Flower Pot Size Calculator (호 ⇄ cm, soil volume)

Understanding the flower pot size calculator — concept and principle

In Korea and Japan, plant pots are sold by number (호 in Korean, 号 in Japanese) rather than by centimetres. This calculator turns a pot number into its top diameter and estimates how much potting soil the pot holds, so you can buy the right pot for repotting and the right bag of soil.

How it is calculated

• Top diameter: D = pot number × 3 cm. A 5호 pot is 15 cm across the top.
• Height: if you leave height blank or at 0, the calculator assumes H = 0.85 × D.
• Bottom diameter: assumed to be 75% of the top diameter, so the radii are R = D ÷ 2 and r = 0.75 × R.
• Soil volume: the pot is treated as a frustum (a cone with its tip cut off): V = π × H ÷ 3 × (R² + R × r + r²). With lengths in cm the result is in cm³, and dividing by 1,000 gives litres.

The principle

The numbering comes from the traditional unit sun (寸), about 3.03 cm, which is why each step adds roughly 3 cm of diameter. Most pots are tapered so that the root ball slides out easily, so a plain cylinder formula would overestimate the soil. The frustum formula is exact for a straight-sided tapered shape: it averages the top area, the bottom area and their geometric mean, then multiplies by height. Volume grows with the cube of size, so a pot one or two numbers larger holds much more soil than the diameter alone suggests.

Worked example

1. Inputs: pot number 5, height left at 0.
2. Top diameter: 5 × 3 = 15 cm, so R = 7.5 cm.
3. Assumed height: 0.85 × 15 = 12.75 cm, shown as 12.8 cm.
4. Bottom radius: 0.75 × 7.5 = 5.625 cm.
5. Volume: π × 12.75 ÷ 3 × (7.5² + 7.5 × 5.625 + 5.625²) = π × 4.25 × 130.08 ≈ 1,736.8 cm³.
6. Divide by 1,000: ≈ 1.7 L of soil.

How to read the result

Treat the volume as the pot's total capacity. In practice you fill a little less because of a drainage layer and the space left below the rim for watering, but loose soil also settles after watering, so buying about the calculated amount works well. When repotting, the usual advice is to move up one or two sizes (about 3 to 6 cm wider) rather than to a much larger pot, because excess wet soil around a small root ball can stay soggy. For comparison, a straight 15 cm cylinder of the same height would hold about 2.25 L.

Common mistakes

• Assuming the number is in centimetres or inches; 10호 is about 30 cm, not 10 cm.
• Forgetting that shallow bowls and tall long-tom pots have very different heights; enter the real height for these.
• Measuring the outside rim diameter including a thick lip, rather than the inner opening.

Frequently asked questions

How big is a 7호 pot?

About 21 cm across the top.

How much soil does a 10호 pot need?

With the default shape assumptions (30 cm across, about 25.5 cm tall) it holds roughly 13.9 L.

Is soil sold by litre the same as the pot volume?

Yes, bagged potting mix is usually labelled by volume in litres, so you can compare it directly with the result.

Sources: Daniel Zwillinger (ed.), CRC Standard Mathematical Tables and Formulas, CRC Press (volume of a frustum of a cone)