FORMULA SHELF
18 of 370
The arithmetic behind the work: what to measure, what to type in, and what the answer comes out as. Every formula says what the symbols mean and gives a worked example, so you can check it against a job you have already done.
SHELVES
Geometry
18 formulas
Bending strip, curved edging and the length of a curved wall.
A 90 degree arc on a 2 m radius is 3.14 m long.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Pie-shaped concrete, a curved header bank, or part of a round tank lid.
A 90 degree sector of a 2 m radius circle = 3.14 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Sloping panels, lean-to roofs and fields with parallel sides. Use perpendicular height, not the sloping side.
A 6 m base and 2 m height = 12 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Hexagonal pens, octagonal silos and regular paving. For a hexagon the multiplier is 2.598.
A 2 m hexagon: A = 2.598 x 4 = 10.39 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Diamond-shaped panels, paving patterns and braces. Multiply the diagonals and halve.
Diagonals 4 m and 6 m give 12 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Oval beds, elliptical tank ends and oval pipe openings.
Axes 4 m by 2 m: A = 6.28 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Setting out curved yards and checking whether a point falls inside a round pen.
Centre (2,3), radius 5 passes through (6,6).
Checking a frame is square, ordering a diagonal brace and setting out a building.
A 6 m by 8 m shed has a 10 m diagonal.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Fencing, skirting, edging and the length of timber round a frame. Add the two sides and double it.
A 12 m by 8 m pen needs 40 m of fence.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Any three-sided run: gable ends, braces, triangular beds and roof bays.
Sides 3 m, 4 m and 5 m give a 12 m perimeter.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Scaling a drawing, finding an inaccessible height from a shadow, and setting out a roof.
A 2 m shadow from a 1.5 m post means a 12 m shadow is a 9 m tree.
Roofs, hoppers and conical covers. Slant height is the distance up the slope.
A 2 m radius cone with 3 m slant = 31.42 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Paint and insulation for tanks, silos and drums, including both ends.
A 1 m radius, 3 m tall tank has 25.13 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Paint, coating and insulation on spherical or domed tanks.
A 1 m radius sphere has 12.57 m2 of surface.
Convenience only. Double-check the result against the worked example or a second method before you use it.
When you can measure the three sides but not the height. Useful for odd yard patches.
Sides 3, 4 and 5 m: s = 6, A = 6 m2.
Tapered tanks, silage pits, hoppers and the volume of a truncated cone.
End areas 4 m2 and 9 m2 over 3 m = 18.5 m3.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Grain heaps, gravel piles and pyramidal roofs. A third of the box it sits in.
A 4 m x 4 m base and 3 m height = 16 m3.
Round tanks, ballast, domes and spherical stock waterers.
A 1 m radius sphere holds 4.19 m3.
Convenience only. Double-check the result against the worked example or a second method before you use it.
SOURCES & PROVENANCE
1 listed
This page is an AI-organised index. The label means the grouping and cross-links were compiled with AI; the information itself comes from the public-domain books, reports and manuals listed below. Open any source to read the local copy or follow the link to the original publication.