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Soil Volume, Bag, Weight, Coverage, and Cost Formulas

Use soil formulas for cubic feet, cubic yards, cubic meters, liters, whole bags, bulk weight, coverage by depth, extra material, and cost estimates.

How do the Soil Calculator formulas work?

This formula page defines the variables used by the Soil Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

The engine normalizes the entered dimensions, calculates rectangular volume, applies extra soil, rounds the volume to whole bags, and uses the entered density and prices for weight and cost estimates.

Variable Definitions

  • L: inside length and W: inside width
  • D: finished fill depth
  • q: number of identical areas
  • e: entered extra-soil percentage
  • b: entered volume per bag
  • ρ: entered bulk density
  • Pbulk: entered price per cubic yard
  • Pbag: entered price per bag

Area and Net Soil Volume

A=L×W×qA=L\times W\times q
Vnet=A×DV_{net}=A\times D
Vyd3=Vft327V_{yd^3}=\frac{V_{ft^3}}{27}

All dimensions are normalized before multiplication. When depth is entered in inches, it is divided by 12 before cubic-foot volume is calculated.

Order Volume and Whole Bags

Vorder=Vnet(1+e100)V_{order}=V_{net}\left(1+\frac{e}{100}\right)
Bags=⌈Vorderb⌉Bags=\left\lceil\frac{V_{order}}{b}\right\rceil

Bag volume is converted from cubic feet or liters to a common base unit. The ceiling function rounds any partial package up to a whole bag.

Soil Weight

Weightlb=Vorder,ft3×ρlb/ft3Weight_{lb}=V_{order,ft^3}\times\rho_{lb/ft^3}
US tons=Weightlb2000US\ tons=\frac{Weight_{lb}}{2000}
Metric tonnes=Weightlb×0.00045359237Metric\ tonnes=Weight_{lb}\times0.00045359237

Weight is an estimate tied directly to the entered bulk density and order volume.

Coverage and Material Cost

Coverageft2/yd3=27DftCoverage_{ft^2/yd^3}=\frac{27}{D_{ft}}
Bulk cost=Vorder,yd3×PbulkBulk\ cost=V_{order,yd^3}\times P_{bulk}
Bagged cost=Bags×PbagBagged\ cost=Bags\times P_{bag}

Coverage changes only with finished depth. Bulk and bag costs use the exact order volume and rounded bag count respectively.

Unit Conversions

  • 12 inches = 1 foot
  • 3 feet = 1 yard
  • 1 cubic yard = 27 cubic feet
  • 1 foot = 0.3048 meters
  • 1 cubic foot = 0.028316846592 cubic meters
  • 1 cubic foot = 28.316846592 liters
  • 2,000 pounds = 1 US ton

The engine uses Decimal.js for intermediate unit calculations. Displayed calculator values are rounded to two decimal places.

Worked Raised-Bed Calculation

For an 8 ft × 4 ft bed filled 12 in deep:

V=8×4×1=32.00 ft3V=8\times4\times1=32.00\ ft^3
Vyd3=3227=1.185 yd3V_{yd^3}=\frac{32}{27}=1.185\ yd^3

At 75 lb/ft³, net weight is 2,400 lb. With 10% extra soil, the order becomes 35.20 ft³ or about 1.304 yd³. At 2 ft³ per bag, the calculator rounds 17.6 up to 18 bags.

Assumptions and Boundaries

  • Entered areas are uniform rectangles.
  • Depth is the finished soil thickness.
  • Bulk density applies uniformly to the selected product.
  • The extra percentage applies before bag and weight calculations.
  • Bag volume and prices come from user-entered product information.
  • Delivery, labor, product suitability, and site design are excluded.

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