| Plant / use | Shape model | Sample dimensions | Approx. volume | Practical note |
|---|---|---|---|---|
| Tomato in grow bag | Cylinder | r=15 cm, h=25 cm | ≈ 17.67 L | Good for container mixes and deep watering. |
| Tree transplant root ball | Ellipsoid | a=12 cm, b=12 cm, c=18 cm | ≈ 32.57 L | Matches rounded nursery root balls well. |
| Raised bed section | Rectangular prism | L=120 cm, W=60 cm, H=30 cm | ≈ 216.00 L | Use for rows, beds, and soil amendments. |
| Conical plug tray cell | Cone | r=2.2 cm, h=5.0 cm | ≈ 0.25 L | Helps compare plug sizes across brands. |
- Cylinder: V = πr²h
- Cone: V = (πr²h) / 3
- Cone frustum: V = (πh (R² + Rr + r²)) / 3
- Ellipsoid: V = (4/3)πabc
- Rectangular prism: V = L × W × H
- Select the closest shape model to your root zone or container.
- Choose metric or imperial, then enter the required dimensions.
- Add number of plants and a fill factor to scale total volume.
- Optionally enter soil bulk density and moisture percentages for watering estimates.
- Press Calculate to view results above the form, then export CSV or PDF.
Root-zone geometry for common garden setups
The calculator models the root zone as a simple solid so you can size containers, beds, and planting holes consistently. Cylinders suit pots and grow bags, cones approximate narrowing root spread, frustums fit tapered planters, ellipsoids represent nursery root balls, and boxes match raised bed sections. These shapes simplify irregular roots into repeatable numbers for purchasing media and comparing designs.
Choosing dimensions that reflect active roots
Measure the zone that actually contains fine feeder roots, not the maximum reach. For many vegetables, active depth is often 15–30 cm, while perennial shrubs may use 30–60 cm depending on soil structure. If you know diameter, divide by two to enter radius accurately. When using imperial inputs, enter inches and let the tool convert internally.
Interpreting fill factor and plant count
Fill factor scales volume when the root zone is partially occupied, such as coarse mixes with air voids or young plants with incomplete rooting. A 70% fill factor means only 0.70 of the geometric volume is treated as effective root volume. Established containers are often 85–100%, while new transplants may be lower. Plant count multiplies the per-plant estimate to produce a site total.
Linking volume to soil mass and water holding
Bulk density (g/cm³) converts volume to an estimated soil mass, useful for planning media purchases and load limits. Typical garden soils range about 1.1–1.6 g/cm³, while light potting mixes are often lower. Field capacity and wilting point represent volumetric water content, entered as percentages. Together they estimate stored water and plant-available water within the calculated volume.
Using outputs for planning amendments and irrigation
Use liters or gallons to compare container sizes, mix batches, and irrigation targets. The total volume helps estimate compost additions: for example, adding 10% compost by volume equals 0.10 × total liters. Plant-available water supports scheduling; larger volumes buffer heat and wind, reducing stress and transplant shock. For planting holes, match volume to the root ball and loosen surrounding soil for expansion.
FAQs
Which shape should I pick for a typical pot?
Choose Cylinder for most round pots and grow bags. If the container tapers strongly, use Frustum. For nursery root balls or transplant plugs, Ellipsoid often matches real root shape best.
Do I enter diameter or radius?
Enter radius. If you measured diameter, divide by two first. Keeping radius consistent prevents doubling volume errors, because radius is squared in several formulas.
What depth should I use for garden beds?
Use the depth of active roots and workable soil, not the full bed height. Vegetables often use 15–30 cm, while deep-rooted crops or shrubs may benefit from 30–60 cm, depending on compaction and moisture.
How should I set the fill factor?
Use 100% for mature, fully rooted containers. Use 60–90% for young plants, coarse mixes, or partial rooting zones. It scales total volume only; per-plant geometric volume remains unchanged.
Are the water estimates exact irrigation targets?
No. They are planning estimates based on your volume and moisture percentages. Real watering depends on climate, plant size, drainage, and soil texture. Use the values to compare setups and refine schedules with observation.
How do the CSV and PDF downloads work?
After you calculate, the latest result and a session history are saved. Use the buttons to export the last run or the last 50 runs. Clearing history removes saved entries from this browser session.
No saved runs yet. Calculate once to populate history.