Work out earthwork by the mean depth method for a road or embankment. Enter the formation level, width and side slopes, and the ground level at each chainage, and the calculator gives the banking and cutting quantity for every section, ready to check against your own working. Part of our quantity surveying tools.
How to use the earthwork calculator
- Enter the formation level at the first station, and the gradient if the formation is not level.
- Enter the formation width and the side slopes for banking and cutting.
- Enter the chainage and ground level of each station, or paste a list of levels.
- Read the banking, cutting and net quantity, and the working for each section.
- Compare the result with the mean area and prismoidal methods, then download it as CSV, print it or share a link.
Earthwork Calculator: Mean Depth Method
Banking and cutting quantities for a road or embankment from ground levels at each chainage
Paste a list of levels
Earthwork by section
Depth at each station
Compare the methods
Checks
Educational quantity estimate. The method assumes level ground across the width of the work. It does not design the bank or cutting, and is not a substitute for a survey or an engineer's measurements.
Formulas used
| Step | Formula |
|---|---|
| Depth at a station | D = formation level − ground level (positive is banking, negative is cutting) |
| Mean depth | d = (D1 + D2) ÷ 2 |
| Area of the centre | B × d |
| Area of the two sides | S × d² |
| Total area | A = B × d + S × d² |
| Quantity of a section | Q = A × L |
| Zero point between fill and cut | x = L × D1 ÷ (D1 + D2), using depths without their signs |
| Mean area method | Q = (A1 + A2) ÷ 2 × L, with an area worked out at each station |
| Prismoidal formula | Q = L ÷ 3 × (A1 + 4A2 + 2A3 + … + 4An−1 + An), for an odd number of equally spaced stations |
B is the formation width, S the side slope (sideways per 1 vertical) and L the distance between stations, all in metres.
Worked example
A bank with a formation level of 101.00 m, 6 m wide, with 2:1 side slopes and ground levels every 30 m:
| Chainage | Ground level | Depth D | Mean depth d | Area A (6d + 2d²) | Quantity (A × 30) |
|---|---|---|---|---|---|
| 0 | 99.20 | 1.80 | |||
| 30 | 99.60 | 1.40 | 1.600 | 14.720 | 441.60 |
| 60 | 100.10 | 0.90 | 1.150 | 9.545 | 286.35 |
| 90 | 99.75 | 1.25 | 1.075 | 8.761 | 262.84 |
| 120 | 99.30 | 1.70 | 1.475 | 13.201 | 396.04 |
The total banking is 1,386.83 m³. For the same levels, the mean area method gives 1,397.85 m³ and the prismoidal formula gives 1,390.80 m³.
Frequently asked questions
What is the mean depth method of earthwork?
The mean depth method takes the average of the depths at the two ends of a section, works out the cross-sectional area at that average depth, and multiplies by the length of the section. The total earthwork is the sum of all the sections.
What is the formula for earthwork by mean depth?
Mean depth d = (D1 + D2) ÷ 2. Area A = B × d + S × d², where B is the formation width and S is the side slope, sideways per 1 vertical. Quantity Q = A × L. For B = 6 m, S = 2, D1 = 1.8 m, D2 = 1.4 m and L = 30 m: d = 1.6 m, A = 14.72 m² and Q = 441.6 m³.
What does a side slope of 2:1 mean?
A side slope of 2:1 means 2 units sideways for every 1 unit of height, so S = 2 in the formula. A bank 1.5 m high with this slope spreads 3 m sideways on each side.
What is the difference between the mean depth, mean area and prismoidal methods?
The mean depth method finds one area at the average depth. The mean area method finds the area at each end and averages them. The prismoidal formula uses Simpson’s rule, Q = L ÷ 3 × (A1 + 4A2 + 2A3 + … + An), and needs an odd number of equally spaced sections. Because area grows with the square of depth, the three give slightly different answers.
How is a section that changes from filling to cutting calculated?
Find the zero point where the depth is nil: distance from the first station = L × D1 ÷ (D1 + D2), using depths without their signs. Treat the part before the zero point and the part after it as two separate sections, each with a mean depth of half its end depth.
What are the limits of the mean depth method?
It assumes the ground is level across the width of the work and changes evenly between stations. On uneven ground, take sections closer together or use a more detailed method. It gives a quantity estimate and does not design the bank or the cutting.
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Disclaimer: Online educational publication only. Not a substitute for a survey, design or measurement by a qualified engineer. Full disclaimer · contact@speakarch.com
Last updated: 9 November 2026