Potting Soil and Pot Volume Calculator

How it works

The mix fills the pot from the base up to the headspace line, so the volume is that of the solid below the line. A straight-sided round pot is a cylinder, πr² × fill height; a rectangular box or trough is length × width × fill height.

A tapered pot is a frustum, a cone with its tip cut off. Its volume is π × h ÷ 3 × (R² + R × r + r²), where R and r are the radii of the two ends and h is the height between them. Because the pot is only filled to the headspace line, R here is the radius at that line, found by moving up the sloping wall in proportion to the fill height.

Bagged potting mix is sold in US dry quarts or cubic feet. The volume in cubic inches is divided by 67.2 cubic inches per dry quart (1 cu ft = 25.71 dry qt; 1 dry qt = 1.101 L), multiplied by the number of pots, and divided by the bag size, rounded up to whole bags.

Formula

fill height  h = pot height − headspace
tapered:     r_fill = r_bottom + (r_top − r_bottom) × h ÷ pot height
             V = π × h ÷ 3 × (r_fill² + r_fill × r_bottom + r_bottom²)
cylinder:    V = π × r² × h
rectangular: V = length × width × h
dry quarts   = V (cu in) ÷ 67.200625;   liters = V × 0.016387064
bags         = ⌈ pots × dry quarts ÷ bag size (dry qt) ⌉

Example

A tapered pot 12 in across the top, 9 in across the bottom and 10 in tall, filled to 1 in below the rim, has a fill height of 9 in. The radius at the fill line is 4.5 + 1.5 × 0.9 = 5.85 in, so the pot takes π × 9 ÷ 3 × (5.85² + 5.85 × 4.5 + 4.5²) = 761.50 cu in of mix: 11.33 dry qt or 12.48 L.

Four such pots need 45.33 dry qt (49.91 L, 1.763 cu ft), which is 3 bags of 16 dry qt.

Assumptions and limitations

• Measurements are inside dimensions. The walls of a tapered pot are treated as straight; pots with a rolled rim, a bulging belly or a raised base hold a different amount.
• Nursery trade sizes such as "1-gallon" or "#5" are names, not measured volumes, and usually hold less than the name suggests; the calculator works from measured dimensions.
• Potting mix is sold by its loose volume in the bag. It settles after watering, so a pot often takes somewhat more mix over time than the first fill.
• Drainage material at the base of the pot is not subtracted.

Frequently asked questions