Calculate Solid and Hollow Hemisphere Concrete
Estimate hemisphere volume, cubic yards, surface area, shell volume, bag quantity, concrete weight and material cost for half-sphere concrete features, domes, landscape forms, architectural elements and specialty pours.
Choose solid volume, diameter input, hollow shell or weight-and-cost calculation.
Calculate half-sphere concrete volume from radius and estimate bags or ready-mix quantity.
Bag yields are approximate. Verify product yield and ready-mix supplier ordering increments.
Enter diameter to calculate radius, concrete volume, curved surface area and total area including the base.
Estimate concrete for a hollow half-sphere using outside radius and uniform shell thickness.
Uniform-shell geometry only. Openings, ribs, thickened edges, foundations and structural reinforcement must be calculated separately.
Convert hemisphere concrete volume into approximate weight and optional ready-mix material cost.
Calculate a true half-sphere using radius or diameter.
Estimate curved area and total area including the circular base.
Subtract the inner hemisphere from the outer half-sphere.
Convert concrete volume into pounds, tons and optional material cost.
The Concrete Hemisphere Calculator is designed for true half-sphere concrete shapes. A hemisphere is exactly one half of a sphere cut through its center. Because of that geometry, the required inputs are simple: radius or diameter for a solid hemisphere, and outside radius plus shell thickness for a hollow hemisphere.
Start with the Solid Hemisphere panel when the entire half-sphere will be concrete. Use the Diameter & Area panel when your drawing gives overall diameter instead of radius. For dome-like concrete shells, use the Hollow Shell panel. If you already know the volume, the Weight & Cost panel converts cubic yards into approximate concrete mass and budget.
Find finished radius or outside diameter.
Choose solid hemisphere or uniform shell.
Enter the number of identical concrete hemispheres.
View ft³, yd³, m³, bags and area.
Check forms, thickness, openings and final dimensions.
A full sphere has a volume of four-thirds times pi times radius cubed. A hemisphere is exactly half of that volume, so the half-sphere formula becomes two-thirds times pi times the radius cubed.
Use radius in feet to produce cubic feet, then divide by 27 to convert cubic feet to cubic yards.
Measure from the sphere centerline to the outside surface.
Volume increases rapidly as hemisphere radius increases.
Use cubic yards for most ready-mix ordering in the U.S.
Suppose a solid concrete hemisphere has a radius of 3 feet. Cube the radius first: 3 × 3 × 3 = 27. Multiply by pi, then multiply by two-thirds. The result is approximately 56.55 cubic feet.
With a 10% planning allowance, the project estimate becomes approximately 2.30 cubic yards. Supplier minimums and ordering increments can affect the actual quantity purchased.
Radius and diameter describe the same half-sphere in different ways. Diameter is the full width across the circular base through the center. Radius is exactly half of that distance. Many architectural and landscape drawings provide outside diameter, so the calculator automatically converts diameter to radius.
| Diameter | Radius | Approx. Solid Volume | Approx. Cubic Yards |
|---|---|---|---|
| 2 ft | 1 ft | 2.09 ft³ | 0.08 yd³ |
| 4 ft | 2 ft | 16.76 ft³ | 0.62 yd³ |
| 6 ft | 3 ft | 56.55 ft³ | 2.09 yd³ |
| 8 ft | 4 ft | 134.04 ft³ | 4.96 yd³ |
| 10 ft | 5 ft | 261.80 ft³ | 9.70 yd³ |
Surface area is useful for estimating coatings, waterproofing, form liners, architectural finishes and membrane systems. A hemisphere has a curved outer area and a flat circular base. Which area you need depends on the work.
This includes only the rounded half-sphere surface.
This adds the flat circular base area, πr², to the curved hemisphere area.
Hollow concrete hemispheres are common in shell-like architectural features, dome forms and some specialty landscape structures. For a uniform shell, calculate the volume of the outside hemisphere and subtract the volume of the smaller inside hemisphere.
R is the outside radius and r is the inside radius after subtracting shell thickness.
For example, a 6 ft outside radius with a 6 in shell thickness has an inside radius of 5.5 ft. The calculator subtracts those two hemisphere volumes to estimate the concrete contained in the curved shell.
Shell thickness must be measured radially through the curved concrete, not as a vertical height at one arbitrary point. If the shell thickness changes near the base, includes ribs or has a thickened ring beam, a single uniform thickness will not represent the real project accurately.
Small half-sphere features can sometimes be mixed from bagged concrete. Once the calculator determines total cubic feet, divide by the bag yield and round up. This page includes approximate planning yields for 40 lb, 60 lb and 80 lb bags.
| Bag Size | Approx. Yield Used | Bags per 10 ft³ | Bags per 1 yd³ |
|---|---|---|---|
| 40 lb | 0.30 ft³ | About 34 | About 90 |
| 60 lb | 0.45 ft³ | About 23 | About 60 |
| 80 lb | 0.60 ft³ | About 17 | About 45 |
Actual bag yield varies by manufacturer. If you are mixing several cubic yards, compare the labor and production rate with ready-mix delivery or use the Concrete Mixer Capacity Calculator.
A hemisphere's material weight is its concrete volume multiplied by concrete density. Normal-weight concrete is often approximated around 145 to 150 lb per cubic foot for planning, although actual density can differ.
For a detailed unit conversion, use the Concrete Volume to Weight calculator.
Reinforcing steel is not included in the concrete weight result. If the hemisphere contains significant rebar, estimate that separately with the Concrete Rebar Weight Calculator.
The Weight & Cost panel can apply a local price per cubic yard to the concrete volume. This gives a basic material-cost estimate only. Specialty hemispherical work may require substantial formwork, reinforcing, pumping, finishing and skilled labor that can cost much more than the concrete itself.
Delivery, minimum load, pumping, reinforcement, forms, labor and finishing are excluded.
True half-sphere forms appear in architectural domes, protective bollard shapes, landscape features, art pieces, fountain elements and specialty precast products. The formula is the same as long as the final geometry is a true hemisphere.
Because a hemisphere is exactly half of a sphere, its volume is also exactly half when both shapes use the same radius. This relationship is useful when comparing specialty forms or splitting a spherical element into two identical halves.
| Shape | Formula | At Radius 3 ft | Relative Volume |
|---|---|---|---|
| Full Sphere | 4/3 × π × r³ | 113.10 ft³ | 100% |
| Hemisphere | 2/3 × π × r³ | 56.55 ft³ | 50% |
For a complete sphere rather than a half-sphere, use the Concrete Sphere Calculator.
Hemispherical concrete forms can be much more difficult to build than rectangular forms. Curved formwork must maintain the intended radius and resist fresh-concrete pressure without excessive distortion. Hollow shells may require inner and outer forms, spacers and carefully supported reinforcement.
This calculator does not determine structural shell thickness, rebar spacing, form pressure, construction sequence or support conditions. Those decisions should follow project drawings and qualified design input where applicable.
Visualize radius, diameter, curved surface and shell thickness for a true concrete half-sphere.
Answers about half-sphere volume, radius, diameter, surface area, shell concrete, bags, weight and cost.