Estimate Cone Volume, Frustum Volume, Bags & Ready-Mix Cost
Use the Concrete Cone Calculator to estimate cubic feet, cubic yards, concrete bags and optional material cost for full cone shapes, truncated cones or frustums, multiple identical cones, and cone-shaped concrete placed over a cylindrical base.
Choose the shape that best matches the finished concrete and enter its dimensions.
Calculate a cone with a circular base and a top that tapers to a point.
Use vertical height, not sloped side length.
Material estimate only. Verify finished form dimensions, supplier increments and project requirements before ordering.
Calculate a truncated cone with a circular bottom, circular top and straight tapered sides.
Use actual inside form dimensions for tapered concrete shapes.
Estimate total concrete, bags and cost for several identical full cones or frustums.
Ignored when Full Cone is selected.
Do not multiply one representative size across a project if actual forms vary materially.
Add a full cone or frustum above a cylindrical concrete base and calculate the combined volume.
Ignored for a full cone.
Use actual finished dimensions from the form or approved drawing.
A Concrete Cone Calculator is a specialized concrete volume estimator for circular shapes that taper from a wide base toward a smaller top. The simplest case is a full cone, which has one circular base and a single point at the top. A more common construction shape is a truncated cone, also called a frustum, where the taper stops before reaching a point and therefore has both a bottom diameter and a top diameter.
These geometries appear in decorative concrete, architectural pedestals, monuments, tapered equipment bases, precast landscape units, sloped caps, sculptural work, custom foundations and special formed concrete. Because the sides are sloped, a standard rectangular slab formula will not produce an accurate quantity. Likewise, treating the shape as a full cylinder can substantially overestimate concrete.
This page uses exact geometric formulas for cone and frustum volume. After calculating cubic feet, it converts the result to cubic yards, applies an optional ordering allowance, estimates concrete bags from the yield you enter, and multiplies the ordering volume by an optional ready-mix price.
The calculator is a material estimator only. It does not design the shape structurally. Reinforcement, formwork strength, concrete pressure, lifting inserts, anchorage, stability, bearing, curing and construction joints must be addressed separately when they apply to the project.
The volume of a full cone is one-third of the volume of a cylinder with the same base radius and vertical height. The base area is π times radius squared. Multiply that area by height and divide by three.
Where V is volume, r is base radius and h is vertical height. Radius equals diameter ÷ 2.
For example, a cone with a 6 ft base diameter has a 3 ft radius. If the vertical height is 4 ft, the volume is one-third × π × 3² × 4 = approximately 37.70 ft³. Divide by 27 to convert the result to about 1.40 yd³ before any ordering allowance.
The important measurement is vertical height. Do not enter the sloped side length, also called slant height, unless you first convert it to vertical height. The volume formula depends on the perpendicular distance from the base plane to the apex.
A truncated cone or frustum has two circular faces: a larger bottom circle and a smaller top circle. Its volume is not the simple average of the two circle areas multiplied by height. The exact formula accounts for the taper continuously.
R is the bottom radius, r is the top radius and h is vertical height.
If the top radius is zero, the formula reduces to the normal full-cone formula. If the top and bottom radii are equal, the expression becomes the formula for a cylinder. This makes the frustum equation useful across a wide range of tapered concrete forms.
Suppose a concrete frustum is 6 ft in bottom diameter, 3 ft in top diameter and 4 ft high. The bottom radius is 3 ft and the top radius is 1.5 ft. The exact volume is approximately 65.97 ft³, or about 2.44 yd³ before allowance.
Measure the finished inside diameter of the concrete form, not its outside shell.
Use perpendicular height from bottom plane to top plane or apex.
Use the frustum formula when the top remains circular instead of closing to a point.
Break complex forms into cone, frustum, cylinder and other simple components.
Select full cone, frustum, multiple cones or cone + cylindrical base.
Measure the finished circular bottom and top dimensions where applicable.
Use vertical height rather than sloped surface distance.
Enter the number of identical shapes plus your ordering allowance.
Check cubic feet, yards, bag count, cost and PDF output.
Select the first calculator when the concrete starts at one circular base and tapers all the way to a point. Enter base diameter and perpendicular height. The calculator converts diameter to radius automatically.
Select the second calculator when the concrete has a circular top smaller than the circular bottom. Enter both diameters and vertical height. The top diameter can be zero, but it cannot be larger than the bottom diameter in this calculator.
If the project contains several identical decorative units, bollard caps, tapered pads or precast forms, use the quantity mode. You can select either a full cone or a frustum and multiply the exact volume by the number of units.
Many concrete forms combine a tapered upper portion with a straight-sided lower base. The fourth calculator adds one cone or frustum to a cylinder. It assumes the shapes meet at a plane and do not overlap.
A mathematical formula can only be as accurate as the dimensions entered. Tapered forms are particularly sensitive to measurement because both diameter and height affect volume. Measure the final concrete cavity or finished formed shape rather than estimating from the outside of formwork.
If concrete is poured inside a mold or form, use the internal diameter that the concrete will actually occupy. Form thickness should not be included. For a round form that is slightly out of shape, take several diameter measurements and review whether an average is appropriate.
The calculator uses the height measured perpendicular to the base. For a cone standing upright, this is the straight vertical distance from the base plane to the apex. For a frustum, it is the perpendicular distance between the two circular faces.
The sloped side length is longer than the vertical height. Using it in the volume formula will overestimate concrete. If only slant height and radius are known for a right circular cone, vertical height can be obtained from the Pythagorean relationship h = √(s² − r²), where s is slant height.
A frustum needs both bottom and top diameters. Do not substitute an average diameter into a cylinder formula. Although that can look reasonable, it is not generally the exact tapered-shape volume.
| Shape | Required Inputs | Volume Formula | Typical Use |
|---|---|---|---|
| Full cone | Base diameter + height | ⅓πr²h | Pointed concrete forms, decorative cones, tapered caps |
| Frustum | Bottom diameter + top diameter + height | (πh/3)(R² + Rr + r²) | Tapered pedestals, truncated forms, architectural bases |
| Cylinder | Diameter + height | πr²h | Round piers, columns, straight-sided bases |
| Cone + cylinder | Both shape input sets | Cone/frustum + cylinder | Pedestals, monuments, bollards, custom formed assemblies |
The calculator changes formulas automatically. If a shape looks tapered but the sides are actually straight and vertical, use a cylinder calculator instead. If the shape changes diameter in multiple steps, calculate each segment separately and add the volumes.
A full cone occupies exactly one-third of the volume of a cylinder that has the same base radius and height. This is a useful mental check when reviewing a calculation. If a 6 ft diameter × 4 ft high cylinder contains about 113.10 ft³, a cone with the same diameter and height should contain about 37.70 ft³.
A frustum falls between a full cone and a cylinder when its top diameter is greater than zero but smaller than the bottom diameter. As the top diameter increases, the volume approaches the cylinder volume. This relationship is useful when estimating tapered pedestals because small changes in top diameter can add noticeable concrete.
For large architectural or precast elements, even a few inches of diameter difference can translate into significant cubic volume. Verify dimensions against current shop drawings or form drawings before ordering material.
Consider a full concrete cone with a 5 ft base diameter and a vertical height of 3 ft. The radius is 2.5 ft. Square the radius to get 6.25. Multiply by π and by the 3 ft height, then divide by three. Because multiplying by three and dividing by three cancel in this specific example, the volume is approximately π × 6.25 = 19.63 ft³.
Convert to cubic yards by dividing 19.63 by 27, giving approximately 0.73 yd³ exact. If a 10% ordering allowance is entered, the planning volume becomes about 0.80 yd³. If bagged concrete yields 0.60 ft³ per bag, the same 10% ordering volume is about 21.6 ft³ and therefore requires 36 whole bags.
The bag calculation should use the yield printed on the actual product. Do not assume every bag of a given weight has exactly the same yield across all formulations.
Suppose a tapered concrete pedestal has a 5 ft bottom diameter, 2 ft top diameter and 3 ft vertical height. The bottom radius is 2.5 ft and the top radius is 1 ft. Using the frustum formula:
V = π × (6.25 + 2.5 + 1) = π × 9.75 ≈ 30.63 ft³.
That equals approximately 1.13 yd³ exact. A 10% allowance gives about 1.25 yd³ for planning. The frustum contains more concrete than the full cone with the same bottom diameter and height because the top remains 2 ft in diameter rather than tapering to zero.
Volume tells you how much concrete fills a solid cone or frustum. Surface area answers a different question: how much exterior or form-contact area the shape has. Surface area can matter for form liners, coatings, sealers, waterproofing or finishing, but it does not determine cubic yards directly.
The Concrete Cone Calculator focuses on volume because its purpose is material quantity. If you need coating or preparation quantities for a tapered concrete surface, calculate the sloped lateral area separately and use a coverage-based tool such as the Concrete Surface Preparation Calculator.
Do not multiply exterior surface area by vertical height to estimate volume. Tapered geometry requires the actual cone or frustum volume equation.
Bagged concrete can be practical for small decorative cones, landscape forms, small pedestals and precast units. The calculator estimates bag quantity by dividing the ordering volume in cubic feet by the bag yield you enter, then rounding up to the next whole bag.
If the exact cone volume is 10 ft³ and you apply a 10% ordering allowance, the planning volume becomes 11 ft³. At a product yield of 0.60 ft³ per bag, 11 ÷ 0.60 = 18.33, so the calculator reports 19 bags.
For repeated molds, actual loss can include residue in the mixer, tools, transfer containers and forms. Use an allowance that reflects your production process rather than assuming a universal percentage for every job.
Large cone-shaped bases or architectural forms can require several cubic yards. In those cases, ready-mix delivery may be more efficient than mixing bags. Enter the current supplier price per cubic yard to generate a simple material multiplication.
The cost output does not include short-load charges, delivery fees, pumping, crane buckets, labor, formwork, reinforcing steel, admixtures, finishing, curing or taxes. Tapered forms can also require slower placement or special consolidation to avoid voids, which may affect labor and equipment requirements.
Before ordering, confirm the final inside form dimensions. A cone or frustum can be difficult to adjust after forms are complete, and a small diameter change affects volume over the entire height.
Forming a circular tapered shape is more complex than forming a rectangular slab. Depending on size and finish requirements, contractors may use custom plywood segments, steel forms, fiberglass molds, flexible liners, precast molds or fabricated assemblies. Form pressure, bracing and joints should be designed for the placement method and concrete characteristics.
The calculator does not size formwork or bracing. It assumes the finished concrete shape matches the dimensions entered. If the form is segmented, check the actual internal profile rather than relying only on nominal outer dimensions.
For a decorative cone with a sharp apex, placement and consolidation near the point can be challenging. A truncated top may be more practical depending on the project, but that is a design decision rather than a quantity-calculator choice.
Some cone-shaped concrete is purely decorative or lightly loaded, while other tapered elements can be structural. Reinforcement can include circular bars, vertical bars, cages, dowels, welded reinforcement, fibers or engineered reinforcement arrangements. Bar spacing and cover change with geometry and exposure.
This page does not design reinforcement. Once the bar layout is known, estimate steel separately with the Concrete Rebar Calculator. For concrete mixture quantity comparisons, see the Concrete Mix Ratio Calculator, but do not treat a nominal mix ratio as a substitute for the specified structural concrete mixture.
A hollow cone or frustum requires subtraction. First calculate the volume of the outside cone or frustum. Then calculate the volume of the inside void using its own diameters and height. Subtract the inner volume from the outer volume.
Both shapes must use consistent reference planes and height assumptions.
This method is useful for tapered shells, planters, hollow architectural units and other formed cavities. Be careful when wall thickness is measured perpendicular to the sloped surface because that does not translate directly into a constant difference in horizontal radius. For accurate shell geometry, use the actual inside and outside diameters shown on the drawing.
The formulas on this page assume a right circular cone or frustum: the top circle or apex is centered over the bottom circle and the circular faces are parallel. If the apex is offset, the shape becomes an oblique cone. Interestingly, an oblique cone with the same base area and perpendicular height has the same volume as a right cone, so the full-cone formula still applies when those quantities are known.
Irregular tapered shapes with elliptical bases, nonparallel faces or changing cross sections require different geometry. Divide the element into measurable components or use drawing/CAD volume data when available. Do not force a complex architectural form into the circular cone calculator simply because it looks approximately tapered.
The formula uses radius squared. The calculator divides entered diameter by two automatically. In manual calculations, forgetting this step can overstate volume by a factor of four.
Cone volume uses perpendicular vertical height, not the length along the tapered side.
A tapered shape is not a cylinder unless top and bottom diameters are equal. Using the bottom diameter through the whole height will overestimate volume.
For a frustum, simply averaging top and bottom diameters and using a cylinder formula is generally not exact. Use the dedicated frustum equation.
Concrete occupies the inside of the form. Thick steel, plywood or fiberglass molds can make outside dimensions noticeably larger.
A tapered upper section may sit on a cylindrical base, square plinth or footing. Calculate all concrete components instead of estimating only the visible cone.
If you calculate several shapes separately, consider adding exact volumes first and applying one final allowance. Applying an allowance to each subtotal and again to the total double counts contingency.
The same volume formulas can be used across many concrete applications. A small landscape cone may require only a few bags. A large tapered monument base may require a ready-mix truck. A precast operation may cast dozens of identical frustums and therefore benefit from the Multiple Cones calculator.
For structural work, material volume is only one part of the design. Concrete strength, reinforcement, anchorage, stability, lifting, bearing and connection design can govern the element. Use approved drawings and specifications for those requirements.
If the tapered element is connected to a foundation, you may also use the Concrete Foundation Size Calculator for separate foundation planning. If the base is a cylindrical pier, the Concrete Pier Calculator may be useful when available in your site structure.
The optional price field gives a concrete-material estimate based on the cubic yards to order. It is useful for comparing scenarios such as changing bottom diameter, reducing height or casting multiple units. Because volume increases with radius squared, diameter changes can affect cost quickly.
For example, increasing a full cone’s base diameter from 4 ft to 5 ft while keeping height unchanged increases base area by 56.25%, and therefore increases cone volume by the same percentage. This squared relationship is why diameter should be measured carefully.
Volume changes with radius squared, so small diameter changes can materially affect quantity.
For a fixed profile, volume changes directly in proportion to vertical height.
Repeated identical forms scale linearly with the number of pieces.
For broader concrete construction guidance, the American Concrete Institute publishes codes, guides and technical resources covering structural concrete, placement, formwork, repair and materials. For unit-system reference and measurement practice, the National Institute of Standards and Technology SI Units resources provide official information on measurement units and conversions.
These sources do not provide a project-specific cone volume for you; the calculator performs the geometry from your dimensions. They are included as authoritative external references for concrete practice and measurement context.
Use base diameter, top diameter and vertical height. The figure shows why a frustum needs two circular dimensions while a full cone uses a top diameter of zero.
Common questions about cone volume, frustum volume, cubic yards, bags and tapered concrete forms.