How this instrument works
Filling a sandbox is a straightforward volume calculation once you know the shape: base area times fill depth gives volume, and volume times sand's density gives weight. The tricky part people usually get wrong is the base-area formula itself, which is genuinely different for each shape — round, square, and rectangular sandboxes use elementary area formulas, but regular pentagonal and hexagonal sandboxes need their own less-obvious polygon-area formulas that aren't as commonly memorized.
This calculator handles five shapes: round (area = pi times radius squared), square (side squared), rectangular (length times width), regular pentagon, and regular hexagon — the last two using the standard geometric formulas for a regular polygon's area given its side length. Dry sand's density is taken as roughly 100 pounds per cubic foot, a commonly cited figure (close to Engineering ToolBox's own listed value of 97 lb/ft³ for dry sand) that's in the right range for typical bagged play sand.
Fill depth is left as a direct input you choose rather than something the calculator guesses at from, say, a child's age — recommended play-sand depths vary by source and by what the sandbox is used for, and 6 inches is used here as a commonly cited practical minimum for a comfortably diggable, playable depth, not a safety-specific recommendation. Adjust it to whatever depth actually suits your setup.
- Select Sandbox shape — Round, Square, Rectangular, Regular pentagon, or Regular hexagon.
- Enter the Radius / side / length in inches — for round it's the radius, for square/pentagon/hexagon it's the side length, for rectangular it's the length.
- Enter Width in inches — only used for the rectangular shape.
- Enter Sand depth in inches — how deep you want the sand fill (6in is a common practical default).
- Read Sand volume, weight, and bags needed — the cubic feet, pounds, and number of standard 50 lb bags of sand required.
Worked example — a 4ft round sandbox, 6 inches deep
A round sandbox with a 24-inch (2ft) radius, filled 6 inches deep: base area = pi x 24^2 = 1,809.56 sq in. Volume = 1,809.56 x 6 / 1728 = 6.2832 cubic feet (the same result you'd get computing pi x 2^2 x 0.5 directly in feet, a useful cross-check). Weight = 6.2832 x 100 = 628.32 lb. Bags needed = ceil(628.32/50) = 13 standard 50 lb bags.
A 3ft (36-inch side) square sandbox at the same 6-inch depth is simpler arithmetic: area = 36^2 = 1,296 sq in; volume = 1,296 x 6 / 1728 = 4.5 cubic feet exactly; weight = 450 lb; bags = ceil(450/50) = 9 exactly, no rounding needed. And a regular hexagonal sandbox with 24-inch sides at 6 inches deep uses the less-common polygon formula: area = (3 x sqrt(3)/2) x 24^2 = 2.598076 x 576 = 1,496.49 sq in; volume = 5.196 cu ft; weight = 519.6 lb; bags = ceil(519.6/50) = 11.
Questions
How much does dry sand weigh per cubic foot?
Roughly 100 lb per cubic foot is the commonly cited figure used here, close to Engineering ToolBox's own reference value of about 97 lb/ft³ for dry sand (dry sand runs lighter than wet sand, which packs closer to 120 lb/ft³ due to the water filling the gaps between grains). This calculator uses the dry-sand figure since bagged play sand is sold and measured dry.
Why do pentagon and hexagon sandboxes need a different area formula?
Because a regular polygon's area isn't simply side-length squared the way a square's is — it depends on the specific number of sides through a geometric relationship involving that count. A regular pentagon's area works out to (side^2) x sqrt(25+10xsqrt(5))/4, and a regular hexagon's to (3xsqrt(3)/2) x side^2 — both standard, independently verifiable formulas for a regular polygon's area given its side length, just less commonly memorized than a square's.
How deep should sand be in a sandbox?
There's no single universal number — it depends on what the sandbox is for and who's using it. 6 inches is used as this calculator's default because it's a commonly cited practical minimum for comfortable digging and play; some setups go deeper (8-12 inches) for more substantial building and digging, especially for older kids. Adjust the depth input to whatever suits your actual sandbox and use case.
Why does the calculator round the bag count up?
Because you can't buy a fraction of a bag, and running short mid-fill means an extra trip to the store — rounding up (ceiling) guarantees the calculated bag count covers the full volume needed, with any small leftover from the final bag being the acceptable tradeoff for not coming up short.
Does sand type (play sand vs. builder's sand vs. polymeric sand) change the calculation?
It can shift the weight estimate somewhat, since different sand products vary a bit in density depending on grain size, moisture content, and additives, but roughly 100 lb/cu ft is a reasonable estimate across most dry bagged sand products sold for general fill and play use. For an unusual sand product, check its bag's stated weight and coverage — most 50 lb bags of standard play sand cover close to half a cubic foot, consistent with this calculator's assumptions.