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Overall Slope Angle Calculator

Work out the overall (inter-ramp) angle of a stacked-bench pit slope from the bench height, face angle, catch-berm width and number of benches. Used by open-pit and quarry geotechnical engineers to check that a bench stack meets the design slope angle.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the bench height H and the bench face angle αf for a single bench.
  2. Enter the catch-berm width b and the number of benches n in the stack.
  3. Read the overall slope angle (IRA), plus the total slope height and horizontal setback.

How it works

Each bench contributes a vertical rise of H and a horizontal advance of H/tan(αf). A flat catch berm of width b sits between successive benches, so a stack of n benches has (n−1) berms.

The totals are vertical = n·H and horizontal setback = n·(H/tan αf) + (n−1)·b, and the overall inter-ramp angle is IRA = atan(total vertical / total horizontal). Steepening the bench faces, narrowing the berms, or adding benches all steepen the overall slope.

Worked example

Five 15 m benches at 70° with 8 m berms. Bench face run = 15/tan70° = 5.460 m. Total vertical = 75 m. Total horizontal = 5×5.460 + 4×8 = 59.30 m. Overall slope angle = atan(75/59.30) = 51.7°.

Common mistakes

  • Counting n berms instead of (n−1) — there is one fewer berm than benches.
  • Using the overall angle where the steeper bench face angle applies (or vice versa).
  • Mixing crest-to-crest and toe-to-toe berm-width definitions; keep b as the horizontal catch width.

Frequently asked questions

What is the difference between bench face angle and overall slope angle?

The bench face angle is the steep angle of one batter (often 60–80°). The overall or inter-ramp angle is the flatter average from the toe of the lowest bench to the crest of the highest, once the catch berms are included.

Why are there (n−1) berms and not n?

Berms are the flat catch benches between stacked faces. With n benches there are n−1 gaps, so the horizontal setback adds (n−1)·b.

Does berm width change the overall angle much?

Yes. Wider catch berms add horizontal distance without adding height, so they flatten the overall angle. Set b to zero and the overall angle equals the bench face angle.

Is this a slope-stability check?

No. It is pure geometry. The overall angle still has to be checked against a stability analysis for the actual rock mass, structure and groundwater.

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