Authoritative Data Source & Methodology
AuthoritativeDataSource: Standard geometric volume and packing relations, unit conversions (NIST Guide to SI), and hexagonal packing density from classical circle packing in a plane.
- NIST, Guide for the Use of the International System of Units (SI), conversions between ft–in–yd–m–cm–L–m³. Direct reference: NIST SI Units
- Hexagonal packing surface efficiency \( \eta_{\mathrm{hex}}=\frac{\pi}{2\sqrt{3}}\approx 0.9069 \) (e.g., circle packing in a plane, MathWorld).
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Volume (rectangular bed): \( V = L \times W \times D \).
Unit conversions: \( 1\,\text{ft}^3=28.3168466\,\text{L} \), \( 1\,\text{yd}^3=27\,\text{ft}^3 \), \( 1\,\text{m}^3=1000\,\text{L} \).
Bag count: \( \text{Bags}=\left\lceil \dfrac{V}{V_{\text{bag}}} \right\rceil \).
Plant count (square grid) (with area \(A=L\times W\), spacing \(s\)): \( N_{\square} \approx \left\lfloor \dfrac{A}{s^2} \right\rfloor \).
Plant count (hex packing): \( N_{\hexagon} \approx \left\lfloor \dfrac{\eta_{\mathrm{hex}}\,A}{s^2} \right\rfloor \), where \( \eta_{\mathrm{hex}}\approx0.9069 \).
Blend components for total volume \(V\) and percentages \(p_i\): \( V_i = p_i \times V \).
Glossary of Variables
| Symbol / Field | Meaning | Units |
|---|---|---|
| L, W, D | Inside length, width, depth | ft/m (L,W), in/cm (D) |
| V | Volume | ft³, yd³, m³, L |
| s | Plant spacing (center-to-center) | cm |
| \( \eta_{\mathrm{hex}} \) | Hexagonal packing efficiency | — |
| Bag Size | Volume per bag | L or ft³ |
| Blend % | Component allocation | % |
Come Funziona: Un Esempio Passo-Passo
Scenario: Raised bed 6 ft × 3 ft × 10 in depth. Metric bags of 50 L, add 10% for settling.
- Convert depth: 10 in = 0.8333 ft. \(V=6\times3\times0.8333 \approx 15\,\text{ft}^3\).
- Convert volume: \(15\,\text{ft}^3 \approx 15\times 28.3168 \approx 425\,\text{L}\).
- Add 10%: \(425\times1.10 \approx 468\,\text{L}\).
- Bags: \(468/50 \approx 9.36 \Rightarrow 10\) bags.
- Plant spacing 30 cm, hex packing on area \(6\text{ ft} \approx 1.8288\text{ m}\), \(3\text{ ft}\approx0.9144\text{ m}\), \(A\approx1.673\,\text{m}^2=16730\,\text{cm}^2\). \(N_{\hexagon}\approx \left\lfloor 0.9069\times 16730 / 30^2 \right\rfloor \approx 16\) plants.
Frequently Asked Questions
Should I include the bed walls in dimensions?
Use inside dimensions—the space that actually holds soil or mulch.
How much extra should I order for settling?
10–20% is common for fresh mixes; wood-heavy mixes may settle more.
Is hex spacing always better?
Only when airflow/disease pressure allows. In humid climates, square spacing may reduce crowding.
Can I change bag units?
Yes. Switch between liters and cubic feet; bag count updates instantly.
Does the calculator support circular beds?
This version targets rectangles. For circles: \(V=\pi r^2 D\). We’ll add a circle mode soon.
Tool developed by Ugo Candido. Content reviewed by CalcDomain Editorial Board.
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