Estimate Semicircular & Segmental Arch Concrete, Bags & Cost
Use the Concrete Arch Calculator to estimate cubic feet, cubic yards, concrete bags and optional material cost for semicircular arch rings, segmental arches, arch-plus-pier assemblies and multiple identical concrete arches.
Choose the geometry that matches your formed concrete arch and enter the actual finished dimensions.
Calculate a half-circle arch ring from the clear opening span and outer arch span.
For a true semicircle, span equals inner diameter.
Outer diameter of the semicircular ring.
Material estimate only. Structural arch dimensions, reinforcement and temporary formwork must follow the approved design.
Calculate concrete between two circular segments using separate inner and outer span-and-rise dimensions.
Use drawing dimensions from the same spring-line reference. Irregular or noncircular arches require different geometry.
Add two rectangular piers or legs beneath a semicircular arch ring.
Quantity only. This tool does not design abutment resistance, foundations, reinforcement or arch thrust.
Estimate several identical semicircular or segmental arch rings with one quantity calculation.
Ignored for semicircular mode; rise is span ÷ 2.
Ignored for semicircular mode.
Do not multiply one representative arch across a structure if opening geometry varies.
A Concrete Arch Calculator estimates the volume of concrete in a curved arch ring by subtracting the opening profile from the outer concrete profile. Once the net cross-sectional arch area is known, multiply that area by the depth of the arch through the wall, bridge, portal, landscape structure or architectural element. The result can then be converted from cubic feet to cubic yards or concrete bags.
Arches can look similar while having very different geometry. A true semicircular arch has a rise equal to half its clear span. A segmental arch is shallower and represents part of a circle cut by a chord. Some structures use pointed, parabolic, elliptical, three-centered or custom curves. This page supports circular semicircular and circular segmental arches because their geometry can be calculated from a small set of dimensions.
The calculator is intended for estimating concrete quantity, not for structural arch design. Real concrete arches develop compression and horizontal thrust, and their behavior depends on geometry, loading, reinforcement, abutments, foundations, construction sequence, formwork and support conditions. Use approved drawings or a qualified structural design for those requirements.
A semicircular arch ring is the difference between two half-circles. If the clear opening is a true half-circle, its radius equals half the clear span. The outer arch radius equals half the outer span. Subtract inner half-circle area from outer half-circle area and multiply by arch depth.
Concrete volume = arch area × depth. R is outer radius and r is inner opening radius.
For example, an 8 ft clear semicircular opening has an inner radius of 4 ft. If the outer arch span is 10 ft, the outer radius is 5 ft. The ring cross-sectional area is ½π(25 − 16) = approximately 14.14 ft². If the arch is 1 ft deep through the structure, one arch contains about 14.14 ft³, or 0.52 yd³ before ordering allowance.
This method is exact for concentric semicircles sharing the same spring line. If the outer profile is offset, flattened or differently centered, use the actual outer geometry instead of assuming a uniform ring.
A segmental arch is part of a circle bounded by an arc and a straight chord. If chord span and rise are known, first calculate the parent circle radius. Then calculate the segment’s central angle and area.
c is chord span and h is segment rise.
θ = 2 × asin[c ÷ (2R)] in radians.
To find concrete in a segmental arch ring, calculate the outer circular-segment area from the outer span and rise. Calculate the inner opening segment area from the inner span and rise. Subtract inner area from outer area, then multiply by arch depth.
This two-profile method is useful because drawings often provide separate dimensions for the clear opening and top of arch. It avoids making an unsupported assumption about constant radial thickness. The inner and outer curves still need to represent circular segments measured from a consistent spring-line reference.
Measure clear opening chord width or outer arch chord width at the spring line.
Measure from the spring line to the crown of the circular arch profile.
Measure concrete thickness through the wall or structure perpendicular to the elevation.
Subtract the clear opening from the outer arch before calculating concrete volume.
Choose semicircular or segmental geometry from the project drawing.
Enter the clear inner span and rise where applicable.
Enter the outer span and outer rise or diameter.
Measure the concrete depth through the structure.
Check exact volume, allowance, bag count and optional cost.
Start by confirming what curve is shown on the drawings. If rise equals half the span and the curve is a half-circle, use Semicircular Arch. If the rise is smaller than half the span and the curve is circular, use Segmental Arch. If the structure includes concrete legs beneath the spring line, add the side piers with the third calculator.
Use inside dimensions of the concrete form or finished concrete profile rather than outside formwork dimensions. On large arches, a few inches of difference in span, rise or depth can produce a meaningful quantity change.
| Arch Type | Key Geometry | Typical Inputs | Calculator Method |
|---|---|---|---|
| Semicircular | Half of a full circle | Inner span, outer span, depth | Outer half-circle minus inner half-circle |
| Segmental | Less than a semicircle | Inner span/rise, outer span/rise, depth | Outer circular segment minus inner circular segment |
| Arch + piers | Curved ring over straight legs | Arch dimensions + pier width/height | Arch ring plus two rectangular prisms |
| Multiple arches | Repeated identical openings | One arch geometry + quantity | Single arch volume × count |
A segmental arch is not just a semicircular arch with a smaller height entered into a half-circle formula. The circle radius changes with chord and rise, so the circular-segment formula is required.
The clear span is the horizontal chord width of the opening at the spring line. For a semicircle it is also the inner diameter. For a segmental arch it is the chord length used with the rise to reconstruct the circular curve.
Rise is the perpendicular distance from the spring line to the crown of the arch. Do not measure along the curved surface. A true semicircular opening has rise equal to one-half the span. A segmental arch has a smaller rise relative to its span.
Measure the outer concrete profile independently when it is shown on the drawing. If the outer curve is not concentric with the inner opening, independent outer dimensions are necessary for an accurate material estimate.
Depth is the thickness through the structure, not the vertical height of the arch. A decorative 10 ft wide arch may be only 8 inches deep, while a bridge barrel or thick wall opening may extend several feet.
For a concentric semicircular arch, radial ring thickness is simply outer radius minus inner radius. If the inner span is 8 ft and outer span is 10 ft, radial ring thickness is 1 ft. This is because the diameters differ by 2 ft and the radius difference is half of that.
For a segmental arch, “ring thickness” can be defined in several ways. A constant radial thickness would create concentric circular arcs with the same center, but architectural drawings may instead define a vertical crown thickness or separate outer span and rise. The calculator avoids ambiguity by asking for the complete inner and outer segment dimensions.
If your drawing provides only one thickness dimension, use the geometric method that actually matches the detail. Do not assume radial, vertical and normal-to-curve thickness are interchangeable.
Many architectural arches include vertical concrete supports beneath the spring line. These can be estimated as rectangular prisms if their cross section is constant. For two identical piers:
Total assembly volume = arch ring volume + pier volume.
The third calculator combines these two quantities. It assumes the arch ring begins at the spring line and the piers stop at that line. If the curved ring extends down the sides, the piers taper, or the pier heads overlap the arch ring, split the geometry more carefully to avoid double counting.
Consider a semicircular opening with an 8 ft clear span and an outer arch span of 10 ft. The inner radius is 4 ft and the outer radius is 5 ft. Outer half-circle area is ½π × 5² = 39.27 ft². Inner half-circle opening area is ½π × 4² = 25.13 ft².
The concrete arch ring area is therefore 14.14 ft². If the arch is 1.5 ft deep through the wall, exact concrete volume is 21.21 ft³. Divide by 27 to obtain approximately 0.79 yd³. With a 10% ordering allowance, the planning quantity becomes about 0.86 yd³.
If bagged concrete yields 0.60 ft³ per bag, the 23.33 ft³ ordering volume would require approximately 39 whole bags. For a large structural arch, ready-mix placement would usually require additional planning for formwork, access, consolidation and temporary support.
Assume an inner opening chord of 10 ft with a 3 ft rise. The parent-circle radius is calculated as 10² ÷ (8 × 3) + 3 ÷ 2 = approximately 5.67 ft. The central angle and circular-segment formula then give the inner opening segment area.
If the outer arch is defined by a 12 ft chord and 4 ft rise, calculate its parent radius and outer segment area independently. Subtract the inner segment area from the outer segment area. Multiply the resulting arch-ring area by the depth through the structure.
This example demonstrates why segmental arch volume should not be estimated with a rectangle minus a rough curved opening. The exact segment formulas improve quantity accuracy, especially when the ring is thick or the arch is wide.
Repeated arches appear in arcades, landscape walls, culvert portals, decorative facades and bridge structures. If every opening has the same geometry and depth, calculate one exact arch-ring volume and multiply by the number of arches.
The Multiple Arches calculator supports both semicircular and segmental profiles. For a semicircular set, only the inner and outer spans are required because rise is fixed by the diameter. For segmental arches, enter inner and outer rise values as well.
If end arches differ from interior arches, or if some openings have wider piers or different depths, calculate separate groups. Do not average the geometry unless that approximation is intentionally accepted in your estimate.
Bagged concrete can be practical for small decorative arches, garden features, small precast forms or minor infill.
Ready-mix may be more suitable for large arches or deep structural elements where continuous placement and consistent supply matter.
The cost output on this page is a simple material multiplication based on the ready-mix price per cubic yard you enter. It does not include pumping, forms, reinforcing steel, labor, bracing, shoring, curing or finishing.
Concrete arches usually require curved formwork or centering until the concrete has developed sufficient strength and the structure can safely transfer loads. Formwork for a curved soffit can be made from ribs, plywood, steel, modular systems or custom fabricated forms depending on size and finish requirements.
The Concrete Arch Calculator does not design forms or temporary support. Fresh concrete pressure, construction loads, vibration, placement sequence and stripping time can all affect formwork design. A large arch can place substantial load on its centering before the permanent structural load path is active.
For quantity estimating, use inside form dimensions because they define the concrete surface. Do not include plywood, liners, ribs or external bracing in the concrete geometry.
Concrete can carry compression effectively, but structural concrete arches may still require reinforcement for bending, crack control, temperature effects, construction stages, local stresses and load combinations. Reinforcement can follow the curved arch, run longitudinally through the barrel, anchor into abutments or connect to piers and foundations.
This calculator does not determine bar size, spacing, cover or development. Once reinforcement details are approved, estimate steel separately with the Concrete Rebar Calculator. Keep rebar quantities separate from concrete volume so changes in bar layout do not alter the geometric concrete estimate.
An arch transfers vertical load and horizontal thrust to its supports. The supports, abutments and foundations must resist those reactions without unacceptable movement. A visually modest arch can therefore require substantial support depending on span, rise, loading and structural system.
The quantity tools on this page only calculate the curved arch ring and optional rectangular side piers. Foundations and abutments should be calculated separately from their approved dimensions. For simple footing quantity planning, use the Concrete Foundation Size Calculator or Concrete Strip Calculator where appropriate.
Concrete arches can serve very different purposes. A landscape arch may be primarily decorative. A wall opening can carry limited gravity load. A bridge arch or culvert can be a major structural system. The same geometric volume formula can estimate material in each case, but the design requirements are not interchangeable.
Appearance, form finish, symmetry and reveal dimensions can be as important as structural requirements.
Small spans may use simple forms, but footing support and reinforcement still need appropriate design.
Loads, thrust, reinforcement, abutments, foundations and temporary support require engineered analysis.
A rectangle around the arch includes the clear opening and overstates concrete unless the opening is subtracted accurately.
A segmental arch has a different radius and area relationship. Use chord and rise geometry.
Concrete occupies the inside of the form. Measure the actual finished concrete profile.
Rise is vertical geometry in the arch elevation. Depth is thickness through the wall or structure.
Concrete ring volume depends on both inner and outer curves. Opening dimensions alone are not enough.
If the arch ring overlaps pier volume below the spring line, account for the overlap instead of simply adding both shapes.
End conditions, pier widths or spans can vary. Group only truly identical geometries together.
Concrete material cost is only one part of an arch project. Curved formwork, temporary centering, reinforcement bending, pumping or bucket placement, access, lifting, vibration, finish work and stripping can be substantial cost items. Small architectural arches can also have high labor cost per cubic yard because the geometry is detailed even when concrete volume is modest.
The calculator’s optional ready-mix price lets you compare material scenarios without implying a complete installed cost. For budgeting, create separate line items for concrete, reinforcing steel, formwork, shoring, labor, equipment, curing and finishes.
For structural concrete design, the American Concrete Institute ACI CODE-318-25 provides current structural concrete code requirements and commentary. Arch behavior and complete structural analysis can also involve project-specific bridge, building or civil design standards depending on the application.
For general concrete construction practice, ACI publishes guides on formwork, placement, consolidation, curing and structural concrete. These references are broader than a geometric arch-volume estimate, but they provide authoritative context for construction requirements that the calculator intentionally does not design.
When estimating a concrete arch, it helps to keep three quantities separate: the area of the clear opening, the area enclosed by the outer arch profile, and the net concrete ring area between them. The clear opening is empty space and must never be counted as concrete. The outer profile includes both the opening and the concrete. Net concrete area is therefore always the difference between the two.
This separation is especially important for thick arches. A quick estimate based only on average ring thickness times curved length can introduce error because the width of the ring may not be uniform in the direction being measured. The area-subtraction method works directly from the geometry shown on the drawing and is easier to audit. For semicircular arches, the half-circle areas are simple. For segmental arches, each circular segment is calculated from its own chord and rise.
Once net ring area is known, multiplying by the depth through the structure converts a two-dimensional elevation into three-dimensional concrete volume. This assumes the arch profile is constant through that depth. If the arch barrel tapers in plan, steps in thickness, changes cross section or includes ribs and recesses, divide it into smaller zones and calculate each zone separately.
Curved forms can make concrete placement more demanding than a simple wall or slab. Reinforcement congestion, narrow ring thickness, high crown elevations and limited access can affect how the concrete is delivered and consolidated. A mathematically correct cubic-yard estimate does not guarantee that the concrete can be placed efficiently without a suitable sequence.
Before pour day, confirm the placement method, access points, form cleanouts, concrete delivery path, vibration strategy and temporary support. When an arch is poured monolithically with piers or walls, the sequence may be defined to control form pressure and construction behavior. Large structural arches may require engineered placement procedures and staged work.
For estimating purposes, separate concrete quantity from logistics cost. Pumping, crane buckets, tremie-type placement, extra labor, form access and waiting time can add substantial cost even when the concrete volume is modest. The optional material-price field on this calculator intentionally excludes those project-specific costs.
The figure shows the key dimensions used by the calculator: clear span, rise, outer arch profile, ring thickness and depth through the structure.
Common questions about semicircular and segmental arch volume, bags, span, rise and concrete quantity.