How to Calculate Trench Slopes and Top Width

A sloped trench is wider at the top than at the bottom, sometimes a lot wider. The side slope you dig to sets how much ground you open up, how much dirt comes out, how much goes back in, and whether the trench fits between the curb and the utility on the other side. This guide explains what slope ratios mean, shows how to figure top width by hand, walks through the four trench profiles, and then shows how to set it all up in Trench Calculator.

Trench Calculator app icon
Trench Calculator app icon

Angle = arctan(V ÷ H). For 1½:1, that's arctan(1 ÷ 1.5) = 33.7°.

In Trench Calculator: the Angle of Repose buttons use the same H:V order: 3/4:1, 1:1, 1.5:1, 2:1 and Custom. For Custom, enter the horizontal number, so 1.5 for a 1½:1 slope.

What a slope ratio means

Trench side slopes are written as a ratio of horizontal to vertical (H:V). That's how OSHA's excavation standard writes them too.

  • 1:1 means the wall goes 1 ft out for every 1 ft down.

  • 1½:1 means 1.5 ft out for every 1 ft down. That's flatter.

  • ¾:1 means 0.75 ft out for every 1 ft down. That's steeper.

The bigger the first number, the flatter the wall and the wider the trench at the top.

You'll also see the same slope written as an angle or a percent:

Slopes ½:1 to 2:1 with angle from horizontal, wall percent, and lay-back per side for 8 ft of depth
Slopes ½:1 to 2:1 with angle from horizontal, wall percent, and lay-back per side for 8 ft of depth

The formula: top width from bottom width, depth and slope

For a trench with the same slope on both sides:

Top width = bottom width + 2 × (depth × H)

H is the horizontal number from the H:V ratio (1 for 1:1, 1.5 for 1½:1, 0.75 for ¾:1). Each wall lays back depth × H, and there are two walls.

The cross-section is a trapezoid, so:

Area = (bottom width + top width) ÷ 2 × depth
Volume (yd³) = area (ft²) × length (ft) ÷ 27

Measure depth to the bottom of the excavation, not just to the pipe. If you dig below the pipe for bedding, that extra depth widens the top too (more on that below).

Worked example: 3 ft bottom, 8 ft deep, 1:1

  • Bottom width: 3 ft

  • Depth to the bottom of the trench: 8 ft

  • Side slope: 1:1 (H:V)

  • Lay-back per side = 8 × 1 = 8 ft

  • Top width = 3 + 2 × 8 = 19 ft

  • Area = (3 + 19) ÷ 2 × 8 = 11 × 8 = 88 ft²

  • Volume per 100 ft = 88 × 100 ÷ 27 = 325.9 yd³

Check it: split the trapezoid into a 3 ft × 8 ft rectangle (24 ft²) and two triangles, each 8 ft wide × 8 ft tall ÷ 2 = 32 ft². 24 + 32 + 32 = 88 ft². ✓

Same trench, different slopes

Same 3 ft bottom and 8 ft depth, per 100 ft of trench (table below)

Top width, area and yd³ per 100 ft, 3 ft wide 8 ft deep trench: vertical, ¾:1, 1:1, 1½:1 and 2:1
Top width, area and yd³ per 100 ft, 3 ft wide 8 ft deep trench: vertical, ¾:1, 1:1, 1½:1 and 2:1

Going from 1:1 to 1½:1 on this trench adds 8 ft of top width and about 118 yd³ of excavation, and the same amount of backfill, for every 100 ft of trench. Slope is often the biggest number in a trench quantity, so get it right before you bid or order material.

The four trench profiles

In Trench Calculator, every trench run starts with a profile. These are the shapes on the app's Select Trench Profile screen:

Trench Calculator Select Trench Profile screen showing Profiles A, B, C and D in a 2 by 2 grid
Trench Calculator Select Trench Profile screen showing Profiles A, B, C and D in a 2 by 2 grid
Trench Calculator Profiles A–D: sloped, vertical cut then slope, vertical walls, and stepped benches
Trench Calculator Profiles A–D: sloped, vertical cut then slope, vertical walls, and stepped benches

Profile B: vertical cut, bench, then slope

Profile B has three parts, from the bottom up:

  1. A vertical cut at the bottom, as wide as the Bottom Width (W) and as tall as the Bench Height (H).

  2. At the top of that cut, a flat shoulder that steps out by the Bench Width - Horizontal Extension (BW) on each side. So the trench is W + 2 × BW wide at that level.

  3. The sloped walls start at the outer edge of each shoulder and run up to grade at your side slope.

In formula form, with D = total excavation depth (invert depth + bedding below the pipe):

  • Width at the bench = W + 2 × BW

  • Top width = (W + 2 × BW) + 2 × (D − H) × S, where S is the horizontal number of the slope (1 for 1:1). On this profile, H means Bench Height, not the slope.

  • Area = W × H + [(W + 2 × BW) + top width] ÷ 2 × (D − H)

Worked example (from Trench Calculator):

(see the inputs table at the end of this section)

  1. Total depth D = 8 ft + 4 in of bedding below the pipe = 8 + 0.333 = 8.333 ft

  2. Vertical cut: 3 ft wide × 2 ft tall = 6.00 ft²

  3. Width at the bench = 3 + 2 × 3 = 9 ft

  4. Sloped part: 8.333 − 2 = 6.333 ft tall. At 1:1, top width = 9 + 2 × 6.333 = 21.67 ft

  5. Sloped area = (9 + 21.67) ÷ 2 × 6.333 = 97.11 ft²

  6. Excavation area = 6.00 + 97.11 = 103.11 ft²

Bedding and pipe:

  • Bedding zone height = 4 in below + 6 in pipe + 12 in cover = 22 in (1.833 ft). That's less than the 2 ft vertical cut, so the bedding sits entirely in the 3 ft-wide box: 3 × 1.833 = 5.50 ft².

  • Pipe = π × (0.5 ft)² ÷ 4 = 0.20 ft²

  • Bedding = 5.50 − 0.20 = 5.30 ft²

  • Backfill = 103.11 − 5.50 = 97.61 ft²

Check it: bedding 5.30 + pipe 0.20 + backfill 97.61 = 103.11 ft², which matches the excavation. These are the same areas the app shows for this run: Excavation 103.11, Backfill 97.61, Bedding 5.30 and Pipe 0.20 ft². Per 100 ft of trench, that's 103.11 × 100 ÷ 27 = 381.9 yd³ of excavation.

Profile B inputs and results: 8 ft to invert, 3 ft bottom, 2 ft bench, 3 ft bench width, 1:1
Profile B inputs and results: 8 ft to invert, 3 ft bottom, 2 ft bench, 3 ft bench width, 1:1
Profile B inputs: 8 ft to invert, 3 ft bottom, 2 ft bench height, 3 ft bench width, 6 in pipe, 1:1
Profile B inputs: 8 ft to invert, 3 ft bottom, 2 ft bench height, 3 ft bench width, 6 in pipe, 1:1

Profile D: stepped benches

On Profile D you enter the Number of Benches and the Bench Width - Horizontal Extension (BW) along with the usual depth, bottom width, pipe and bedding fields. There's no Angle of Repose picker on this profile, because the steps set the shape instead of a slope.

How the depth is split: the app divides the total dig depth into equal rises, and there's always one more rise than benches: the vertical cut at the bottom, plus one rise above each bench. So each rise is depth ÷ (Number of Benches + 1). You don't set a separate height for each rise. The app shows it as Bench Height (per rise). Each bench steps out by BW on each side, so every level is 2 × BW wider than the one below it.

In formula form, with D = total excavation depth, N = Number of Benches and W = Bottom Width:

  • Rise height = D ÷ (N + 1)

  • Top width = W + 2 × N × BW

  • Area = D × (W + N × BW)

More benches means shorter rises. If OSHA or your competent person limits how tall each step can be, pick enough benches to keep the rise under that height.

Worked example (from Trench Calculator):

(see the inputs table at the end of this section)

  1. Total depth D = 7.50 + 0.50 = 8.00 ft

  2. With 2 benches there are 3 rises: 8.00 ÷ (2 + 1) = 2.67 ft per rise

  3. Widths, from the bottom up: 3 ft (the bottom cut), 3 + 2 × 3 = 9 ft (above the first bench), 9 + 2 × 3 = 15 ft (above the second bench, the top width)

  4. Area = 2.667 × 3 + 2.667 × 9 + 2.667 × 15 = 2.667 × 27 = 72.00 ft² (or with the formula: 8 × (3 + 2 × 3) = 72)

Check it: the app shows the same numbers for this run: a 15.00 ft top, 8.00 ft depth, 3.00 ft bottom, Bench Height (per rise) 2.67 ft and Excavation 72.00 ft². With bedding off, everything around the pipe is backfill, so Backfill 71.80 ft² is 72.00 − 0.20 ft² of pipe. ✓ Per 100 ft of trench, that's 72 × 100 ÷ 27 = 266.67 yd³ of excavation (computed here from the app's ft², since the screenshot shows areas only).

For this trench, the two benches give the same 15 ft top width and 72 ft² area as a smooth ¾:1 slope (see the table below), but with flat steps instead of one sloped wall.

Profile D cross-section: 3 ft bottom, 8 ft deep, 2 benches of 3 ft, 15.00 ft top, 72.00 ft² dig
Profile D cross-section: 3 ft bottom, 8 ft deep, 2 benches of 3 ft, 15.00 ft top, 72.00 ft² dig
Profile D example inputs: bedding off, 7.5 ft to invert, 3 ft bottom, 2 benches 3 ft wide, 6 in pipe
Profile D example inputs: bedding off, 7.5 ft to invert, 3 ft bottom, 2 benches 3 ft wide, 6 in pipe

Doing it in Trench Calculator

  1. Tap + New Project and name the job. Open the project, then tap + Add Trench Run.

  2. On Select Trench Profile, tap the profile that matches how you'll dig: A, B, C or D.

  3. On Edit Trench Run, fill in Run Name, Category (Storm, Sanitary, Water or Other), Pay Item Number and Trench Length. You can also use Station From / Station To with Calc. The card shows Selected: Profile A (or whichever you picked), and you can tap Change to switch.

  4. Under Measurements, set Include Bedding (and Foundation Undercut if you need it). Pick a Depth Input: Uniform, Start/End or Elevations. Then enter Trench Depth to Bottom of Pipe (Invert), Bottom Width (W), Pipe Shape, Pipe Outside Diameter and the bedding thicknesses. Each length field has an ft / in toggle.

  5. With Include Bedding off, Minimum Cut Below Pipe replaces Minimum Bedding Thickness (Below Pipe). Enter 0 to dig exactly to the invert depth, or the extra depth you'll dig below the pipe.

  6. Profile B adds Bench Height (H) and Bench Width - Horizontal Extension (BW).

  7. Profile D adds Number of Benches and Bench Width - Horizontal Extension (BW).

  8. On Profiles A and B, tap the side slope under Angle of Repose. Profile C has vertical sides only, so it has no picker. The choices are 3/4:1, 1:1, 1.5:1, 2:1 or Custom, all written H:V. Profile D has no Angle of Repose picker. Tap Calculate Volumes, and Save Run to keep it.

Custom slope: tap Custom and enter the horizontal number in Custom slope (H:V). For example, enter 2 for a 2:1 slope (2 ft out for every 1 ft down), or 1.5 for 1½:1.

  1. Check the cross-section. The app draws the profile with the top width across the top, the bottom width and depth, and the area of each part (bedding, backfill, excavation, pipe).

Where the app's depth comes from

The depth the app uses for the slope is the invert depth plus whatever you dig below the pipe, because that's the true bottom of the excavation. With Include Bedding on, that's Minimum Bedding Thickness (Below Pipe). With it off, it's Minimum Cut Below Pipe (enter 0 to dig exactly to invert). In the watermain example from the excavation, backfill and bedding guide, the inputs are 5.67 ft to invert + 4 in bedding below = 6.00 ft (6.003 unrounded), 3 ft bottom and 1:1:

Top width = 3 + 2 × 6.003 × 1 = 15.01 ft. That's exactly what the app's cross-section shows.

To match the 8 ft worked example above in Profile A, use the inputs in the table below:

Dig depth = 7.50 + 0.50 = 8.00 ft. Top width = 3 + 2 × 8.00 × 1 = 19.00 ft. Excavation area = (3 + 19) ÷ 2 × 8 = 88.00 ft².

The app's cross-section shows exactly that: a 19.00 ft top, 8.00 ft depth and 3.00 ft bottom, with Excavation 88.00 ft². With bedding off, there's no bedding zone, so everything around the pipe is backfill. The 6 in pipe is π × 0.5² ÷ 4 = 0.20 ft², and the app's Backfill 87.80 ft² is 88.00 − 0.20. ✓

For a 100 ft run, that's 88 × 100 ÷ 27 = 325.93 yd³ of excavation (computed here, since the screenshot shows areas only).

Depth changes along the run? Use Start/End or Elevations instead of Uniform. The trench gets wider at the top where it's deeper, and the cross-section shows the range of top widths.

When you've added every run, export a PDF or CSV with project totals and subtotals by category and pay item. For bedding, backfill and the in-place vs. loose volume note, see How to Calculate Trench Excavation, Backfill and Bedding.

Profile A cross-section: 3 ft bottom, 8 ft deep, 1:1 slope, 19.00 ft top width, 88.00 ft² excavation
Profile A cross-section: 3 ft bottom, 8 ft deep, 1:1 slope, 19.00 ft top width, 88.00 ft² excavation
Profile A inputs: 7.50 ft invert, bedding off, 6 in pipe, 6 in cut below, 3 ft bottom, 1:1, 100 ft
Profile A inputs: 7.50 ft invert, bedding off, 6 in pipe, 6 in cut below, 3 ft bottom, 1:1, 100 ft

Safety note: the slope is a safety decision, not just a quantity

This guide covers the geometry and the math. It isn't safety advice and doesn't replace the regulations or your competent person.

  • In the U.S., trench protection falls under OSHA 29 CFR 1926 Subpart P (Excavations). Each worker in an excavation must be protected from cave-ins by an adequate protective system. The exceptions are excavations made entirely in stable rock, or less than 5 ft deep where a competent person finds no sign of a potential cave-in (29 CFR 1926.652(a)(1)).

  • Under OSHA's Appendix B, the maximum allowable slope depends on the soil or rock type, which has to be classified under Appendix A. For excavations under 20 ft deep, Table B-1 lists Type A ¾:1 (53°), Type B 1:1 (45°) and Type C 1½:1 (34°). Deeper sloping or benching has to be designed by a registered professional engineer. Signs of distress, or surcharge loads from spoil, equipment or traffic, call for a flatter slope (Appendix B to Subpart P).

  • Vertical lower portions (Profile B) and benches (Profile D) come with their own limits in Appendix B. For example, in Type B and C soil, a vertically sided lower portion must be shielded or supported to at least 18 in above the top of the vertical side, and Appendix B has no benching configuration for Type C soil.

  • If you don't classify the soil, OSHA's default option is to slope no steeper than 1½:1 (34°) (1926.652(b)(1)).

Trench Calculator figures quantities from the slope you pick. It doesn't classify soil or check your protective system. Your competent person decides the slope and protection on site, and your state or local rules may add requirements.

FAQ

Is 1:1 the same as 45 degrees? Yes. 1 ft out for every 1 ft down is a 45° wall, or 100% as a percent.

Is a 1½:1 slope steeper or flatter than 1:1? Flatter. The wall goes 1.5 ft out for every foot down, so the trench is wider at the top: 34° instead of 45°.

Why is my top width wider than I expected? You probably measured depth to the invert instead of the bottom of the excavation. Add the bedding or cut below the pipe to the depth, then lay it back on both sides.

Do I use the same slope on both sides? This guide and the formula above assume both sides match.

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