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Side Slope Calculator

Calculate side-slope angle and horizontal run from vertical height and a V:H slope ratio for quick earthwork geometry checks.

Slope ratioSlope angleHorizontal run1V:nH
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Side Slope Calculator

Calculate side-slope length, horizontal run, H:V ratio, percent grade and angle from slope ratio, dimensions or angle.

Horizontal run H0.00 m
Slope face length0.00 m
Slope angle0.00°
Percent grade%0.00
H = V × (H:V ratio) · L = √(H² + V²) · Angle = arctan(V/H)
H:V ratio1,50:1
Slope face length0.00 m
Slope angle0.00°
Percent grade%0.00
H:V = H / V : 1 · L = √(H² + V²) · Grade (%) = 100 × V/H
Horizontal run H0.00 m
H:V ratio1,50:1
Slope face length0.00 m
Percent grade%0.00
H = V / tan(α) · L = V / sin(α) · H:V = H/V : 1

This tool performs geometric slope calculations only. Whether a soil or rock slope is safe depends on material properties, groundwater, loads, stratification and a proper stability analysis.

Calculation method and use

Converts horizontal-to-vertical slope ratio into angle, horizontal projection and sloping length for cut/fill geometry checks.

Slope length = √(Horizontal² + Vertical²)

Example and practical interpretation

For a 2H:1V slope with 3 m vertical height, horizontal run is 6 m and slope length is about √(6²+3²)=6.71 m.

Points to check

  • Confirm whether the ratio is entered H:V or V:H.
  • Do not use geometry alone as a stability check.
  • Consider geotechnical conditions and applicable safety requirements.

Frequently asked questions

What does a 2:1 slope mean?

Commonly it means 2 horizontal units for every 1 vertical unit.

How is slope angle calculated?

Angle can be found from arctan(vertical/horizontal).

How is slope length calculated?

Treat horizontal and vertical components as a right triangle and use Pythagoras.

Side Slope: 1V:nH Ratio, Percent Grade, Angle and Slope Length

The same side-slope geometry can be expressed as a 1V:nH ratio, percent grade, or angle from horizontal. CivilCalc converts between these forms and calculates horizontal run and sloping face length for a given vertical height. These quantities are useful for earthwork cross-sections, layout checks and preliminary surface or quantity calculations.

Engineering content: 19 September 2026

Convert ratio, percent and angle

In 1V:nH, one unit of vertical change corresponds to n units of horizontal run. For example, 1V:2H means 2 horizontal for 1 vertical.

Grade (%) = (V / H) × 100
θ = arctan(V / H)
H = n × V

Drawings and specifications may instead state the ratio as H:V. Confirm the stated convention before using the numbers.

Sloping face length

With vertical height and horizontal run known, the face length follows from right-triangle geometry.

L = √(H² + V²)
Example: For a 12 ft vertical height at 1V:2H, H = 24 ft and L = √(24²+12²) = 26.83 ft. The angle is about 26.6° and the geometric grade is 50%.

Common side-slope ratios

Slope (V:H)H:VGradeAngleHorizontal run for 10 ft rise
1V:0.5H0.5:1200%63.4°5 ft
1V:1H1:1100%45.0°10 ft
1V:1.5H1.5:166.7%33.7°15 ft
1V:2H2:150%26.6°20 ft
1V:3H3:133.3%18.4°30 ft

These are geometry conversions only; the table does not establish that any ratio is safe for a particular soil or rock.

Triangular cross-section area

If the side slope forms a simple triangular wedge between top and toe elevations, its geometric cross-sectional area is:

A = H × V / 2
A 12 ft high 1V:2H slope has H=24 ft, giving a triangular area of 144 ft². Actual cut/fill volume requires cross-sections along the alignment and the real ground geometry.

Geometry is not stability

This calculator determines slope geometry, not factor of safety. A safe soil or rock slope depends on strength, stratification/discontinuities, groundwater, drainage, surcharge, seismic effects, erosion and construction duration. Critical or permanent slopes require geotechnical stability assessment.

Six engineering checks

1. Ratio convention
1V:2H and 2V:1H are not equivalent. Verify V:H or H:V on the drawing.
2. Elevation difference
Use reliable survey/design elevations for vertical height and interpret the direction correctly.
3. Available footprint
Check that the required horizontal run fits property, roadway, structure and easement constraints.
4. Water and drainage
Surface water and groundwater can materially change stability even though the geometry is unchanged.
5. Surcharge
Vehicles, stockpiles, structures and equipment near the crest belong in the stability assessment.
6. Quantity limits
Do not treat one triangular cross-section as total earthwork volume; evaluate changing sections along the alignment.

Frequently asked questions

What percent grade is a 1V:2H slope?

V/H = 1/2, so the geometric grade is 50% and the angle from horizontal is about 26.6°.

Does a 50% slope mean 50 degrees?

No. Percent grade and degrees are different measures. A 50% grade corresponds to about 26.6°.

What does a 2:1 side slope mean?

The notation can be ambiguous without a stated convention. It commonly means 2H:1V in civil drawings, but always confirm whether the project uses H:V or V:H.

Does the calculated ratio prove the slope is stable?

No. The tool performs geometry only. Stability requires geotechnical evaluation of soil or rock, water, loads and required factors of safety.

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