Work out cut and fill volumes for a road from the ground and formation levels at each chainage. The calculator gives the cut, the fill and the balance, so you can see whether soil will be left over or has to be brought in, with the working for every section. Part of our quantity surveying tools.
How to use the road earthwork calculator
- Enter the formation width and any extra width in cutting, such as side drains.
- Enter the side slopes for fill and cut, on the left and right.
- Enter the chainage, ground level and formation level at each station, or paste the ground levels and set the formation from a gradient.
- Choose the method for the main result. The prismoidal formula is selected by default.
- Add a compaction allowance if your specification gives one, then read the cut, fill and balance and download the schedule as CSV.
Road Earthwork Calculator
Cut and fill volumes and the balance between them, from ground and formation levels at each chainage
Set formation levels from a gradient
Paste a list of ground levels
Volume by section
Levels and areas at each station
Compare the methods
Checks
Educational quantity estimate. It assumes level ground across the width of the road. It is not a survey or a road design; alignments, sections and quantities must come from your engineer's drawings and measurements.
Formulas used
| Step | Formula |
|---|---|
| Depth at a station | D = formation level − ground level (positive is fill, negative is cut) |
| Cross-section area | A = B × d + (S1 + S2) ÷ 2 × d² |
| Prismoidal formula | V = L ÷ 6 × (A1 + 4Am + A2), where Am is the area at the mean depth |
| Mean area method | V = L × (A1 + A2) ÷ 2 |
| Mean depth method | V = L × Am |
| Zero point | x = L × D1 ÷ (D1 + D2), using depths without their signs |
| Balance | Cut − fill × (1 + allowance % ÷ 100). Positive is surplus, negative is borrow. |
B is the formation width (with the extra width added in cutting), S1 and S2 the side slopes (sideways per 1 vertical) and L the distance between stations, all in metres.
Worked example
A 7.5 m road, 150 m long, with its formation level at 100.00 m, fill slopes of 2:1 and cut slopes of 1:1:
| Section | Type | A1 (m²) | A2 (m²) | L (m) | Volume (m³) |
|---|---|---|---|---|---|
| 0–30 | Fill | 7.28 | 3.32 | 30 | 157.40 |
| 30–45 | Fill | 3.32 | 0 | 15 | 24.10 |
| 45–60 | Cut | 0 | 3.16 | 15 | 23.30 |
| 60–90 | Cut | 3.16 | 7.56 | 30 | 159.55 |
| 90–120 | Cut | 7.56 | 2.34 | 30 | 146.70 |
| 120–131.25 | Cut | 2.34 | 0 | 11.25 | 12.99 |
| 131.25–150 | Fill | 0 | 4.25 | 18.75 | 38.28 |
The total cut is 342.54 m³ and the total fill is 219.78 m³, which leaves a surplus of 122.76 m³. The stations at 45 m and 131.25 m are zero points, where the road meets the ground.
For a bank only, or to see each step of the classroom method, use our earthwork calculator by the mean depth method.
Frequently asked questions
How is road cut and fill volume calculated?
Take the depth of cut or fill at each chainage: formation level − ground level. Work out the cross-section area at each station, then find the volume between stations. The calculator’s main result uses the prismoidal formula, V = L ÷ 6 × (A1 + 4Am + A2), where Am is the area at the mean depth.
What is the formula for the cross-section area of a road embankment?
A = B × d + (S1 + S2) ÷ 2 × d², where B is the formation width, d the depth, and S1 and S2 the side slopes on the left and right, sideways per 1 vertical. For B = 7.5 m, d = 0.8 m and slopes of 2:1 on both sides, A = 6 + 1.28 = 7.28 m².
Which method gives the most accurate earthwork volume?
The prismoidal formula is the most accurate of the three when the depth changes evenly between stations, because it accounts for the area changing with the square of depth. The mean area method tends to give a slightly higher answer and the mean depth method a slightly lower one.
What do surplus and borrow mean in road earthwork?
If the cut soil is more than the fill needs, the extra is surplus and has to be carted away or used elsewhere. If the fill needs more than the cut provides, the shortfall has to be borrowed from another source.
How is a section that changes from cut to fill calculated?
Find the zero point where the road meets the ground: distance from the first station = L × D1 ÷ (D1 + D2), using depths without their signs. Each part is then treated separately, with an area of zero at the zero point.
Why add a compaction allowance to the fill?
Soil from the cut often takes up less space once it is compacted in the embankment, so a cubic metre of fill can need more than a cubic metre of cut soil. Enter an allowance from your soil tests or specification. The calculator starts at 0%.
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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