Plant Calculator

Background.

A plant calculator converts a bed area and an on-centre spacing into a number of plants, which sounds like division and is not quite. The complication is packing. Lay plants out in a straight grid and each one owns a square of ground with sides equal to the spacing. Offset every other row by half a spacing, so the plants sit in equilateral triangles, and each one owns a slightly smaller parallelogram — and the same bed at the same spacing takes about 15.5 percent more plants. Both layouts are correct, both keep every plant exactly the stated distance from its nearest neighbours, and the difference between them on a large bed is hundreds of plants and hundreds of dollars. This calculator does both and tells you which it used.

The factor behind the offset pattern is 0.866, or more precisely the square root of three divided by two. It is the height of an equilateral triangle relative to its side, and it appears because shifting alternate rows lets those rows nest closer together than the plants within a row. So a triangular planting at 12 inches on centre has plants 12 inches apart along each row but the rows themselves only 10.39 inches apart. Nothing is being squeezed: every plant still has 12 inches of clear space to its six nearest neighbours instead of four. That is the whole trick, and it is why nurseries and landscape specifications default to it for groundcover.

The reference table this page is checked against is UGA Extension Bulletin 931's Table 31, which prints both patterns at spacings from 4 to 14 inches — 100 plants per 100 square feet at 12 inches square, 115 at 12 inches triangular, and so on up and down the range. Every one of those twelve cells is reproduced by this calculator and asserted in its test suite. There is a wrinkle worth knowing about: the table's own explanatory sentence says the row offset is 0.886 times the spacing, but the numbers printed in the same table are 0.866 times the spacing, and only 0.866 reproduces the plant counts beside them. The sentence is a transposition typo. This page follows the numbers.

The calculator was independently checked against a second land-grant extension service. Iowa State's Yard and Garden programme publishes a plants-per-square-foot table and a worked example: daylilies at 15 inches apart in a 28 square foot bed need 28 × 0.64 = 17.92, rounded to 18 plants. This page returns 17.92 and 18 for the same inputs, and 0.64 plants per square foot at 15 inches, matching all three of Iowa State's printed figures exactly.

Two honest limits go with the answer rather than beneath it. First, the count is geometric. A real bed edge is never a clean multiple of the spacing, and whether you set the outer row half a spacing or a full spacing in from the edge moves the total by several percent on a small bed. No source I could find settles that convention, so this page does not attempt an edge correction and says so — treat the number as an order quantity, not a planting plan. Second, the calculator does not choose your spacing. That is a species decision, and it is the one that actually matters. Maryland Extension's groundcover guidance puts it well: close spacing covers open ground faster, which means less erosion and fewer weeds, but it also raises disease risk where air movement is poor and eventually costs you individual plants to competition. Read the tag, look up the mature spread, then come back and price it.

What is plant calculator?

On-centre spacing, usually written as "o.c.", is the distance from the centre of one plant to the centre of the next. It is the number printed on plant tags and written into landscape specifications, and it is measured centre to centre rather than edge to edge precisely because the edges move as the plant grows.

The two standard layouts are square and triangular. In a square, or grid, pattern the distance between rows equals the distance between plants within a row, so the plants form a rectangular lattice and each one occupies an area equal to the spacing squared. In a triangular, offset or staggered pattern, alternate rows are shifted half a spacing sideways, which lets them move closer together; the row-to-row distance becomes the spacing multiplied by 0.866 and the ground each plant occupies falls to 0.866 of the spacing squared. Triangular is sometimes called equilateral spacing, because each plant sits at the corner of an equilateral triangle formed with its neighbours.

Density is normally quoted one of two ways. UGA Bulletin 931 uses plants per 100 square feet, which suits landscape beds. Iowa State's Yard and Garden material uses plants per square foot, which suits smaller plantings and mental arithmetic. They are the same figure a factor of a hundred apart, and this calculator reports the per-100 form because that is what the reference table it is checked against uses.

A flat, or tray, is the unit groundcover and bedding plants are usually sold in. Common cell counts are 18, 32, 38 and 50. Rounding to whole flats is what actually determines how many plants come home, which is why the calculator reports flats as well as plants and rounds both up.

One term this page deliberately does not use is plants per acre. That is the row-crop measure, it depends on two different spacings — between rows and within the row — and it belongs on the plant population calculator, which also handles germination and field emergence. Triangular packing has no meaning in a row crop, and a seeding rate has no meaning for a container-grown perennial, so the two pages stay disjoint and link to each other.

How to use this calculator.

1. 01Measure the bed and enter its area in square feet. Break an irregular shape into rectangles, triangles and half-circles, work each one out and add them together.
2. 02Deduct anything inside the bed outline that is not getting planted — stepping stones, an existing shrub, a utility cover. Enter 0 if there is nothing to take out.
3. 03Enter the on-centre spacing from the plant tag, in inches. If the tag gives a range, run the calculator at both ends: the difference is usually larger than people expect.
4. 04Choose the pattern. Triangular fits about 15.5 percent more plants at the same spacing and is the nursery default for groundcover; square is easier to lay out with a string line and is the safer choice if you are planting alone.
5. 05Enter the cells per flat and the price per plant. Divide a tray price by its cell count to get the price per plant, and enter 1 for flats if you are buying individually.
6. 06Read the plants-per-100-square-feet figure and check it against the table on the back of a nursery catalogue or against UGA Bulletin 931 — they should agree.
7. 07Read the note beside the result. It says why the number is an order quantity rather than a planting plan, and it repeats that spacing is a species decision the calculator cannot make for you.

The formula.

Start with the net area: bed area minus whatever you deducted. Then work out how much ground one plant occupies at your spacing and pattern.

In a square grid, each plant owns a square of side s, so the area per plant is s² square inches, or s² ÷ 144 square feet. In a triangular pattern, alternate rows shift half a spacing, which puts the rows a distance s × √3⁄2 apart — the height of an equilateral triangle of side s. Each plant then owns a parallelogram of base s and height s × √3⁄2, so the area per plant is s² × 0.8660254 square inches. Because the area per plant is smaller by that factor, the plant count is larger by its reciprocal: 1 ÷ 0.8660254 = 1.1547005, which is the 15.5 percent more plants the offset pattern buys.

The count is then net area divided by area per plant, and the density per 100 square feet is 100 divided by area per plant. Working the default through: 12 inches triangular gives 144 × 0.8660254 = 124.7076581 square inches per plant, which is 0.8660254038 square feet, so a 240 square foot bed takes 240 ÷ 0.8660254038 = 277.128129211 plants and the density is 100 ÷ 0.8660254038 = 115.4700538379 per 100 square feet.

The packing factor is exact geometry, not a measured constant, so the module derives it from the square root of three at full precision rather than storing 0.866 as a literal. That matters at the fourth digit and beyond, and it is what lets the calculator reproduce UGA's printed table cells rather than approximately matching them.

Two roundings happen, and both are physical rather than cosmetic. Plants are rounded up, because you cannot buy 277.13 of them, and the exact figure is reported separately so nothing is hidden. Flats are rounded up from the rounded-up plant count, because that is the number of plants you are actually carrying to the till, and the cost is calculated the same way. Everything else is carried at full precision and rounded once at the end.

A worked example.

Frequently asked questions.

References& sources.

1. [1]University of Georgia Cooperative Extension, Bulletin 931, "Conversion Tables, Formulas and Suggested Guidelines for Horticultural Use", Pennisi, B.V., published 7 November 2024. Table 31, "Estimated number of plants to fill 100 ft² of bed area for square (row) and triangular (equilateral) planting patterns using 4- to 14-in. spacing distances", adapted from Bailey, D.A. and Powell, M.A., 1999. Primary source for both patterns and for the row-offset column. Note that the table's prose states the offset as 0.886 X while its own printed Y values (3.46, 5.20, 6.93, 8.66, 10.39, 12.12) and its plant counts are 0.866 X; this page follows the numbers. Retrieved 2026-07-31; open access.
2. [2]Iowa State University Extension and Outreach, Yard and Garden, "How to Determine Plant Quantity for Planting Beds", Steil, A., last reviewed February 2025. Source of the independent check: the plants-per-square-foot table (4 in → 9, 15 in → 0.64, 48 in → 0.06) and the worked daylily example, 28 square feet × 0.64 = 17.92 rounded to 18 plants, all three of which this calculator reproduces exactly. Retrieved 2026-07-31; open access.
3. [3]University of Maryland Extension, "Groundcovers", updated 10 April 2026. Source of the spacing guidance quoted beside the result: spacing depends on the species chosen; close spacing gives faster coverage and less opportunity for erosion and weed colonisation, but greater risk of plant disease and the eventual decline of individuals facing too much competition. Retrieved 2026-07-31; open access.
4. [4]National Institute of Standards and Technology, Handbook 44 – 2026, Appendix C, "General Tables of Units of Measurement". Units of Area: 144 square inches = 1 square foot, and 43,560 square feet = 1 acre. Source of the square-inch to square-foot conversion used throughout this page. Retrieved 2026-07-31; open access PDF, downloaded and text-extracted.
5. [5]Iowa State University Extension and Outreach, Yard and Garden, "How do I determine the size of my garden bed or lawn in square feet?". Source of the method for measuring an irregular bed by breaking it into rectangles, triangles and circles and adding the results. Retrieved 2026-07-31; open access.