SAS Triangle Area Calculator
Find the area of a triangle from two sides and the angle between them (the side-angle-side, or SAS, case) using Area = ½ × a × b × sin(C). Enter the two side lengths and the included angle in degrees, and the calculator returns the area in square units.
Formula
Area = ½ × a × b × sin(C)
- Use this when you know two sides and the angle between them (SAS). The included angle must be the one formed by sides a and b.
- The angle is entered in degrees and converted to radians (× π/180) before taking the sine.
- The area is largest when C = 90° (sin = 1), giving ½ × a × b, and approaches zero as C nears 0° or 180°.
- The area uses the square of the side units: sides in cm give an area in cm².
Example: a = 8, b = 6, C = 50°
Inputs
- Side a: 8
- Side b: 6
- Included Angle C (degrees): 50
With a = 8, b = 6 and C = 50°, the area is ½ × 8 × 6 × sin(50°) ≈ 24 × 0.766 ≈ 18.38 square units.
Frequently asked questions
What does SAS mean here?
SAS stands for side-angle-side: you know two sides of the triangle and the angle that sits between them. That is exactly what this formula needs.
Why must the angle be the included angle?
The formula ½·a·b·sin(C) only works when C is the angle between sides a and b. Using a different angle would give the wrong area.
What units should the angle be in?
Enter the angle in degrees. The calculator converts it to radians internally before applying the sine.
When is the area largest?
For fixed sides a and b, the area is greatest when the included angle is 90°, because sin(90°) = 1. The area then equals ½ × a × b.
Can I use this if I only know three sides?
No — with three sides and no angle, use Heron's formula instead. This calculator is for the two-sides-and-included-angle case.