 8 m (AAS)

      Angle C
      50 °
      Side b
      15.76 m
      Side c
      12.26 m
      Area
      48.28 m²
      Type of triangle
      Obtuse, scalene

      What the letters mean

      SSS is three sides. SAS is two sides and the angle between them. ASA is two angles and the side between them. AAS is two angles and a side that is not between them. Each of these fixes exactly one triangle.

      Two sides and an angle that is not between them (SSA) can match two different triangles, one, or none, so it is not offered here.

      When a triangle is impossible

      Three sides only close up if the longest is shorter than the other two combined: 3, 4 and 8 cannot make a triangle. Two angles must add to less than 180° to leave room for the third.

      Questions people ask

      How do I find the angles of a triangle from its three sides?

      Use the law of cosines: cos(A) = (b² + c² − a²) ÷ (2bc). For sides 3, 4 and 5 the angles are 36.87°, 53.13° and 90°.

      How do I find the third side from two sides and an angle?

      With the angle between them, use c² = a² + b² − 2ab × cos(C). Sides 5 and 7 with 60° between them give a third side of √39 = 6.24.

      What is the third angle if two are 45° and 60°?

      75°, because the three angles of any triangle add up to 180°.

      Related calculators

      Right Triangle CalculatorSolve a right triangle from two sides, or one side and an angle.Triangle Area CalculatorArea from base and height, three sides, or two sides and an angle.Pythagorean Theorem CalculatorFind the missing side of a right triangle with a² + b² = c².Hypotenuse CalculatorLongest side of a right triangle from legs, an angle or the area.Perimeter CalculatorDistance around a rectangle, triangle, circle, polygon or ellipse.