Cubic Yard Formulas & Mathematical Equations

Master the mathematics behind cubic yard calculations with these essential formulas for different shapes and scenarios.

Basic Cubic Yard Formula

Cubic Yards = (Length × Width × Height) ÷ 27

Where all measurements are in feet

This is the fundamental formula for calculating cubic yards. Since there are 27 cubic feet in one cubic yard (3×3×3), we divide the total cubic feet by 27.

Formulas for Different Shapes

Rectangle/Square

CY = (L × W × H) ÷ 27

Most common shape for patios, driveways, and garden beds.

Example: 10ft × 8ft × 0.33ft = 26.4 ÷ 27 = 0.98 CY

Circle

CY = (π × r² × H) ÷ 27

For circular patios, planters, or round areas.

Example: 5ft radius, 4in deep = (3.14 × 25 × 0.33) ÷ 27 = 0.96 CY

Triangle

CY = (0.5 × B × L × H) ÷ 27

For triangular areas or corner sections.

Example: Base 6ft, Length 8ft, Height 0.25ft = 0.22 CY

Trapezoid

CY = (0.5 × (B1 + B2) × L × H) ÷ 27

For sloped areas or retaining walls.

Example: Bases 4ft & 6ft, Length 10ft, Height 0.5ft = 0.93 CY

Unit Conversion Formulas

Feet to Cubic Yards

Cubic Yards = Cubic Feet ÷ 27

Inches to Cubic Yards

Cubic Yards = Cubic Inches ÷ 46,656

Meters to Cubic Yards

Cubic Yards = Cubic Meters × 1.308

Mixed Units

Convert all to feet first, then calculate

Material-Specific Calculations

Concrete

Bags needed = Cubic Yards × 45

For 60lb concrete bags. Add 10% for waste.

Standard slab thickness: 4-6 inches

Gravel/Stone

Tons = Cubic Yards × 1.3

Average weight conversion for most gravel types.

Compaction factor: Add 15-20%

Mulch

Bags = Cubic Yards × 13.5

For 2 cubic foot mulch bags.

Recommended depth: 2-3 inches

Topsoil

Tons = Cubic Yards × 1.0

Average weight for dry topsoil.

Settling factor: Add 10-15%

Formula FAQs

Why do we divide by 27?

Because 1 cubic yard = 3 feet × 3 feet × 3 feet = 27 cubic feet. This converts cubic feet to cubic yards.

What if I have measurements in different units?

Convert all measurements to the same unit (preferably feet) before applying the formula, or use our calculator which handles mixed units automatically.

How do I calculate for irregular shapes?

Break the irregular shape into simpler shapes (rectangles, triangles, circles), calculate each separately, then add the results.

Should I always add a waste factor?

Yes, especially for materials like concrete and gravel. A 10% waste factor is standard, but use 15-20% for materials that compact.

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