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Rebuilding civilization

Geometry and measurement

Slope and height difference

Convert between percent, degrees and 1:n ratio, and work out the drop of a ditch, a road or a roof.

m

Difference in height between the two points.

m

Measured horizontally, not along the slope. Optional if you know the % or the angle.

Result

Slope
— %
Angle
— °
Ratio 1:n (n)
—
Height difference per kilometre
— m/km
Height difference over that distance
— m
Length along the slope
— m

How it is calculated

Slope (%) = 100 × height difference ÷ horizontal distance. Angle = arctan(height difference ÷ distance). Ratio 1:n with n = distance ÷ height difference.

Example: 1.5 m of drop over 30 m → 5 %, 2.86° and 1:20. 100 % is 45°, not 90°.

To measure it without an optical level: stretch a horizontal string using a water level (clear hose) or a spirit level and measure the height left to the ground at the end of the stretch.

Keep in mind

  • Rough references: earth ditches and channels, 0.1-0.5 % (1-5 m per km) so water flows without eroding; drains and sewers, 1-2 %; accessible ramps, ≤ 6-8 %; cart roads, ≤ 8-10 %.
  • On land steeper than 15-20 % it is best to farm on terraces or along contour lines to slow erosion.

See also

More tools in “Geometry and measurement”