What this calculator does
A typical plant pot or window box is wider at the top than at the bottom, with sloping straight sides. Geometrically this shape is a rectangular frustum — a truncated, pyramid-like box bounded by two parallel rectangular faces. This calculator works out exactly how much potting soil you need to fill it to a chosen depth, returning the answer in liters, cubic centimeters and cubic meters.
How to use it
Measure five lengths and pick a unit (the same unit is applied to all of them). Enter the soil height h (how deep you want the soil, not necessarily the full pot height), the two sides of the top opening a and b, and the two sides of the bottom A and B. The tool converts your inputs to centimeters, computes the volume, and shows liters so you can match it to bags of compost.
The formula explained
The volume comes from the prismatoid (Simpson) rule, which is exact for any solid whose cross-sectional area varies linearly between two parallel faces:
$$V = \frac{h}{6}\left( a\cdot b + A\cdot B + (a+A)(b+B) \right)$$
Here \(a\cdot b\) is the top area, \(A\cdot B\) is the bottom area, and \((a+A)(b+B)\) equals four times the mid-height cross-section area. If the top and bottom are identical, the formula correctly collapses to the simple box volume \(V = h\cdot a\cdot b\).
Worked example
For \(h = 18\) cm, top \(65 \times 23\) cm, bottom \(60 \times 20\) cm: top area = 1495, bottom area = 1200, \((65+60)(23+20) = 125 \times 43 = 5375\). Sum = 8070. $$V = \frac{18}{6} \times 8070 = 3 \times 8070 = 24{,}210 \text{ cm}^3 = 24.21 \text{ L}$$
FAQ
Should I fill the pot completely? No — leave 1–3 cm of headroom below the rim so water does not overflow. Set the soil height to the depth you actually fill.
What if my pot is round? This tool assumes rectangular top and bottom faces. A round or oval pot needs a circular-frustum calculator instead.
How many liters are in a bag? Potting soil is commonly sold in 10, 20, 40 or 50 L bags, so the liters figure tells you directly how many bags to buy.
