What this calculator does
Find out how much sand to buy for a sandbox, a paver base or a play area. Sand is sold in bulk by the cubic yard, cubic meter or ton, or in small bags by weight. Either way, the amount comes from the same three numbers. You need the area to fill, the depth of sand, and how much a set amount of sand weighs. The calculator works out the volume (the space the sand fills). It adds a bit extra for settling and waste. Then it turns that into a weight and a number of bags.
The density (how much a set amount of sand weighs) is a typical value you can change. It's about 100 pounds per cubic foot (1.6 tonnes per cubic meter) for dry, loose sand. Wet sand and packed-down sand weigh noticeably more, and different grades vary. So if your supplier gives a figure, use theirs.
Where it's used
Why this math matters outside the classroom:
- Sandboxes. A 6 × 6 ft sandbox filled 1 ft deep needs 36 ft³, which at about 100 lb/ft³ is roughly 3,600 lb of play sand.
- Paver bedding. A 1 in layer of bedding sand under a 200 ft² patio is about 16.7 ft³.
- Bag counts. Homeowners divide the total weight by 50 lb per bag, so 3,600 lb is 72 bags.
- Tons for delivery. Landscape suppliers sell sand by the ton, and 3,600 lb is 1.8 US tons.
- Volleyball courts. Groundskeepers estimate the sand for a backyard volleyball court by multiplying its area by the planned depth.
Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.G.A.2, 6.RP.A.3.d, 7.G.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose US or metric units and whether the area is a rectangle or a circle.
- Enter the dimensions and the depth of sand you want.
- Check the density and the bag size. Then set how much extra to allow for settling and waste.
- Read the amount to order in bulk, its weight, and how many bags that would be.
What the inputs mean
- Depth
- The sand layer under pavers is commonly about 1 inch (2–3 cm) after screeding (leveling it flat with a straight board). Children's sandboxes are usually filled 6–12 inches (15–30 cm) deep.
- Sand density
- 100 lb/ft³ (about 2,700 lb per cubic yard) is a typical figure for dry, loose sand. Damp sand can be 10–20% heavier. That matters when you buy by the ton.
- Bag size
- Use the weight printed on the bag. The bag count is the total weight divided by the bag weight, rounded up.
- Extra for compaction and waste
- Sand settles when it's tamped or gets wet, and some always ends up outside the area. 5–15% extra is a common allowance.
Formula and method
area = length × width or area = π × (diameter ÷ 2)² volume = area × depth × (1 + allowance % ÷ 100) weight = volume × density bags = ceil(weight ÷ bag weight) 1 yd³ = 27 ft³ = 0.764554857984 m³; 1 US ton = 2,000 lb; 1 tonne = 1,000 kg
π (pi) is about 3.14159, the number used for circles. "ceil" means round up to the next whole number. Depth is converted to feet (inches ÷ 12) or meters (centimeters ÷ 100), so it matches the area's units. Then the volume is increased by the allowance. Multiplying by the density gives the weight.
Bags are rounded up to whole bags. Weights convert between US and metric using the exact pound, 0.45359237 kg.
Worked example
You want to fill a 6 ft × 4 ft sandbox 8 inches deep with play sand at 100 lb/ft³. You allow 10% extra and use 50 lb bags.
- Area: 6 × 4 = 24 ft².
- Volume: 24 × (8 ÷ 12) = 16 ft³.
- With 10% allowance: 16 × 1.1 = 17.6 ft³, or 17.6 ÷ 27 = 0.65 yd³.
- Weight: 17.6 × 100 = 1,760 lb, which is 0.88 US tons.
- Bags: 1,760 ÷ 50 = 35.2, rounded up to 36 bags.
Result: The sandbox needs about 0.65 cubic yards of sand, roughly 0.88 US tons, or 36 bags of 50 lb.
Understanding the result
For small jobs, bags are often more practical. For anything over about half a cubic yard, a bulk delivery is usually cheaper per ton. Compare the bag count with your supplier's smallest bulk order.
Say you're buying by weight and the sand arrives wet. It will weigh more for the same volume. So you may get a little less sand than the dry figure suggests.
Assumptions and limitations
- The sand layer has a uniform depth over a flat rectangle or circle.
- The density entered applies to the sand as delivered.
- One allowance covers both settling (compaction) and spillage.
- Density changes with grain size, moisture and how packed the sand is. So weights and bag counts are estimates.
- Split odd-shaped or sloping areas into simpler shapes, then add them together.
- Bags of the same weight can hold slightly different volumes, depending on how damp the sand is.
Frequently asked questions
How much does a cubic yard of sand weigh?
At the typical 100 lb/ft³ for dry, loose sand, a cubic yard (27 ft³) weighs about 2,700 lb, or 1.35 US tons. Wet or packed-down sand can be closer to 1.5 tons or more.
How many 50 lb bags of sand make a cubic yard?
At 2,700 lb per cubic yard, it takes 54 bags of 50 lb. If your sand is heavier, fewer bags make up the same weight, but each one holds less volume.
How deep should sand be under pavers?
A leveled (screeded) sand layer of about 1 inch (2–3 cm) over a packed gravel base is common. The sand isn't meant to hold up the load. So a thicker layer doesn't make the paving stronger, and it can let pavers shift.
Why add extra sand?
Loose sand has air gaps. Tamping, rain or foot traffic packs it down. So a layer that looked deep enough when you spread it ends up thinner. A little extra keeps the finished depth where you want it.
How this calculator is checked
Method: Prism volume (area × depth) with an allowance; weight = volume × user-editable density; exact US–metric factors. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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