About Earthwork Cut & Fill Calculator
The earthwork cut and fill calculator estimates excavation (cut) and embankment (fill) volumes along an alignment from a set of cross-section stations. For each station you enter the chainage and the cut and fill areas; the tool integrates the areas between stations to give volumes, sums them, and reports the net balance so you can see whether the job has surplus material to haul off or needs borrow.
Two integration methods are offered. The average-end-area method averages the end areas of each segment and multiplies by its length. The prismoidal method applies Simpson’s rule across equally spaced station triples for a more accurate result when the cross-section varies non-linearly. A compaction (shrinkage) factor converts the required compacted fill back to an in-situ bank volume so cut and fill are compared on the same basis.
How It Works
- Add a station for each surveyed cross-section: enter its chainage and the cut and fill areas in square metres.
- Choose the average-end-area or prismoidal method (prismoidal needs equally spaced stations).
- Enter the compaction / shrinkage factor (compacted fill per bank volume).
- The calculator integrates between stations, totals cut and fill, and reports the net haul balance.
Worked Example
Three stations are surveyed at chainage 0, 20, and 40 m. Cut areas are 10, 12, and 14 m^2 and there is no fill. By the average-end-area method, segment 1 is 20 x (10 + 12) / 2 = 220 m^3 and segment 2 is 20 x (12 + 14) / 2 = 260 m^3, totalling 480 m^3 of cut. By the prismoidal method over the 40 m span, V = 40 x (10 + 4 x 12 + 14) / 6 = 40 x 72 / 6 = 480 m^3, which agrees here because the section tapers linearly. With no fill the entire 480 m^3 is surplus cut to haul off-site.
Formulas
- Average-end-area volume (per segment)
V = L * (A1 + A2) / 2- Prismoidal volume (Simpson, per station triple)
V = L * (A1 + 4 * Am + A2) / 6- Fill as bank volume (shrinkage)
V_bank = V_fill / shrinkageFactor- Net earthwork balance
V_net = V_cut - V_fill / shrinkageFactor
Standards & References
- Average-end-area method (route surveying)
- Prismoidal formula / Simpson’s rule for earthwork
- Typical soil shrinkage factors 0.80–0.95
Frequently Asked Questions
What is the difference between the average-end-area and prismoidal methods?
The average-end-area method simply averages the two end areas of a segment and multiplies by length; it slightly over-estimates volume when the section is convex. The prismoidal method uses Simpson’s rule with the mid-section area for a more accurate result, but it requires equally spaced stations.
What is a shrinkage or compaction factor and why does it matter?
Soil loses volume when it is excavated and recompacted in an embankment. A shrinkage factor of 0.90 means 1 m^3 of compacted fill needs about 1.11 m^3 of in-situ (bank) cut. Applying it lets you compare cut and fill on the same volume basis when balancing haul.
What does a positive or negative net volume mean?
A positive net volume means there is surplus cut that must be hauled off-site or stockpiled. A negative net volume means the site is short of material and you must import (borrow) fill to complete the embankment.
How many stations should I use?
At least two are required to form one segment. Closer station spacing improves accuracy, especially where the ground profile changes rapidly; for the prismoidal method use an odd number of stations at equal spacing so they group into complete triples.