The complete formula reference for operators, foremen, and apprentices. Bookmark this page. You'll come back.
Every heavy equipment operator eventually hits the same wall: you need to run a calculation in the field, you can't remember the formula, and the person who could tell you is on another machine 400 yards away.
This article fixes that. Every formula an operator, foreman, or estimator actually uses on a job site is below — with the formula, a plain-English explanation, a worked example, and a link to the live calculator.
Formula:
The foundation formula. Everything in earthwork builds from this. Multiply the three dimensions, convert to cubic yards by dividing by 27.
Worked example: Building pad 80 ft × 50 ft × 2 ft deep:
Formula:
Soil expands when you dig it out because air gets introduced between particles.
| Material | Swell % |
|---|---|
| Gravel | 8–12% |
| Sand (dry) | 10–15% |
| Common earth | 20–25% |
| Clay | 25–35% |
| Rock (blasted) | 35–50% |
Worked example: 400 BCY of clay with 30% swell:
You're hauling 520 loose cubic yards on trucks, not 400. Critical for planning haul truck capacity.
Formula (working backwards from required fill):
When loose fill is compacted, it shrinks smaller than its original bank volume. To know how much material you need to dig, work backwards.
| Material | Shrink % |
|---|---|
| Gravel | 5–8% |
| Sand | 5–10% |
| Common earth | 10–15% |
| Clay | 15–25% |
Worked example: Need 500 CCY of common earth fill with 12% shrink:
You need 568 BCY in the ground to produce 500 CCY of compacted fill.
Formula:
The most important grade formula in the trade. Rise is vertical distance, run is horizontal distance.
Worked example: Rise of 3 feet over a run of 100 feet:
That's a 3% grade — a common haul road or drainage slope.
Formula:
A 2:1 slope means 2 feet horizontal for every 1 foot vertical. A 3:1 slope is gentler. A 1:1 slope is steep.
| Slope Ratio | Percent Grade | Angle |
|---|---|---|
| 3:1 | 33% | 18.4° |
| 2:1 | 50% | 26.6° |
| 1.5:1 | 67% | 33.7° |
| 1:1 | 100% | 45.0° |
Formula:
How long one truck takes to make one complete trip.
Worked example:
That truck makes 4 trips per hour (60 ÷ 15).
Formula:
Use loose volume (LCY), not bank (BCY), because trucks hold loose material.
Worked example: 600 LCY to haul. Tandem truck holds 12 LCY:
At 15-minute cycles per truck, that's 750 minutes = 12.5 hours (roughly 1.5 shifts with one truck). With three trucks running: 4.2 hours.
Formula:
How many trucks you need to keep the excavator or shovel fully loaded without idle waiting.
Worked example: Load time 3 min. Full cycle time 18 min:
Six trucks means the excavator is loading one truck while the other five are hauling, dumping, and returning.
Formula (simplified):
Reference blade loads (LCY per pass, straight blade):
| Machine | Blade Capacity |
|---|---|
| Cat D3 | 3–4 LCY |
| Cat D6 | 8–12 LCY |
| Cat D8 | 14–18 LCY |
| Cat D10 | 30–40 LCY |
| Cat D11 | 45–55 LCY |
Formula:
Reference burn rates:
| Machine | L/hr (approx.) |
|---|---|
| Cat 320 excavator | 18–24 |
| Cat D6 dozer | 24–32 |
| Cat D10 dozer | 55–70 |
| Cat 740 articulated dump truck | 28–40 |
Worked example: Cat D10 at 60 L/hr, 10-hour shift, $1.75/L diesel:
Formula:
The real cost of running a machine per hour. Small contractors chronically underestimate this and go broke.
Worked example (Cat 330 excavator):
If you're billing this machine at $125/hr, you're losing $12/hr.
Formula:
Worked example: $55/hr base. 14-on/14-off pipeline rotation. 12-hour days × 7 days = 84 hrs/week. $200/day LOA:
Formula:
Worked example: A cylinder with a 4-inch diameter piston at 3,000 psi:
Volume:
Linear:
Weight:
Area:
Print this. Put it in your truck. Put it in the shop lunchroom.
Every formula here has a live calculator on Dirt Calculator. 22 free tools. Works offline after first install.
Get it on your phone:
1. Visit dirtcalculator.ca
2. Tap Share → Add to Home Screen (iPhone) or install icon (Android)
3. Done. Works offline forever.
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