Slope ratios, pitch, and foundation fall

Fundamental Slope Formulas and Mathematical Conversions

All surface grading calculations rely on the direct mathematical relationship between vertical elevation change (Rise) and horizontal distance (Run). Before performing any slope calculation, contractors must ensure that both Rise and Run are expressed in the exact same unit of measurement (either decimal feet or inches).

The Three Core Slope Formulas

1. Calculating Slope Percentage ($S\%$):

$$\text{Slope } \% = \left( \frac{\text{Rise}}{\text{Run}} \right) \times 100$$

1. Calculating Vertical Rise (Elevation Drop or Gain):

$$\text{Rise} = \text{Run} \times \left( \frac{\text{Slope } \%}{100} \right)$$

1. Calculating Horizontal Run (Distance Required):

$$\text{Run} = \frac{\text{Rise}}{\left( \frac{\text{Slope } \%}{100} \right)} = \left( \frac{\text{Rise}}{\text{Slope } \%} \right) \times 100$$

Slope Expressions: Percentage, Ratio ($H:V$), and Pitch (Inches per Foot)

Landscape plans and civil engineering specifications express slope in three distinct formats:

• Percentage of Slope ($S\%$): The vertical rise in feet per 100 feet of horizontal run. A grade dropping 2.0 feet over a 100-foot run has a $2.0\%$ slope.
• Horizontal-to-Vertical Ratio ($H:V$): Expresses the horizontal run ($H$) required for every single unit of vertical rise ($V$). For example, a $3:1$ slope indicates a 3-foot horizontal distance for every 1-foot vertical drop: $S\% = (1 / 3) \times 100 = 33.33\%$. A $2:1$ slope indicates 2 feet of run per 1 foot of rise: $S\% = (1 / 2) \times 100 = 50.0\%$.
• Pitch in Inches per Foot: Commonly used for flatwork, patios, and drainage pipe runs.
  • $1/4" \text{ per foot} = 0.25" / 12" = 0.02083 = 2.08\%$
  • $1/8" \text{ per foot} = 0.125" / 12" = 0.01042 = 1.04\%$
  • $1/2" \text{ per foot} = 0.500" / 12" = 0.04167 = 4.17\%$

These are mathematical conversions, not safe-mowing limits or approval of a planted slope. One-eighth and one-quarter inch per foot are commonly rounded construction pitches; they do not exactly equal one and two percent.

Step-by-Step Slope Calculation Examples

• Example 1 (Finding Required Vertical Drop for a Patio): A concrete paver patio extends out $28.0\text{ feet}$ horizontally from a home foundation. The project specifications call for a positive drainage pitch of $1/4" \text{ per foot}$ ($2.08\%$). What is the total vertical drop required across the patio?

$$\text{Rise} = \text{Run} \times \text{Pitch} = 28.0\text{ ft} \times 0.25"/\text{ft} = 7.0\text{ inches} \quad (0.583\text{ ft})$$

The outer patio edge must be set exactly 7 inches lower than the foundation line.

• Example 2 (Finding Percentage Slope from Field Elevation Shots): A laser level survey reads an elevation of $142.50\text{ ft}$ at the upper end of a lawn and $139.80\text{ ft}$ at the lower property line. The horizontal distance between the two survey pins is $45.0\text{ feet}$. What is the slope percentage?

$$\text{Rise} = 142.50\text{ ft} - 139.80\text{ ft} = 2.70\text{ ft}$$ $$\text{Slope } \% = \left( \frac{2.70\text{ ft}}{45.0\text{ ft}} \right) \times 100 = 0.060 \times 100 = 6.0\%$$

Standard Regulatory and Functional Slopes in Landscape Construction

Operating in compliance with the Oregon Residential Specialty Code (ORSC) and standard landscape architectural practices requires adhering to strict slope boundaries:

Positive Drainage Away from Building Foundations

Water pooling against foundation walls causes basement flooding, crawlspace rot, mold growth, and structural settlement. Under standard building codes (ORSC R401.3):

• Standard Code Mandate: The ground surface immediately adjacent to foundation walls must slope positively away from the building at a minimum of 5% slope for the first 10 feet of horizontal distance.
• Physical Measurement: A 5% slope over 10 feet equates to a minimum vertical fall of 6 inches ($10\text{ ft} \times 0.05 = 0.50\text{ ft} = 6\text{ inches}$).
• Restricted Space: Where lot lines, walls, slopes, or other physical barriers prevent the prescribed fall, provide drains or swales as required by the applicable provision to carry water away. Check the approved alternate and impervious-surface requirements rather than assuming every alternate must retain five-percent grade.