Calculation of length
The maths is about right angle triangles. The dimension of the vertical part of the right angle triangle is the height of the lampshade. The horizontal dimension is the radius of the bottom minus the radius of the top. The length of the angle is the square root of the sum of the square roots of the vertical and horizontal sides.
E.g., a lampshade 200mm high with a 50mm vase cap and 400mm bottom width:
The vertical of the triangle is 200mm.
The horizontal is 400/2 = 200mm – 25mm (half the diameter of the vase cap) = 175mm.
The length of the panel is equal to the square root of the sum of the squares of the sides.
In this example, 40000+30625=70625 of which the square root is 265. So the panel is 265mm long.
Measuring the length
If you don’t want to do the maths, do a scaled or full size drawing. It only needs to be one side of the shade, but it can be the full shade.
- Draw a vertical the length of the shade.
- At the top draw the radius of the vase cap on each side of the vertical.
- At the bottom draw the radius of the shade on each side of the vertical.
- Join the two end points of the horizontal lines on each side of the vertical.
- Measure this line to determine the length of the panel.
This drawing method does have the advantage of allowing you to see the angle of the proposed shade and adjust it if necessary.