Berm Width Calculator
Works out the catch-bench (berm) width you need between benches to hit a target overall (inter-ramp) slope angle, for a single-bench geometry. Used by geotechnical and mine engineers laying out open-pit and quarry slopes.
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How to use this calculator
- Enter the bench height H and the bench face angle αf (the steep cut angle of each face).
- Enter the target overall slope angle you want the stacked benches to average.
- Read the required berm width b — the horizontal shelf left on each bench to flatten the slope to the target.
How it works
Each bench contributes a horizontal run of H/tan(αf) for its face plus the berm width b, so tan(overall) = H / (H/tan αf + b).
Rearranging for the berm width gives b = H/tan(overall) − H/tan(αf). Because tangent increases with angle, the overall angle must be flatter than the face angle — a berm can only reduce the slope, so an overall angle equal to or steeper than the face is impossible and is rejected.
Worked example
15 m benches at 70° face, 50° overall target. H/tan(50°) = 12.587 m and H/tan(70°) = 5.460 m, so b = 12.587 − 5.460 = 7.13 m of berm on each bench.
Common mistakes
- Setting the overall angle equal to or steeper than the face angle — impossible, since a berm can only flatten the slope.
- Confusing this geometric berm with the rockfall catch-berm width (use the Catch Berm Width Checker).
- Mixing bench face angle (steep individual cut) with overall/inter-ramp angle (the flatter stacked average).
Frequently asked questions
What is a berm in an open pit?
A berm (catch bench) is the flat horizontal shelf left between successive bench faces. It flattens the overall slope and catches rockfall from above.
Why must the overall angle be flatter than the face angle?
Stacking steep faces separated by flat berms always produces an average slope shallower than the faces themselves.
Does bench height change the berm width?
Yes — the required berm scales directly with bench height. Doubling H doubles the berm width needed for the same face and overall angles.
Is this the same as the rockfall catch-berm rule?
No. This is pure geometry for a target overall angle. Rockfall containment uses an empirical rule such as the modified Ritchie 0.2H+4.5 m — see the Catch Berm Width Checker.
Related tools
- Catch Berm Width Checker
- Overall Slope Angle Calculator
- Kinematic Wedge Intersection Calculator
- RQD Calculator
- Bench Face Height Calculator
- Batter Ratio Calculator
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