Estimate substrate for a rectangular aquarium using its internal length, front-to-back width and substrate depths at the front and back. The bed is assumed to slope evenly between these depths. Enter equal depths for a flat bed.
Enter your product’s bulk density in kg/L and its net bag mass in kg to calculate mass and whole bags. No universal gravel or aquasoil density is assumed; density and bag mass are deliberately left without defaults.
Measure inside the tank: length runs left to right, width runs front to back, and substrate depths are vertical distances from the bottom. Either end may be deeper. Length and width accept 0.1–1000 cm; each depth accepts 0–100 cm. These are calculator input limits, not recommended aquarium dimensions or planting depths.
Bulk density accepts 0.001–20 kg/L and bag mass accepts 0.001–1000 kg. Both must be positive. Use the product’s stated bulk density, or weigh a known bulk volume and divide its net mass in kilograms by its volume in litres. Include the spaces between grains in that volume; solid-particle density is not a substitute. Match packing and moisture conditions to the product being purchased. If the same bag states both net mass and bulk volume, their ratio can provide a product-specific estimate.
Missing density prevents mass and bag estimates; missing bag mass prevents bag estimates. An unavailable result does not mean zero. With both substrate depths set to zero and valid density and bag mass, volume, mass and bag count are zero.
A linear front-to-back slope forms a trapezoidal side section. Applying the trapezoid area formula and extending that section along the tank length gives footprint area multiplied by the mean of the two depths. This is a geometric application of the Wolfram MathWorld trapezoid formula.
Mass equals density multiplied by volume, rearranging the density definition described by OpenStax. Here the density must describe the bulk substrate, including inter-grain space; the source does not supply a gravel or aquasoil density.
The bag count rounds the unrounded mass-to-bag-mass ratio upward using the registered ceiling operation. Display rounding does not determine the bag count. No extra waste allowance is added.
| Case | Length × width | Front / back depth | Calculation | Whole bags and unused mass |
|---|---|---|---|---|
| Linear slope | 60 × 30 cm | 3 / 7 cm | Mean depth = 5 cm; volume = 60 × 30 × 5 / 1000 = 9 L. At an assumed 1.2 kg/L, mass = 10.8 kg. | With 5 kg bags: ceil(10.8 / 5) = 3 bags; unused mass = 15 − 10.8 = 4.2 kg. |
| Flat bed | 80 × 35 cm | 4 / 4 cm | Mean depth = 4 cm; volume = 11.2 L. At an assumed 0.75 kg/L, mass = 8.4 kg. | With 3 kg bags: ceil(8.4 / 3) = 3 bags; unused mass = 9 − 8.4 = 0.6 kg. |
| Exact bag multiple | 50 × 40 cm | 5 / 5 cm | Volume = 10 L. At an assumed 1 kg/L, mass = 10 kg. | With 5 kg bags: ceil(10 / 5) = 2 bags; unused mass = 0 kg. |
Example densities are invented arithmetic inputs, not material specifications or recommendations. Replace them with evidence for your own product.
The model assumes a rectangular, level tank bottom, a uniform substrate across the length, and a straight slope from front to back. It does not subtract space occupied by rocks, wood, equipment or raised supports, and it does not model terraces, curved profiles, compaction, swelling or material lost during rinsing. Calculate distinct layers separately using each layer’s thickness and density; only combine masses when the materials are the same.
Bulk substrate volume includes spaces between grains, so it is not the volume of water displaced. The result also does not assess aquarium support loads or recommend a suitable substrate depth.
Formula sources
- Wolfram MathWorld: Trapezoid — area of a trapezoidal section.
- OpenStax: University Physics Volume 1, §14.1 — density as mass divided by volume.
No registered thumbnail asset was supplied. Create and register a 400 × 400 pixel WebP thumbnail, then insert it as the first image block. Use the existing cheerful yellow five-point star mascot, floating with hands and no separate legs or feet, on a white background with navy, blue and teal educational graphics. Show a rectangular aquarium with a sloping substrate bed and a small measuring scoop. Inspect neighboring thumbnails for style consistency before creation.