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Rectangular Soil Volume Mass and Cost

Plan soil volume, delivered mass and cost from a rectangular bed, a measured bulk density and one price basis.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 5 × 4 m bed filled 10 cm deep needs 2 m³. At 1500 kg/m³ it weighs 3 tonnes; at $50/m³ the soil cost is $100.

V = length × width × depth; mass = density × V; cost = mass × price_per_mass = V × price_per_volume.

Worked example

Enter these known values and leave the other values blank.

Length
5 m
Width
4 m
Depth
10 cm
Density
1500 kg/m³
Price per unit volume
50 USD / m³
Area
20 m²
Volume needed
2 m³
Weight needed
3 t
Price per unit mass
33.33 USD / t
Total cost
100 USD

Assumptions and limitations

  • The bed is rectangular with uniform depth and no compaction or settlement allowance. Depth initially uses centimeters; volume uses cubic meters.
  • Density is bulk mass per delivered volume, not particle density. Use a supplier measurement matched to moisture and compaction conditions.
  • The mass display initially uses metric tonnes. Price per mass and price per volume are alternative ways to represent the same cost, not additive charges.
  • All quantities and prices must be positive. Delivery, tax and minimum-order charges are outside the model. Density starts locked as in the captured controls.

Common questions

Which density should I use?

Use the bulk density of the soil under the delivery and moisture conditions you expect.

Should I add both price calculations?

No. They represent the same soil cost on two pricing bases.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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