How to use this calculator
- Identify the measurements labelled Side a, Side b, Included angle θ. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
Side a = 8; Side b = 5; Included angle θ = 60
Worked example
For Side a = 8 cm, Side b = 5 cm, Included angle θ = 60°, applying the displayed relationship gives area ≈ 34.641016 cm². The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Adjacent angles add to 180 degrees. The diagonals bisect one another but are generally neither equal nor perpendicular. Area is base times the perpendicular distance between the parallel base lines.
A sloping side is not generally the height. Base and height alone do not determine perimeter. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.