195/3336–9FE Reference Handbook 10.4 · Civil · Surveying · Grades

Handbook formula

Percent Grade and Slope Distance

Grade is rise/run, not rise/slope length. Vertical curves connect grades g1 and g2. A 6% grade is 6 ft per 100 ft horizontal.

Percent grade
Horizontal distance
Slope distance

Step-by-step solved example

Slope distance 200 m at +5%. Horizontal and rise?

θLsΔH
Grade g% = rise/run; θ = arctan(g/100).
  1. 1. θ

    tanθ=0.05, θ=2.862°, cosθ=0.9988.

  2. 2. Lh, ΔH

    Lh=199.75 m, ΔH=9.99 m ≈ 0.05×200 if using slope as run (small-angle ≈).

Answer: Lh ≈ 199.8 m, rise ≈ 10.0 m

10 practice questions

0/10 correct

1.+2% means

2.A drop of 8 ft in 200 ft horizontal is

3.θ for 100% grade is

4.g1=+3%, g2=−1%: algebraic change A =

5.Horizontal from slope using 5% may be approximated as

6.Railroad 1% vs highway 6% — gradeability is

7.Elevation at 350 ft along a +1.2% from sta 0 elev 100 is

8.Cross-slope 2% on a 12 ft lane is a drop of

9.Grade from elev 52 to 40 over 600 ft H is

10.A vertical curve’s PVC elevation uses