How to Convert Spacing to Plants Per Square Foot

how to convert spacing to plants per square foot starts with division. Divide 144 by the spacing in inches squared for a square grid. Divide 166.28 by the spacing in inches squared for a triangular grid. Divide 10000 by the spacing in centimetres squared for plants per square metre. Reverse it with a square root to find spacing from density.

Why 144 and 10000 Are the Key Numbers

One square foot measures 12 inches on each side. Multiply 12 by 12 to get 144 square inches in one square foot. That is why 144 leads the imperial formula. One square metre measures 100 centimetres on each side. Multiply 100 by 100 to get 10000 square centimetres in one square metre. That is why 10000 leads the metric formula. Use 144 with inches and 10000 with centimetres.

The Square Grid Formula in Inches

A square grid puts plants in straight rows and columns, with the same spacing both ways. Each plant owns a square with side equal to the spacing. Plants per square foot equals 144 divided by spacing in inches squared. For 12 inch spacing, 12 squared is 144, and 144 divided by 144 is 1.00. For 6 inch spacing, 6 squared is 36, and 144 divided by 36 is 4.00. For 3 inch spacing, 3 squared is 9, and 144 divided by 9 is 16.00. Halve the spacing and density rises by four times.

The Triangular Grid Formula

A triangular grid staggers each row so plants in one row sit in the gaps of the row before it. The rows sit closer together, so more plants fit in the same area. The factor is 1.1547. Multiply the square grid density by 1.1547 to get the triangular density. In inches, plants per square foot equals 166.28 divided by spacing in inches squared. The number 166.28 is 144 multiplied by 1.1547. For 12 inch spacing, 166.28 divided by 144 is about 1.15. For 6 inch spacing, 166.28 divided by 36 is about 4.62. Triangular planting gives about 15 percent more plants than a square grid at the same spacing.

The Metric Formula in Centimetres

For a square grid, plants per square metre equals 10000 divided by spacing in centimetres squared. For a triangular grid, plants per square metre equals 11547 divided by spacing in centimetres squared. The number 11547 is 10000 multiplied by 1.1547. For 30 centimetre spacing, 30 squared is 900, and 10000 divided by 900 is 11.11 on a square grid. The triangular value is 11547 divided by 900, which is 12.83. That matches the site FAQ. For 15 centimetre spacing, 15 squared is 225, and 10000 divided by 225 is 44.44 on a square grid. The triangular value is 11547 divided by 225, which is 51.32. For 10 centimetre spacing, 10 squared is 100, and 10000 divided by 100 is 100.00.

Spacing to Density Table

Read density straight from spacing below. All values are rounded to two decimal places.

Spacing	Square density	Triangular density	Density unit
12 in	1.00	1.15	per square foot
9 in	1.78	2.05	per square foot
6 in	4.00	4.62	per square foot
4 in	9.00	10.39	per square foot
3 in	16.00	18.48	per square foot
30 cm	11.11	12.83	per square metre
20 cm	25.00	28.87	per square metre
15 cm	44.44	51.32	per square metre
10 cm	100.00	115.47	per square metre

Worked Examples From Spacing to Density

Square the spacing first, then divide the starting number by that square.

9 inch spacing, square grid: 9 squared is 81. Divide 144 by 81 to get 1.78 plants per square foot. Triangular grid: divide 166.28 by 81 to get 2.05.

4 inch spacing, square grid: 4 squared is 16. Divide 144 by 16 to get 9.00 plants per square foot. Triangular grid: divide 166.28 by 16 to get 10.39.

20 centimetre spacing, square grid: 20 squared is 400. Divide 10000 by 400 to get 25.00 plants per square metre. Triangular grid: divide 11547 by 400 to get 28.87.

15 centimetre spacing, square grid: 15 squared is 225. Divide 10000 by 225 to get 44.44 plants per square metre. Triangular grid: divide 11547 by 225 to get 51.32, or about 51.3. A bed that measures 2 by 1 metre has an area of 2 square metres. Multiply 2 by 44.44 to get 88.88. Round down to a whole plant, and the total is 88 plants on a square grid.

Worked Examples From Density to Spacing

For a square grid, spacing in inches equals the square root of 144 divided by density. In centimetres, use 10000 in place of 144. For a triangular grid, use 166.28 in inches and 11547 in centimetres.

1 plant per square foot: 144 divided by 1 is 144. The square root of 144 is 12, so spacing is 12 inches.

4 plants per square foot: 144 divided by 4 is 36. The square root of 36 is 6, so spacing is 6 inches.

9 plants per square foot: 144 divided by 9 is 16. The square root of 16 is 4, so spacing is 4 inches.

16 plants per square foot: 144 divided by 16 is 9. The square root of 9 is 3, so spacing is 3 inches.

25 plants per square metre: 10000 divided by 25 is 400. The square root of 400 is 20, so spacing is 20 centimetres.

100 plants per square metre: 10000 divided by 100 is 100. The square root of 100 is 10, so spacing is 10 centimetres.

A target of 2 plants per square foot gives 72, and the square root of 72 is about 8.49 inches. Round that spacing to a measurable value, then check the density again.

Density Back to Spacing Table

Read spacing straight from density for a square grid.

Density	Square spacing	Density unit
1	12 in	per square foot
4	6 in	per square foot
9	4 in	per square foot
16	3 in	per square foot
25	20 cm	per square metre
100	10 cm	per square metre

Converting Between Plants Per Square Foot and Plants Per Square Metre

One square foot equals 0.0929 square metres. To go from plants per square foot to plants per square metre, multiply by 10.76. The number 10.76 is 1 divided by 0.0929. To go the other way, multiply plants per square metre by 0.0929.

1 plant per square foot equals 10.76 plants per square metre. 4 plants per square foot equals 43.04 plants per square metre. 11.11 plants per square metre equals 1.03 plants per square foot, close to 1.00 after rounding. 25 plants per square metre equals 2.32 plants per square foot.

Do not convert spacing with the same factor. Spacing is a length, while density is an area rate. That is why the density factor is 10.76, not the length factor.

Using the Calculator to Check Your Maths

The Plants Per Square Foot Calculator lets you enter spacing and area and see the plant count. Use it to check a result you worked out on paper. Enter the same spacing and compare the two results. If they differ, look first at the grid choice, square or triangular, then at the unit, inches or centimetres, then at the rounding. The Plant Spacing Calculator covers spacing in the other direction, and the Square Foot Garden Planner helps when you plan a grid bed by squares. The guides on the site give more background on planting and spacing.

Common Mistakes

1. Mixing inches with 10000, or centimetres with 144. Match inches to 144 and centimetres to 10000.
2. Forgetting to square the spacing. Dividing 144 by spacing alone gives a much larger and wrong density.
3. Using the square grid formula for a triangular layout. The factor 1.1547 changes the count by about 15 percent.
4. Rounding density up before multiplying by area. Round the final plant total down after the multiplication.
5. Treating density as a plant count. Multiply density by area to get a count, and round that total down.
6. Ignoring edge loss in a small bed. Density assumes a large area.
7. Converting spacing with the density factor 10.76. That factor is for area density only.
8. Reading a table value for the wrong unit. Check the unit column before you copy a number.

Frequently Asked Questions

Q: What is the formula to convert spacing to plants per square foot?
A: Divide 144 by the spacing in inches squared for a square grid. For a triangular grid, divide 166.28 by the spacing in inches squared. The result is plants per square foot.

Q: How do I convert spacing in centimetres to plants per square metre?
A: Divide 10000 by the spacing in centimetres squared for a square grid. For a triangular grid, divide 11547 by the spacing in centimetres squared. The result is plants per square metre.

Q: How do I find spacing from a target density?
A: For a square grid in inches, take the square root of 144 divided by the density. In centimetres, take the square root of 10000 divided by the density. The result is the spacing that gives that density.

Q: How many plants per square foot is 6 inch spacing?
A: Six inch spacing gives 4.00 plants per square foot on a square grid and about 4.62 plants per square foot on a triangular grid. The square grid value matches the calculator site FAQ.

Q: How do I convert plants per square foot to plants per square metre?
A: Multiply plants per square foot by 10.76 to get plants per square metre. To go the other way, multiply plants per square metre by 0.0929 to get plants per square foot.

Q: Why does my total plant count differ from the density multiplied by area?
A: Density assumes a large area. Small or narrow beds lose some plants at the edges because a full spacing unit does not fit. Round the total down to a whole plant and check the edge space before you buy or sow.