Bench Slope Calculator

This bench slope calculator finds slope from rise and run, converts grade formats, checks OSHA trench benching limits, and estimates mining bench stack slope from height, face angle, berm width, and benches.

A bench slope calculator is a versatile tool that determines the slope of a benched excavation or surface directly from rise and run measurements. Depending on your project requirements, it can calculate basic bench slope from rise and run, convert slope formats, or handle OSHA trench benching and mining bench geometry depending on the selected mode.

Users simply enter their known dimensions—such as total vertical drop, horizontal run, bench height, or bench face angle. The tool then instantly generates precise grade percentages, degrees, ratios, and overall excavation widths, making it easy to map out safe and accurate site geometry.

What the Bench Slope Calculator Calculates

This slope grade calculator handles three distinct project types. You can use basic slope and reverse-solve modes for general site grading, switch to the OSHA trench benching quick-reference for compliant safety estimates, or input mining multi-bench geometry for large-scale earthwork calculations.

Mode	Inputs	Outputs	Best use case
Basic Slope	Rise, run, or target slope	Percent grade, degrees, ratio, pitch	General grading and drainage checks
OSHA Benching	Soil type, excavation depth	Max allowable slope, benching allowed status	Trench safety quick checks
Mining Geometry	Bench height, face angle, berm width, bench count	Total width, bench stack slope	Highwall and quarry planning

Bench Slope Formula

The foundational bench slope formula relies on dividing vertical elevation change by horizontal distance. This gives you the core decimal ratio, which serves as the broad target for most grade estimates.

$$\text{grade \%}=\frac{\text{rise}}{\text{run}}\times 100$$

That identical slope value can also be expressed in several different standard formats depending on your industry:

• percent
• degrees
• ratio $1:X$
• pitch $X/12$

Format	Example	Meaning
Percent	50%	The vertical rise is exactly half the length of the horizontal run.
Degrees	26.57°	The exact angle of the slope from a flat horizontal plane.
Ratio	1:2	One unit of vertical rise for every two units of horizontal run.
Pitch	6/12	Six inches of vertical drop per horizontal foot.

How to Calculate Bench Slope From Rise and Run

Finding the exact steepness of your cut requires a few quick steps using the rise and run slope calculator logic.

1. Enter the vertical rise or drop.
2. Enter the horizontal run.
3. Divide the rise by the run to find the decimal slope.
4. Convert to a percent grade by multiplying by 100.
5. Review the tool’s angle, ratio, and pitch outputs.

For example, if an excavation drops 15 feet over a 60-foot distance:

$$\text{decimal slope}=\frac{15}{60}=0.25$$

$$\text{grade \%}=0.25\times 100=25\%$$

Find Rise, Drop, or Run From a Target Slope

Sometimes you already know your required grade and need to determine the physical site dimensions. The tool offers reverse modes to map this out.

Find rise from run and target slope

If you know your available horizontal space and the required grade, you can calculate the maximum elevation change:

$$\text{rise}=\text{run}\times \text{decimal slope}$$

Example: A 40-foot run at a 20% (0.20) target slope yields an 8-foot rise.

Find run from rise and target slope

When your vertical drop is fixed by site conditions but you need to know how far back to extend the cut:

$$\text{run}=\frac{\text{rise}}{\text{decimal slope}}$$

Example: A 10-foot rise requiring a 25% (0.25) slope dictates a 40-foot horizontal run.

Bench Slope Conversion Table

Use this practical reference to translate between common grading formats before locking in your inputs.

Percent grade	Degrees	Ratio	Pitch
5%	2.86°	1:20	0.6/12
10%	5.71°	1:10	1.2/12
25%	14.04°	1:4	3/12
50%	26.57°	1:2	6/12
100%	45.00°	1:1	12/12

OSHA Trench Benching Rules Quick Reference

The OSHA trench benching calculator mode serves strictly as a quick-reference estimator for worker safety, not a full design tool. Under Appendix B guidelines, maximum allowable slopes depend entirely on whether the site features Type A, Type B, or Type C soil. Type B benching is allowed only in cohesive soil. Furthermore, Type C excavations are inherently unstable and are not benched under Appendix B. Any sloping or benching system over 20 ft requires a registered professional engineer design.

Soil type	Benching allowed	Max allowable slope	Key note
Type A	Yes	3/4:1 (53°)	Most stable soil classification.
Type B	Yes	1:1 (45°)	Benching is permitted only if cohesive.
Type C	No	1.5:1 (34°)	Least stable; benching strictly prohibited.

Mining Bench Geometry and Bench Stack Slope

Heavy earthwork utilizes the mining bench slope calculator mode to map out overall highwall geometry. Completely separate from trenching safety limits, this mode processes multiple vertical steps. It calculates the final footprint using your specified bench height, bench face angle, berm width, and the total number of benches.

The tool calculates the horizontal span of a single face and the overall excavation width using these formulas:

$$\text{face run}=\frac{\text{bench height}}{\tan(\text{bench face angle})}$$

$$\text{total excavation width}=(\text{face run}\times N)+(\text{berm width}\times(N-1))$$

For example, calculating a 4-bench stack ($N=4$) with a 20-foot bench height, a 45-degree bench face angle ($\tan(45^\circ)=1$), and a 15-foot berm width:

The face run is $20 / 1 = 20$ feet.

The total width is $(20 \times 4) + (15 \times 3) = 80 + 45 = 125$ feet.

The overall bench stack slope is the total vertical height (80 feet) divided by the total horizontal width (125 feet).

Bench Slope Calculator Inputs and Outputs Explained

Understanding the exact fields ensures accurate tool results. Each variable directly impacts your final geometric profile.

Field	What it means	Common unit options
Rise / Drop	The total vertical elevation change of the slope.	feet, meters
Run	The total horizontal distance the slope covers.	feet, meters
Target Slope	The desired steepness of the proposed cut.	percent, degrees, ratio
Bench Height	The vertical distance of a single mining step.	feet, meters
Berm Width	The horizontal catch space between individual benches.	feet, meters
Bench Face Angle	The exact steepness of an individual mining cut.	degrees
Total Excavation Width	The complete horizontal span from top to bottom.	feet, meters

Common Bench Slope Use Cases

You can apply this tool across several distinct field applications depending on the selected mode:

• site grading and drainage checks
• ramp or access slope checks
• trench benching quick checks
• mining bench stack geometry

Bench Slope Calculator FAQs

Related Tools & Calculators: