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Bench Face Height Calculator

Turn a bench's vertical height and face angle into the batter (along-face) length and the horizontal toe-to-crest run. A quick setting-out geometry tool for open-pit benches, quarry faces and cut batters.

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How to use this calculator

Enter Values

Range 0–90

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 vertical bench height H in metres.
  2. Enter the bench face angle αf in degrees (0–90°).
  3. Read the batter/face length L and the horizontal run R.

How it works

A bench face is a right-angled triangle: the vertical height H, the horizontal run R and the sloping face L. From the face angle αf, the along-face length is L = H/sin(αf) and the horizontal toe-to-crest run is R = H/tan(αf).

The face length is always at least as long as the vertical height, and approaches it as the face gets closer to vertical. This is geometry only — it does not set the maximum safe bench height, which comes from a separate design/stability check.

Worked example

15 m bench at a 70° face angle. Face length L = 15/sin70° = 15.96 m along the batter. Horizontal run R = 15/tan70° = 5.46 m from toe to crest.

Common mistakes

  • Confusing the sloping face length L (uses sin) with the horizontal run R (uses tan).
  • Treating this as a bench-height design tool — the maximum safe height is a stability/blast-design question.
  • Entering the overall slope angle instead of the single bench face angle.

Frequently asked questions

What is the batter length of a bench?

The distance measured up the sloping face from toe to crest: L = H/sin(αf). For a 15 m bench at 70° it is about 15.96 m.

How is this different from a Bench Height Checker?

This tool is pure geometry — face length and run from a chosen height and angle. A Bench Height Checker sizes the maximum safe height from rock strength, structure and equipment reach.

Why is the face length longer than the vertical height?

The face is the hypotenuse of the height–run triangle, so it is always longer than the vertical height, except at a perfectly vertical face where they are equal.

What horizontal room does a bench need?

The toe-to-crest run R = H/tan(αf). A steeper face angle gives a smaller run and a more compact footprint.

Related tools

Explore more in Geology, Geotechnical & Ground Engineering.

Cite this tool

Zerdly. (2026). Bench Face Height Calculator. Retrieved from https://www.zerdly.com/tools/bench-face-height-calculator/

Tip: Enter any known values to calculate the remaining results.

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