You're standing on a site looking at rough plans. The engineer says "cut 500 cubic yards from the north end and move it to the south side for fill." You nod like you know exactly what that means, but in your head you're doing the math. How much material is that really? Will one dozer handle it or do you need two?
Cut and fill calculations look complicated on paper, but they're the foundation of every earthwork job. Get them wrong and you're either underestimating your timeline or eating the cost when you run out of material.
What Are Cut and Fill?
Cut: Material you excavate from higher elevation. It's the "before" state—earth in place, undisturbed.
Fill: Material you place and compact at lower elevation. It's the "after" state—compacted to specification.
The challenge: Material changes volume when you disturb it. When you dig up 100 cubic yards of earth, it becomes 125 loose cubic yards on the truck (swell factor). When you compact it, it shrinks again. If you don't account for this, your material balance is off.
The Three Volume States
Bank Cubic Yards (BCY)
The volume of material in its undisturbed state. This is what the land contains. You estimate BCY from site surveys and grade calculations. BCY is your starting point for every bid.
Loose Cubic Yards (LCY)
The volume of material after excavation. When you dig it up, air spaces between particles expand the volume. Most materials swell 15–30% depending on soil type:
- Sand & gravel: 1.05–1.15 swell factor (5–15% expansion)
- Clay & silt: 1.20–1.40 swell factor (20–40% expansion)
- Rock (blasted): 1.40–1.60 swell factor (40–60% expansion)
Formula: LCY = BCY × Swell Factor
Example: 100 BCY of clay with 1.30 swell factor = 130 LCY on the truck
Compacted Cubic Yards (CCY)
The volume after placement and compaction. Compacted material is denser than loose material. Depending on soil type and moisture, CCY is typically 90–98% of BCY.
Formula: CCY = LCY ÷ Compaction Factor
Example: 130 LCY compacted to 95% Proctor = ~124 CCY
Step-by-Step: Calculate Cut & Fill
Step 1: Determine Site Elevation Change
Get the elevation of the cut area and the elevation of the fill area. The difference tells you how much material needs to move vertically.
Example: Cut area is at elevation 450m. Fill area is at elevation 448m. Difference = 2m (material moves downhill by 2 meters).
Step 2: Calculate Cut Volume (BCY)
Use the area of the cut zone and the average depth of excavation:
Formula for rectangular area:
Volume (BCY) = Length (yards) × Width (yards) × Average Depth (yards)
Example:
Cut area = 100 yards long × 80 yards wide × 1.5 yards average depth
Volume = 100 × 80 × 1.5 = 12,000 BCY
For irregular shapes, break the area into rectangles or triangles, calculate each, and sum them.
Step 3: Apply Swell Factor
When you excavate that 12,000 BCY, it becomes looser. Calculate LCY:
Formula: LCY = BCY × Swell Factor
Example:
12,000 BCY × 1.25 swell factor (typical for mixed soil) = 15,000 LCY
That's 15,000 loose cubic yards on trucks. Knowing this lets you estimate hauling costs and cycle times accurately.
Step 4: Check if Material is Suitable for Fill
Not all excavated material is suitable for fill. Common rejection reasons:
- Too much rock or large boulders
- Organic material or topsoil (not suitable for structural fill)
- Poor drainage characteristics
- Contamination
If the engineer says "50% of cut material is unsuitable," then only 50% of your 12,000 BCY can be used as fill. The other 50% gets hauled to waste.
Suitable material = 12,000 BCY × 0.50 = 6,000 BCY available for fill
Step 5: Calculate Fill Requirement (CCY)
Now determine how much compacted material you need in the fill area:
Formula: Volume (CCY) = Length (yards) × Width (yards) × Thickness (yards)
Example:
Fill area = 120 yards long × 90 yards wide × 1.2 yards thickness
Volume = 120 × 90 × 1.2 = 12,960 CCY
Step 6: Work Backward to Find Haul Volume (LCY)
You need 12,960 CCY in the fill. But material compacts down from loose state. If the compaction factor is 1.10, then:
Formula: LCY needed = CCY required ÷ Compaction Factor
Example:
12,960 CCY ÷ 1.10 compaction factor = 11,782 LCY needed
Step 7: Material Balance
Compare available material to required material:
Available (from cut, after swell): 6,000 BCY × 1.25 swell = 7,500 LCY
Required (for fill): 11,782 LCY
Shortfall: 11,782 − 7,500 = 4,282 LCY of material must be imported
This is where contractors make or lose money. If you didn't calculate this, you'd be surprised halfway through the job when you run out of material.
Real-World Example: A 5-Acre Site
Let's work through a complete cut-and-fill scenario:
Site Overview:
- 5 acres (about 218,000 sq yards)
- Current elevation: 450–452m (varies)
- Target elevation: 450m (level pad)
- Cut area: 3 acres @ 1.5m average depth
- Fill area: 2 acres @ 1.2m thickness
- Soil: Mixed clay and sand (1.25 swell factor)
- Suitable material: 80%
Calculation:
Cut Volume:
3 acres = 130,680 sq yards
Average depth = 1.5 yards
BCY = 130,680 × 1.5 = 196,020 BCY
Suitable Material for Fill:
196,020 × 0.80 = 156,816 BCY suitable
Loose Volume (after excavation):
156,816 × 1.25 = 196,020 LCY available
Fill Requirement:
2 acres = 87,120 sq yards
Thickness = 1.2 yards
CCY = 87,120 × 1.2 = 104,544 CCY needed
LCY Needed (working backward):
104,544 CCY ÷ 1.05 compaction factor = 99,566 LCY needed
Material Balance:
Available: 196,020 LCY
Needed: 99,566 LCY
Surplus: 96,454 LCY to haul away
Use the Calculator
These formulas work, but doing them by hand on every job is slow and error-prone. The Dirt Calculator has dedicated tools for cut & fill, volume calculations, material conversions, and hauling estimates.
In 30 seconds you can:
- Calculate cut volume from elevation and area
- Apply swell and shrinkage factors automatically
- Convert between BCY, LCY, and CCY
- Estimate truck loads and haul costs
- Save material balance sheets for your bid
Key Takeaway
Cut and fill is material accounting. You need to know:
- How much material is in the cut (BCY)
- How much it expands when excavated (LCY)
- How much of it is suitable for fill
- How much compaction reduces it (CCY)
- Whether you have surplus or shortfall
Miss any of these steps and your cost estimates fall apart. Master this and you're the operator contractors call for tricky jobs.