Cubic Yard Calculator Triangle: Formula & Examples

A cubic yard calculator for a triangle determines the volume of a triangular prism (like a wedge-shaped pad, ditch, or ramp) in cubic yards. You enter the triangle’s base, height, and the length of the prism, and the calculator returns the volume in cubic yards, plus often in cubic feet and cubic meters.

Formula

The volume of a triangular prism is the area of the triangular cross-section multiplied by the prism’s length. In plain terms:

Volume (cubic feet) = (Base × Height ÷ 2) × Length

Then convert to cubic yards by dividing by 27 (since 1 cubic yard = 27 cubic feet).

• Base (b) – the width of the triangle’s bottom edge, in feet (or meters).
• Height (h) – the perpendicular distance from the base to the top vertex, in the same unit as the base.
• Length (l) – how far the triangle extends (the depth of the prism), in the same unit.
• Volume – the total space inside, in cubic feet then converted to cubic yards.

Worked Example

Using the calculator defaults: base = 10 ft, height = 4 ft, length = 30 ft.

1. Area of triangle = (10 × 4) ÷ 2 = 20 ft²
2. Volume in cubic feet = 20 ft² × 30 ft = 600 ft³
3. Convert to cubic yards = 600 ÷ 27 = 22.22 yd³

The calculator shows 22.22 cubic yards, 600 cubic feet, and 16.99 cubic meters (600 × 0.0283168).

When to Use a Triangular Volume Calculation

This calculation appears in real projects where the material forms a wedge or a sloped shape:

• Backfilling against a foundation or retaining wall (the fill forms a triangular cross-section).
• Building a ramp, berm, or embankment with a triangular profile.
• Estimating dirt removed from a V-shaped ditch or trench.
• Pouring a concrete footing that has a triangular wedge shape.

For any shape that is not a perfect prism (e.g., the triangle tapers along the length), this formula gives an approximation. For irregular sites, break the shape into several triangular prisms and sum the volumes.

How to Read the Result

The first output, cubic yards, is the number you order from a supplier. Most trucks carry 10–14 cubic yards, so 22.22 yd³ means about two truckloads. The cubic feet value helps when comparing with bagged material (e.g., a 0.5 ft³ bag of soil). The cubic meters value is useful if your supplier quotes in metric.

Remember that volume is not weight. The same cubic yard of dry topsoil weighs far less than a cubic yard of wet concrete. Always check the material’s density (pounds per cubic yard) to estimate weight for transport or structural loads.

Common Mistakes and Misconceptions

• Using the sloped side instead of the perpendicular height. The height must be measured at a right angle to the base, not along the sloped face.
• Forgetting to divide by 27. The area formula gives square feet; multiplying by length gives cubic feet. Only after dividing by 27 do you get cubic yards.
• Mixing units. If the base is in feet and the height in inches, convert everything to the same unit first. The calculator assumes all inputs are in feet.
• Assuming a triangle with equal sides is the same as a right triangle. The formula works for any triangle as long as you know the base and the perpendicular height.

Limits of the Formula

This formula assumes the triangle is constant along the entire length (a prism). Real-world slopes often curve or change width. For a natural hill or irregular excavation, the result is an estimate. Surveyors use cross-sections at regular intervals and average them for better accuracy. Also, the formula gives the theoretical volume; actual material compacts or expands (e.g., soil bulks when excavated and shrinks when compacted). Order 5–10% extra to account for settling and spillage.

Alternative Methods

If you don’t have the perpendicular height, you can still find the area using Heron’s formula (from the three side lengths) or by trigonometry (two sides and the included angle). The volume then follows the same prism formula. For very irregular shapes, consider using a 3D modeling tool or a total station survey. For simple rectangular pads, use a standard length × width × depth calculator instead.

Frequently Asked Questions

How many cubic yards are in a triangle that is 10 ft base, 4 ft height, and 30 ft long?

Exactly 22.22 cubic yards, as shown in the worked example. The area is 20 sq ft, times 30 ft gives 600 cu ft, divided by 27 gives 22.22.

Do I measure the height of the triangle from the ground up?

Yes, the height is the vertical distance from the base to the top point, measured at a right angle to the base. For a ramp, that’s the rise at the highest end, not the length of the sloped surface.

Can I use this calculator for a triangular pond or pool?

Yes, if the pond has a constant depth (the length in this calculator). If the depth varies, treat it as multiple triangular prisms with different depths and sum them.

How do I convert cubic feet to cubic yards myself?

Divide the cubic feet by 27. For example, 600 cu ft ÷ 27 = 22.22 cu yd. Conversely, multiply cubic yards by 27 to get cubic feet.

What if my triangle has unequal sides?

It doesn’t matter. The formula (base × height ÷ 2) works for any triangle as long as you know the base and the perpendicular height. You don’t need the side lengths.

Why does the calculator also show cubic meters?

For international use or when your supplier quotes in metric. One cubic meter equals 35.3147 cubic feet, but the calculator uses the exact conversion factor of 0.0283168 m³ per cubic foot.

Related

• Area Unit Calculator: Convert Units Instantly
• Area to Yards Calculator: Convert Sq Ft & Meters
• Area to Cubic Yards Calculator: How It Works

in b | Base (ft) | ft | 10 | 0
in h | Height (ft) | ft | 4 | 0
in l | Length (ft) | ft | 30 | 0
out cy | Cubic yards | yd³ | (b * h / 2) * l / 27 | 2
out cf | Cubic feet | ft³ | (b * h / 2) * l | 2
out cm | Cubic meters | m³ | ((b * h / 2) * l) * 0.0283168 | 2