Triangle Calculator

Enter any three known values (at least one side) and get every missing side and angle, the area, perimeter and triangle type, with a drawing to scale.

Fill in exactly three boxes. Side a is opposite angle A, and so on.

Which method applies?

You knowNameFirst step
Three sidesSSSLaw of cosines for an angle
Two sides and the angle betweenSASLaw of cosines for the third side
Two angles and any sideASA / AASThird angle = 180° − the other two, then law of sines
Two sides and a non-included angleSSALaw of sines (may give 0, 1 or 2 triangles)

The key formulas

Law of cosines: c² = a² + b² − 2ab·cos(C)
Law of sines: a/sin(A) = b/sin(B) = c/sin(C)
Heron's area: √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2
Angles: A + B + C = 180°

Worked example (SAS)

Sides a = 7 and b = 9 with angle C = 60° between them:

  1. c² = 49 + 81 − 2 × 7 × 9 × cos 60° = 130 − 63 = 67, so c ≈ 8.185
  2. Then the law of cosines (or sines) gives A ≈ 47.79° and B ≈ 72.21°
  3. Area = ½ × 7 × 9 × sin 60° ≈ 27.28

Working with a right triangle? The Pythagorean theorem calculator is faster. Need sine, cosine and tangent values? Try the trigonometry calculator.

Last reviewed October 2026.

Frequently asked questions

What do I need to solve a triangle?

Any three values, as long as at least one is a side: three sides (SSS), two sides and the angle between them (SAS), two angles and a side (ASA or AAS), or two sides and an angle that is not between them (SSA). Three angles alone fix the shape but not the size.

Why does the calculator sometimes show two triangles?

With two sides and an angle opposite one of them (SSA), there can be two different triangles that fit, one with an acute angle and one with an obtuse angle. This is called the ambiguous case, and the calculator shows both solutions.

How is a right triangle handled?

Enter 90 for the right angle and any two other values. For a right triangle with two known sides, the Pythagorean theorem calculator also shows the working step by step.

What formulas does it use?

The law of cosines (c² = a² + b² − 2ab·cos C) for SSS and SAS, the law of sines (a ÷ sin A = b ÷ sin B = c ÷ sin C) for ASA, AAS and SSA, and Heron's formula for the area.

What does the triangle type tell me?

By sides, a triangle is equilateral (all equal), isosceles (two equal) or scalene (none equal). By angles, it is acute (all under 90°), right (one exactly 90°) or obtuse (one over 90°).