Triangle Calculator

Solve any triangle (general and right) with step-by-step explanations

Opposite angle α
Opposite angle β
Opposite angle γ
Opposite side a
Opposite side b
Opposite side c

How to Solve a Triangle

To solve a triangle, you need to provide at least three pieces of information, including at least one side length. The calculator supports the following combinations:

  • SSS (three sides)
  • SAS (two sides and the included angle)
  • ASA (two angles and the included side)
  • AAS (two angles and a non-included side)
  • SSA (two sides and a non-included angle) - This is the ambiguous case that may have 0, 1, or 2 solutions

For right triangles, you only need two values (either two sides or one side and one angle).

Formulas Used

The calculator uses the following mathematical formulas:

  • Law of Sines: a/sin(α) = b/sin(β) = c/sin(γ) = 2R
  • Law of Cosines: a² = b² + c² - 2bc·cos(α)
  • Triangle Angle Sum: α + β + γ = 180° (or Ï€ radians)
  • Heron's Formula for area: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
  • Pythagorean Theorem for right triangles: a² + b² = c²
  • Inradius: r = Area / s
  • Circumradius: R = abc / (4·Area)

Frequently Asked Questions

What is the ambiguous case (SSA)?

The ambiguous case occurs when you know two sides and a non-included angle. Depending on the values, there might be zero, one, or two possible triangles that satisfy the given conditions.

How do I input angles in degrees, minutes, and seconds?

You can enter angles in DMS format like "30°15'20" or "30 15 20". The calculator will automatically convert this to decimal degrees.

Can I use mathematical expressions for angles?

Yes, you can use expressions like "pi/6" for π/6 radians or "2*pi/3" for 2π/3 radians.

What precision should I use?

The "Auto" setting will determine an appropriate precision based on your inputs. You can also manually select 3-6 significant figures for more control.