Area of an Oblique Triangle Calculator

Math

The Area of an Oblique Triangle Calculator finds the area of any triangle that is not right-angled, using two sides and the angle between them. The formula used is: Area = ½ × a × b × sin(C), where a and b are two sides and C is the included angle.

Formula

Area = ½ × a × b × sin(C)
  • The Area of an Oblique Triangle Calculator updates instantly as you change the sides or the included angle.
  • Formula: Area = ½ × a × b × sin(C)
  • Input definitions: • Side a and Side b: the two sides that meet at the included angle • Included Angle C: the angle between sides a and b, in degrees
  • An oblique triangle has no right angle; this side-angle-side (SAS) formula works for both acute and obtuse triangles.
  • Make sure angle C is the angle between the two sides you entered, not one of the other angles.
  • Area and side lengths share the same unit (area is that unit squared).

Example Calculation

Inputs
  • Side a: 8
  • Side b: 6
  • Included Angle C (degrees): 50

With sides a = 8 and b = 6 and an included angle of 50°: Area = ½ × 8 × 6 × sin(50°) ≈ 0.5 × 48 × 0.766 ≈ 18.39 square units.

Frequently asked questions

What is an oblique triangle?
It is a triangle with no right angle. It can be acute (all angles under 90°) or obtuse (one angle over 90°).
How do I find its area?
Use two sides and the angle between them: Area = ½ × a × b × sin(C). This is the side-angle-side (SAS) area formula.
Which angle should I enter?
Enter the angle that sits between the two sides you provided. Using a different angle will give the wrong area.
Does this work for obtuse triangles?
Yes. The sine formula works for any triangle, since sin(C) is positive for every angle between 0° and 180°.
What if I only know three sides?
Use Heron's formula instead, which finds the area directly from the three side lengths.