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Cubic Yard Calculator

Calculate cubic yards of material needed for a rectangular, circular, or triangular area from its dimensions and depth, with optional waste factor and cost.

Author: Naeem Ullah
•Last Updated: September 17, 2026•
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Active Calculation FormulaCubic Yards = (Length × Width × Depth ÷ 12) ÷ 27

Adjust Variables

ft
length
Min: 1 ftMax: 100 ft
ft
width
Min: 0 ftMax: 20 ft
in
depth
Min: 0 inMax: 8 in
%
waste
Min: 0 %Max: 100 %
Use Real Campaign Presets
Real-Time Results
Cubic Yards (Before Waste)0
Total Cubic Yards to Order0
All calculations are compiled with double-precision floating math directly in this browser frame. Perfect precision guaranteed.

Interactive Step-by-Step Calculation Proofs

View how variables resolve algebraically down to peer-reviewed standard outputs.

Why Use This Calculator

Cubic yards is the standard unit suppliers use to sell bulk materials like concrete, mulch, topsoil, sand, and gravel, since it's practical for large volumes that would be unwieldy in cubic feet or cubic inches. The formula is Cubic Yards = Volume in Cubic Feet ÷ 27, where 1 cubic yard equals a 3 ft × 3 ft × 3 ft cube (27 cubic feet). Our cubic yard calculator supports three common area shapes — rectangle, circle, and triangle — so you can measure irregular yard shapes without converting to a rectangle first. Enter your dimensions in feet, inches, yards, or meters, set your depth, and optionally add a waste percentage (5–10% is typical for spillage and compaction) and a price per cubic yard to get a full material cost estimate.

Mathematical Formula Explanation

Calculated standard benchmarks are based on direct functional dependencies. The primary calculation logic follows this formula:

Cubic Yards = Volume (ft³) ÷ 27

All three shape modes reduce to the same final step: compute the area of the shape in square feet, multiply by depth in feet to get volume in cubic feet, then divide by 27 (since 1 cubic yard = 3 ft × 3 ft × 3 ft = 27 ft³) to get cubic yards. Rectangle uses Length × Width, Circle uses π × Radius², and Triangle uses ½ × Base × Height for the area step — everything downstream of that area calculation is identical.

Worked Examples (Step-by-Step)

These examples show cubic yards for a rectangular slab, a circular bed, and a triangular area, each before any waste factor is applied.

Case Scenario 1

Example 1: Rectangular Concrete Slab

“A homeowner is pouring a 10 ft × 10 ft patio slab at 4 inches deep, with no extra waste factor. How many cubic yards of concrete are needed?”

Given Inputs
  • LENGTH: 10
  • WIDTH: 10
  • DEPTH: 4
  • WASTE: 0
Computed Outputs
  • CUBICYARDS: 1.23
  • TOTALCUBICYARDS: 1.23
Case Scenario 2

Example 2: Circular Mulch Bed

“A gardener wants to mulch a circular bed 10 feet in diameter at 4 inches deep, with a 10% waste factor for spillage. How many cubic yards of mulch should they order?”

Given Inputs
  • DIAMETER: 10
  • DEPTH: 4
  • WASTE: 10
Computed Outputs
  • CUBICYARDS: 0.97
  • TOTALCUBICYARDS: 1.07
Case Scenario 3

Example 3: Triangular Gravel Area

“A contractor needs to fill a triangular side-yard area with a 12 ft base and 8 ft height at 4 inches deep with gravel, no waste factor. How many cubic yards are needed?”

Given Inputs
  • BASE: 12
  • HEIGHT: 8
  • DEPTH: 4
  • WASTE: 0
Computed Outputs
  • CUBICYARDS: 0.59
  • TOTALCUBICYARDS: 0.59

Frequently Asked Questions (FAQ)

Find the area of your shape in square feet, multiply by depth in feet to get cubic feet, then divide by 27 (since 1 cubic yard = 27 cubic feet). For a rectangle: Cubic Yards = (Length × Width × Depth ÷ 12) ÷ 27. For example, a 10 ft × 10 ft area at 4 inches deep is (10 × 10 × 4 ÷ 12) ÷ 27 = 1.23 cubic yards.

1 cubic yard = 27 cubic feet, since a yard is 3 feet on each side (3 × 3 × 3 = 27). To convert cubic feet to cubic yards, divide by 27. To convert cubic yards to cubic feet, multiply by 27.

Use Cubic Yards = (π × Radius² × Depth ÷ 12) ÷ 27, where radius is half the diameter. For example, a circular bed 10 feet in diameter (5 ft radius) at 4 inches deep is (3.14159 × 5² × 4 ÷ 12) ÷ 27 ≈ 0.97 cubic yards before waste.

Ready-mix concrete typically costs $125–$180 per cubic yard delivered. Mulch runs $25–$65 per cubic yard depending on type (bulk dyed mulch is cheaper than premium bark). Topsoil and dirt run $15–$50 per cubic yard, and gravel or crushed stone runs $25–$65 per cubic yard. Prices vary by region, delivery distance, and order size.

A 5–10% waste factor is standard for most bulk material orders to account for compaction, spillage, and uneven ground. For concrete pours specifically, contractors often round up to the nearest half or full cubic yard anyway since most suppliers have minimum order quantities and concrete cannot be easily topped off later.

It depends on depth. At 4 inches deep, a 10 ft × 10 ft area needs (10 × 10 × 4 ÷ 12) ÷ 27 = 1.23 cubic yards. At 2 inches deep it's about 0.62 cubic yards, and at 6 inches deep it's about 1.85 cubic yards. Always calculate using your actual planned depth rather than assuming a standard value.

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