How to use this calculator
- Identify the measurements labelled Symmetry diagonal p, Crossing diagonal q. 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
Symmetry diagonal p = 10; Crossing diagonal q = 6
Worked example
For Symmetry diagonal p = 10 cm, Crossing diagonal q = 6 cm, applying the displayed relationship gives area ≈ 30 cm². The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Its symmetry diagonal bisects the crossing diagonal at a right angle. The two segments of the symmetry diagonal need not be equal. Area is half the product of the perpendicular diagonals.
The symmetry diagonal does not usually get bisected. These tools assume a convex kite, not a dart. 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.