Triangular Spacing vs Square Spacing: Which Fits More?

Triangular Spacing vs Square Spacing: Which Fits More?

Triangular spacing fits about 15 percent more plants than square spacing in a large open area, but it can fit fewer plants in a narrow bed. In a 4 by 8 foot bed at 12 inch spacing, a square grid fits 32 plants and triangular rows fit 30, so the offset layout loses 2 plants there.

Use the Plant Spacing Calculator to run both layouts for your bed size before you buy plants. The calculator counts plants row by row, with each plant half a spacing in from the edge, so it shows the edge loss that a simple area calculation misses.

How square grid spacing works

A square grid puts plants in straight rows and straight columns. Every plant sits the same distance from its neighbours in the row and in the next row. The pattern is easy to mark out, easy to weed, and easy to walk between, because the gaps line up in both directions.

The calculator uses this formula:

plants = floor(length divided by spacing) times floor(width divided by row spacing)

Floor means round down to a whole plant. Each plant sits half a spacing in from the edge, so it has its full share of room and does not crowd the bed wall.

Area per plant on a square grid is spacing times spacing. At 12 inch spacing, each plant gets 1 square foot. At 6 inch spacing, each plant gets 0.25 square feet, or 4 plants per square foot.

Square spacing suits crops that need straight rows for support or for access, such as tomatoes on stakes and pole beans on a trellis. Cornell University gives the same idea in square foot gardening: 1 large plant per square foot, 4 medium plants in a 2 by 2 grid, 9 small plants in a 3 by 3 grid, or 16 tiny plants in a 4 by 4 grid.

How triangular spacing works

Triangular spacing, also called offset rows or hexagonal spacing, shifts every other row sideways by half a spacing. Each plant sits in the gap of the row in front of it, so each plant is the same distance from all of its nearest neighbours. Seen from above, the plants form equilateral triangles.

The rows move closer together. Row spacing is spacing times 0.866. At 12 inch spacing, rows are 10.4 inches apart instead of 12 inches. At 30 cm spacing, rows are 26.0 cm apart.

Area per plant drops to spacing times spacing times 0.866. At 12 inch spacing, each plant gets 0.87 square feet instead of 1 square foot. That is why the theoretical gain is about 15.5 percent: 1 divided by 0.866 equals 1.155.

The calculator uses this formula for triangular rows:

rows = floor((width minus spacing) divided by (0.866 times spacing)) plus 1

Alternate rows are shifted half a spacing. That shift is the key to the whole comparison, because an offset row in a finite bed usually holds one fewer plant than a straight row. In a wide bed, the extra rows you gain outweigh the plants you lose in the offset rows. In a narrow bed, they do not.

Worked example 1: a large plot, 20 by 20 feet at 12 inches

A 20 by 20 foot plot is 400 square feet. At 12 inch spacing, a square grid fits 20 times 20, which is 400 plants.

Triangular rows use a row spacing of 10.4 inches, or 0.87 feet. Rows equal floor((20 minus 1) divided by 0.87) plus 1, which is 22 rows. Odd rows hold 20 plants each, and even rows hold 19 plants each. There are 11 odd rows and 11 even rows, so the total is 220 plus 209, or 429 plants.

Triangular spacing wins here by 29 plants, a gain of 7.2 percent. With 10 percent spares, plants to buy equals ceil(429 times 1.10), which is 472 plants. On a square grid, 400 plants plus 10 percent spares is 440 plants.

Worked example 2: a narrow bed, 4 by 8 feet at 12 inches

A 4 by 8 foot bed is 32 square feet. At 12 inch spacing, a square grid fits 8 times 4, which is 32 plants.

Triangular rows use a row spacing of 10.4 inches. Rows equal floor((4 minus 1) divided by 0.87) plus 1, which is 4 rows. That is the same number of rows as the square grid, so there is no gain from closer rows. Odd rows hold 8 plants each, and even rows hold 7 plants each. The total is 8 plus 7 plus 8 plus 7, or 30 plants.

Triangular spacing loses here by 2 plants, a drop of 6.2 percent. The offset rows each lose a plant and no extra row fits in the width.

Short check: small spacing and the site example

At 6 inch spacing in the same 4 by 8 foot bed, a square grid fits 128 plants and triangular rows fit 140, a gain of 9.4 percent, because a ninth row fits. The site example, a 2.4 by 1.2 metre bed at 30 cm, fits 32 plants on a square grid and 30 on triangular rows, a loss of 2 plants. With 10 percent spares, the square grid needs ceil(32 times 1.10), or 36 plants. The site page text lists 35 spares for this example, which is one less than the ceil formula gives, so this article follows the formula as written and uses 36.

Summary of the worked examples

Bed and spacing	Square grid	Triangular rows	Difference
20 by 20 ft at 12 in	400	429	Plus 29, gain 7.2 percent
10 by 10 ft at 12 in	100	105	Plus 5, gain 5.0 percent
4 by 8 ft at 12 in	32	30	Minus 2, loss 6.2 percent
2.4 by 1.2 m at 30 cm	32	30	Minus 2, loss 6.2 percent
4 by 8 ft at 6 in	128	140	Plus 12, gain 9.4 percent
100 by 100 ft at 12 in	10000	11443	Plus 1443, gain 14.4 percent

In a very large area it approaches the theoretical 15 percent gain. In a 10 by 10 foot plot it gains only 5 percent. In a 4 foot wide bed at 12 inch spacing it loses plants.

When each layout wins

Triangular spacing wins in a large open area, where the width fits many rows and the edge loss is a small share of the total. It also wins for dense plantings of one uniform crop, such as lettuce, spinach, herbs, beets, bush beans and ground cover plants, because the canopy closes evenly.

Square spacing wins in narrow beds, where the width fits only 3 or 4 rows. At 12 inch spacing, a bed 3 or 4 feet wide gains no extra row from the offset, so it only loses plants in the offset rows. Square spacing wins for crops that need stakes, trellises or cages. Tomatoes, pole beans, cucumbers and peas need straight lines for support. It wins for crops that need regular access for picking, pruning or spraying, because the straight gaps give you a clear path. It also wins for mixed beds and square foot gardening. The RHS celery example shows the same idea: celery is planted in a grid, about 23 cm apart in each direction.

Common mistakes with triangular spacing

Using the area gain for a small bed. The 15 percent figure applies to a very large area with no edges. A 4 by 8 foot bed at 12 inch spacing loses plants on triangular rows, not gains them. Always count row by row for your bed size.

Forgetting the offset row loses a plant. An offset row starts half a spacing in and ends half a spacing short, so it usually holds one fewer plant than a straight row. If the offset does not add a whole extra row, that loss is the whole result.

Measuring row spacing as full spacing. Triangular rows are 0.866 times the spacing apart, not the full spacing. If you mark rows at the full spacing and then offset them, you will fit fewer plants than the square grid.

Using triangular spacing for staked crops. Tomatoes, pole beans and cucumbers need straight rows for support. An offset row makes the trellis harder to build and the plants harder to tie, for no useful gain in a narrow bed.

Buying plants from the area figure. Area divided by spacing squared gives a rough total for a large plot, but it ignores the edges. For the 20 by 20 foot example, the area figure gives 462 plants, but the row by row count gives 429, a difference of 33 plants.

Frequently asked questions

Q: Does triangular spacing always fit more plants?

A: No. It fits about 15 percent more in a very large area, and fewer plants in a narrow bed. A 4 by 8 foot bed at 12 inch spacing fits 32 plants on a square grid and 30 on triangular rows.

Q: How do I work out triangular spacing for my bed?

A: Row spacing is spacing times 0.866. Rows equal floor((width minus spacing) divided by row spacing) plus 1. Odd rows hold floor(length divided by spacing) plants, and even rows hold one fewer.

Q: What is the row spacing for triangular planting at 12 inches?

A: 10.4 inches, or 26.0 cm at 30 cm spacing. At 6 inch spacing it is 5.2 inches, and at 18 inch spacing it is 15.6 inches.

Q: Is triangular spacing better for vegetables?

A: It suits uniform leafy crops like lettuce, spinach, beets and bush beans. It does not suit staked crops like tomatoes and pole beans, or mixed beds. Use a square grid for those.

Q: How many plants fit in a 4×8 bed at 12 inch spacing?

A: 32 plants on a square grid, and 30 plants on triangular rows. With 10 percent spares, buy 36 plants for the square grid, or 33 plants for the triangular layout.

Q: Can I use triangular spacing in a square foot garden?

A: You can for a single crop in a large block, but the square foot system is built on a square grid, with 1, 4, 9 or 16 plants per square foot. Keep the grid for mixed beds.

Run both layouts through the Plant Spacing Calculator before you buy plants, and check the plan view for your bed. For more guides, browse the garden guides.