Hemispheres • Spherical Caps • Concrete Shells
Use this Concrete Dome Calculator to estimate concrete volume for hemispherical domes, spherical-cap domes and hollow concrete dome shells. Enter diameter, dome rise and shell thickness to calculate cubic feet, cubic yards, approximate bag quantities and optional ready-mix material cost.
Estimate a solid hemisphere, spherical cap, hollow dome shell, or calculate concrete bags and ready-mix cost.
Estimate a solid half-sphere volume from finished dome diameter.
A solid hemisphere is uncommon for building shells. Use the Dome Shell calculator for hollow concrete domes.
Estimate a solid spherical-cap dome using base diameter and vertical rise.
Estimate a hollow hemispherical concrete shell from outside diameter and radial shell thickness.
This mode assumes a constant radial shell thickness on a hemispherical dome. Openings, ring beams and edge thickening should be calculated separately.
Estimate concrete bags and ready-mix material cost for a hemispherical shell.
Verify actual manufacturer yield.
The Concrete Dome Calculator is designed for curved concrete geometry rather than ordinary flat slabs. Choose the calculator that best matches the project shape. Use Hemisphere for a solid half-sphere, Spherical Cap for a dome with a known base diameter and rise, and Dome Shell for a hollow hemispherical concrete structure.
For most architectural or structural dome shells, the hollow-shell calculator is the more relevant quantity tool because the structure contains an interior void. The calculator finds the outer hemispherical volume, subtracts the inner hemispherical volume and converts the remaining concrete into cubic yards.
Hemisphere, spherical cap or shell.
Use the outside or base diameter specified by the tool.
Add dome rise or shell thickness where required.
Compare exact volume with an optional order percentage.
Check geometry, openings and project drawings before ordering.
A hemisphere is exactly one-half of a sphere. If the dome diameter is known, divide it by two to find the radius.
Where r is the radius of the hemisphere.
The calculator converts the resulting cubic feet to cubic yards by dividing by 27. A solid concrete hemisphere can contain a very large amount of concrete, so verify that a solid form truly represents the intended project.
Many domes are shallower than a hemisphere. A spherical cap is defined by its base radius and vertical rise. The sphere radius corresponding to that cap can be calculated from the base radius and cap height.
Where a is the base radius and h is the vertical cap rise.
The same volume can also be written as πh²(3R − h)/3 when the parent sphere radius R is known. The calculator uses the base-radius form so users can enter the dimensions most often available on a drawing.
A hollow hemispherical concrete shell is calculated by subtracting the inner hemisphere from the outer hemisphere.
R = outside radius; r = inside radius after subtracting shell thickness.
This method assumes the shell thickness is measured radially and remains constant over the hemisphere. Real domes may include ring beams, ribs, thickened edges, openings or variable shell thickness. Those elements should be calculated separately.
| Outside Diameter | Shell Thickness | Approx. Shell ft³ | Approx. yd³ | Geometry |
|---|---|---|---|---|
| 10 ft | 4 in | 48.95 | 1.81 | Hemisphere shell |
| 12 ft | 4 in | 71.29 | 2.64 | Hemisphere shell |
| 16 ft | 6 in | 188.76 | 6.99 | Hemisphere shell |
| 20 ft | 6 in | 298.71 | 11.06 | Hemisphere shell |
| 24 ft | 8 in | 570.30 | 21.12 | Hemisphere shell |
These are geometric examples only. Openings, ring beams and project-specific thickening are not included.
Calculate a simple half-sphere concrete volume.
Use base diameter and rise for shallow dome geometry.
Subtract the inside dome from the outside dome.
Convert curved geometry into cubic yards for ordering.
A solid dome fills the entire curved volume with concrete. A shell uses concrete only in a curved structural layer. The difference in material quantity can be enormous. For a building or enclosure, the shell calculator is usually more representative than the solid hemisphere calculator.
Before calculating, determine whether the stated diameter refers to the outside surface, inside surface or base opening. The Dome Shell mode expects outside diameter and a radial shell thickness.
Shell thickness directly affects material quantity, but the relationship is not exactly linear for thick shells because both the inner and outer radii are curved. As shell thickness increases, the inner void becomes smaller and concrete volume rises.
The calculator does not determine structural shell thickness. Required thickness can depend on span, shell geometry, reinforcement, loads, support conditions, openings, seismic effects and engineering design. Use dimensions from approved plans or a qualified design professional.
Doorways, windows, skylights and service penetrations reduce concrete volume, but their geometry may be complicated because the shell surface is curved. A simple rectangular opening measured on a flat plane does not necessarily equal the true curved shell area removed.
For preliminary estimating, large openings can be handled as separate deductions using project geometry or a detailed takeoff. Small penetrations are often not worth deducting from an early material estimate.
Concrete domes frequently include a ring beam, curb, footing or thickened edge at the base. That component is not included in the simple hemispherical shell volume. Calculate it separately and add it to the dome quantity.
For a continuous rectangular ring or base element, the Concrete Linear Foot Calculator can be useful. For foundation walls or supports, use the Concrete Foundation Wall Calculator.
The optional cost field multiplies estimated cubic yards by the local ready-mix price entered by the user. It represents concrete material only and does not include the many specialized costs associated with dome construction.
Small decorative domes or mockups may use bagged concrete, but larger dome shells can require many cubic yards. The Bags & Cost calculator converts shell volume into an approximate bag count using the product yield entered by the user.
Always verify the actual manufacturer yield because bag size and formulation vary. For larger projects, ready-mix, shotcrete or pumped concrete may be more practical depending on the placement method and structural design.
For pump planning, use the Concrete Pump Capacity Calculator.
Curved concrete work can involve placement losses, varying thickness and complex detailing. The exact mathematical volume assumes perfect geometry and constant thickness.
Use the allowance field for comparison only. Final ordering should reflect the actual construction method and project specification.
Radius is one-half of diameter.
A hollow shell uses far less concrete than a solid hemisphere.
The shell calculator assumes constant radial thickness.
Calculate these additional structural elements separately.
Large doors, skylights and other voids may materially reduce concrete volume.
Shallow domes are often better represented by spherical-cap geometry.
This page estimates material quantity only.
Reinforcement is separate from concrete quantity. Rebar, mesh, fibers or other reinforcing systems should follow the project design. In normal concrete estimating, the physical volume of reinforcement is not subtracted from the formed concrete geometry.
For reinforcement material quantities, use the Concrete Rebar Calculator or Concrete Rebar Length Calculator.
For technical concrete information, construction education and standards, useful resources include the American Concrete Institute and the National Ready Mixed Concrete Association.
Concrete domes can be complex structural systems. Follow approved drawings, project specifications, local requirements and qualified engineering guidance.
A hollow dome is estimated by subtracting the inner curved volume from the outer curved volume.
Consider a hemispherical dome with an outside diameter of 20 feet and a 6-inch radial shell thickness. The outside radius is 10 feet and the inside radius is 9.5 feet.
An optional ordering allowance would be applied after calculating the exact shell volume.
Common questions about hemispheres, spherical caps, shell thickness, cubic yards and concrete dome estimating.