Sloped-Trench Excavation Calculator: Trapezoid Volume, Bank and Loose Volume

A trench with sloped sides is wider at the surface than at the bottom. A rectangular formula applied to either width alone gives the wrong quantity, so this calculator uses the trapezoid cross-section and keeps the bank volume and the loose planning volume as separate results.

How much soil does a sloped trench hold?

Enter the trench length, bottom width, vertical depth, and side-slope ratio. The calculator first works out the top width from the slope, then the trapezoid section area, then the bank volume. It applies a swell percentage only to the loose planning volume, and only when you enter one.

When should you use this sloped-trench calculator?

Use it for one trench run whose cross-section stays the same along its length, with straight sides sloping at one ratio on both sides. Run it separately for each run when length, bottom width, depth, or slope changes.

Use the Trench Excavation Calculator for rectangular, vertical-sided sections. Use the changing trench sections guide when a run changes section along its length.

Which measurements do you need?

You need the trench length, bottom width, vertical depth, side-slope ratio, and a swell percentage only when the project supports one.

Trench length

Measure the run length along the trench centreline for the section the other dimensions describe. A run that changes width, depth, or slope is two or more runs, not one longer run.

Bottom width

Measure the width at the trench floor. The top width is a calculated result, not an input, so entering a surface width here would double count the slope.

Depth

Measure the vertical depth from the surface to the floor. Do not measure along the sloped side. The sloped-side length is longer than the vertical depth, and using it inflates the section area.

Side slope ratio

Enter the slope as horizontal run per 1 unit of vertical rise (H:V). A 1.5:1 slope gains 1.5 units of width per side for each unit of depth. Read the ratio in that order. A 1:1.5 entry inverts the slope and gives a different top width.

Measure the ratio in the field when it is not on a drawing. Measure the horizontal offset from the trench-bottom edge to the surface edge on one side and divide by the depth. If the offset is 9 ft at a 6 ft depth, the ratio is 1.5.

When the two sides were cut to different slopes, enter the average of the two ratios. The average gives the same top width and the same section area as the two separate offsets added together, because top width depends only on the sum of the two offsets.

Identical runs

Use this field only for runs with identical length, bottom width, depth, and slope. Runs that differ in any dimension need separate calculations.

Swell percentage

The swell field starts at 0%. Swell depends on soil type, moisture, and handling, so no single value fits every trench. Enter a percentage only when the project record supports one, and record the reason. The bank volume never changes with swell. Only the loose planning volume moves.

What formulas does the calculator use?

The calculator keeps full precision during the calculation and displays up to 3 decimal places for widths, areas, and volumes.

Top width = bottom width + 2 x depth x slope ratio

Section area = (bottom width + top width) / 2 x depth

Bank volume = section area x length x identical runs

Loose planning volume = bank volume x (1 + swell % / 100)

The compact check gives the same section area without the top width step: section area = (bottom width + slope ratio x depth) x depth. Use it to verify a result by hand before ordering haulage.

NIST Handbook 44 Appendix C supplies the cited volume relationships. Unit switching converts populated length dimensions, leaves the dimensionless slope ratio, run count, and swell percentage unchanged, clears the displayed result, and requires a fresh calculation in the selected units.

Which slope should you check against?

This calculator does not choose a slope. The slope comes from the project drawings, the measured excavation, or the protective-system design. The table below gives the US maximum allowable slopes from OSHA 29 CFR 1926 Subpart P Appendix B for excavations less than 20 ft deep. These are maximums, not recommended project slopes, and soil classification is by a competent person.

Excavations deeper than 20 ft need a registered professional engineer design under the same OSHA appendix, and US excavations 5 ft or deeper need a protective system such as sloping. Quantity planning does not replace excavation safety design, project drawings, specifications, permits, or a qualified professional.

Worked imperial example

A trench run is 120 ft long. The bottom width is 4 ft, the depth is 6 ft, and both sides were cut at a 1.5:1 slope. Swell is 0%.

1. Top width: 4 + 2 x 6 x 1.5 = 22 ft.
2. Section area: (4 + 22) / 2 x 6 = 78 ft2. Compact check: (4 + 1.5 x 6) x 6 = 78 ft2.
3. Bank volume: 78 x 120 = 9,360 ft3, or 346.667 yd3.
4. Loose volume at 0% swell: 9,360 ft3, unchanged.

Result: 346.667 yd3 of bank volume for the 120 ft run. The same numbers through a rectangular formula on the bottom width alone give 2,880 ft3, which is 69% below the correct volume, and on the top width alone give 15,840 ft3, which is 69% above it.

Worked metric example

A trench run is 60 m long. The bottom width is 1.2 m, the depth is 2.0 m, and both sides were cut at a 1:1 slope. Swell is 25%.

1. Top width: 1.2 + 2 x 2.0 x 1 = 5.2 m.
2. Section area: (1.2 + 5.2) / 2 x 2.0 = 6.4 m2. Compact check: (1.2 + 1 x 2.0) x 2.0 = 6.4 m2.
3. Bank volume: 6.4 x 60 = 384 m3.
4. Loose planning volume: 384 x 1.25 = 480 m3, or 480,000 L.

Result: 384 m3 of bank volume and 480 m3 of loose planning volume. The 96 m3 difference is the swell allowance only. It is not extra ground excavated, and it is not a contingency for overbreak.

How are changing sections and benched sides handled?

They are not handled by one calculation. When width, depth, or slope changes along a run, take a section at each change, calculate each uniform segment with this calculator, and add the segment volumes. The changing-sections guide covers the end-area method for segments whose two end areas differ.

For benched sides, treat each bench step as its own trapezoid with its own bottom width and depth, calculate each step, and add the step volumes. A single trapezoid across a benched profile cuts across the bench corners and misstates the area.

When the trench ends also slope, the run behaves like a four-sided pit rather than a prism, so the prism formula does not apply. Use end-area sections for that shape instead.

What does the loose volume not include?

The loose volume is bank volume plus the swell percentage you entered. It does not add overbreak, waste, or contingency, and it does not convert to truck loads. Truck loads need a usable body volume, a legal payload, material mass, route, access, and disposal controls, none of which this calculator takes as inputs. Keep any overbreak, waste, or contingency allowance as a separate record with its own reason.

The calculator also does not deduct pipe, bedding, or backfill volumes, and it does not select a protective system, a soil classification, or a slope. Those items follow the project drawings, specifications, and responsible people.

Common sloped-trench calculation mistakes

• Using the bottom width in a rectangular formula.
• Using the top width in a rectangular formula.
• Reading the slope as vertical:horizontal instead of horizontal:vertical.
• Measuring depth along the sloped side instead of vertically.
• Measuring the top width at a different station from the bottom width and depth.
• Entering a surface width as the bottom width.
• Applying one calculation to a run that changes section.
• Treating a benched profile as one trapezoid.
• Applying swell to the bank volume instead of keeping it as a separate loose figure.
• Using a swell percentage from another soil or project without a project reason.
• Recording the result without the slope ratio and swell percentage used.
• Using the quantity as an excavation safety design.

Questions about sloped-trench quantity

Does this calculator choose the slope for my soil?

It does not. It uses the slope ratio you enter. Project drawings, the measured excavation, soil classification by a competent person, and the governing safety requirements determine the slope.

Can one calculation cover a whole trench route?

It can cover one uniform run, or a group of identical runs. A route that changes width, depth, or slope needs one calculation per uniform segment, added together.

Why is the loose volume larger than the bank volume?

Excavated soil occupies more space than soil in the ground. The loose figure adds only the swell percentage you entered. The bank figure stays as the in-ground volume.

Does the calculator count truck loads?

It does not. Truck loads need a usable body volume and a legal payload, which vary by vehicle, material mass, and route. Use the loose volume as the input to that separate check.

Does the calculator deduct pipe or bedding volume?

It does not. This is a gross excavation volume. Pipe, bedding, and backfill deductions follow separate guides and the project drawings.

What if my trench has vertical sides?

Enter a slope ratio of 0. The top width then equals the bottom width, and the result matches the rectangular calculation. The rectangular calculator covers that case directly.