Plant Spacing
Enter equal spacing s and field area, choose square or triangular layout, to compute planting density (per m²) and total plants — for planning beds and nursery trays.
Input Data
Results
At a glance:The plant spacing calculator derives per-area planting density and total field plants from equal spacing s and layout. The two most common layouts are square layout (plants on square grid points) and triangular layout (triangular, also called hexagonal or staggered). In square layout each plant occupies s² area, density = 1 ÷ s²; in triangular layout neighboring rows are staggered by half a cell, each plant occupies (√3 ÷ 2) × s² area, density = 2 ÷ (√3 × s²), about 15.5% higher than square. Total plants = density × field area. Switching to triangular at the same spacing raises per-area output without shrinking plant spacing — a common trick for high-density beds and nursery trays.
Formula
Square density: ρ = 1 ÷ s².
Triangular density: ρ = 2 ÷ (√3 × s²) ≈ 1.1547 ÷ s².
Total plants: N = ρ × field area.
$$\rho_{square} = \frac{1}{s^{2}}$$$$\rho_{triangular} = \frac{2}{\sqrt{3}\,s^{2}}$$$$N = \rho \times A_{field}$$How to Use
- Enter the equal spacing s (m) and field area (m²).
- Choose square or triangular (hexagonal) layout.
- The tool returns per-m² density and total plants, comparing the two layouts' output.
Planting density per m² at different spacings
| Spacing s | Square (1/s²) | Triangular (2/√3s²) |
|---|---|---|
| 0.10 m | 100 | ~115.5 |
| 0.20 m | 25 | ~28.9 |
| 0.30 m | ~11.1 | ~12.8 |
| 0.40 m | 6.25 | ~7.2 |
| 0.50 m | 4 | ~4.6 |
At the same spacing, triangular density is about 1.155× square (≈15.5% more); halve the spacing and density grows about fourfold.
Case Studies
Plant count of a square vegetable bed
A 100 m² bed, spacing 0.3 m, square layout.
Density = 1 ÷ 0.3² = 1 ÷ 0.09 ≈ 11.11 plants/m².
Total plants = 11.11 × 100 ≈ 1,111, used to estimate seedling demand.
Raise output with triangular layout
Same 100 m² and 0.3 m spacing, switch to triangular (hexagonal) layout.
Density = 2 ÷ (√3 × 0.09) ≈ 12.83 plants/m², total ≈ 1,283 plants.
Without shrinking spacing, triangular plants about 172 more (≈15.5%) than square.
FAQ
How do square and triangular layouts differ?
Square layout puts plants on square grid points, rows and columns aligned. Triangular (hexagonal) staggers adjacent rows by half a cell so each plant is equidistant from six neighbors, forming a honeycomb. Triangular fills the plane more tightly, about 15.5% denser at the same spacing, with more even light and root space per plant.
Why is triangular density about 1.155× square?
Square gives each plant s² area; staggered triangular gives each plant (√3 ÷ 2) × s² ≈ 0.866 s². Smaller area means higher density, ratio 1 ÷ 0.866 ≈ 1.1547, i.e. about 15.5% more plants.
Does this model assume equal row and plant spacing?
Yes. This calculator assumes an equal-spacing layout (row and plant spacing both s). If your plant spacing and row spacing differ, use the Plant Population Calculator, entering independent plant spacing, row spacing and walkway width for a rectangular layout's total plants and density.
Is smaller spacing always better?
Not necessarily. Shrinking spacing multiplies density by the square, but too dense intensifies competition for light, water and nutrients, lowers ventilation and raises disease and etiolation risk, and per-plant yield and quality may drop. Optimal spacing depends on crop canopy, goal and management, not the denser the better.
Is plant spacing suitable for Hong Kong?
Yes. Hong Kong urban farms, rooftop gardens and hydroponic systems have limited area; triangular layout raises per-area output without shrinking spacing. Use this calculator to compare square vs triangular density, then combine with cultivar canopy and harvest needs to plan beds that balance yield and ventilation.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.