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The horizontal clear span of the arch opening.
Measured at the SPRINGLINE, where the arch actually begins, which on a segmental arch springing from skewbacks is between the skewbacks rather than between the jambs below them. Span and rise have to be taken on the same face of the arch and in the same plane; mixing a span at the opening with a rise at the crown of the extrados produces a ratio for an arch nobody is building.
The vertical height from the springline to the crown of the arch.
Springline to crown, on the same face the span was taken on — the intrados for both, normally. Rise is what decides how hard the arch pushes sideways: a shallow arch throws a far larger horizontal thrust into its abutments than a deep one carrying the same load, which is why flat arches need a buttress, a substantial return or a tie, and semicircular ones often need none.
Rise-to-span ratio
0.125 (rise/span)
Classification: Flat / jack arch.
- Radius to strike the curve
- 4.25 ft
- Centre point, below the springline
- 3.75 ft
- Angle the arch subtends at that centre
- 56.14 °
- Skewback, from horizontal
- 61.93 °
- Length along the intrados
- 4.16 ft
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Brick Arch Rise-to-Span Ratio Calculator: 0.125 (rise/span) — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Arch classification by rise-to-span ratio: flat/jack arch ≈ 1/8 or less, segmental arch ≈ 1/8 to 1/2, semicircular arch = 1/2
Inputs used
- Arch Span
- 4 ft
- Arch Rise
- 6 in
Intermediate steps
- Radius to strike the curve
- 4.25 ft
- Centre point, below the springline
- 3.75 ft
- Angle the arch subtends at that centre
- 56.14 °
- Skewback, from horizontal
- 61.93 °
- Length along the intrados
- 4.16 ft
Confidence note: Classification: Flat / jack arch.
What this calculation does not cover
- This classifies a shape; it is not a structural check. It returns no thrust force, no abutment size and no load capacity, so it cannot tell you whether the arch, its supports or the wall above will stand. An arch over a structural opening needs a designer's check, not a ratio.
- The bands describe circular-segment arches. Pointed, Gothic, Tudor, three-centred, elliptical and horseshoe shapes are not distinguished by rise over span, and a ratio much above 1/2 is not a semicircle at all — past a small margin over 1/2 no name is offered, so read the ratio itself against the geometry.
- The set-out above is the CURVE, not the arch. Radius, centre, subtended angle, skewback and the length along the intrados are enough to strike the line and build the centring, and they are exact for a circular segment — but no voussoir is counted or sized here, because that needs the brick, the joint and the ring depth, none of which this page asks for. The brick arch wedge taper calculator takes those.
- The centre point is given as a depth below the springline on the vertical centreline, which is where a trammel is pinned. On a flat or jack arch that depth is large — a 1.2 m (4 ft) span rising 150 mm (6 in) strikes from 1.125 m (3.7 ft) below the springline — so setting one out on site usually means a string and a pin in the floor rather than a beam compass, and the accuracy of the curve is the accuracy of that pin.
- Ring depth, number of rings, brick and mortar type, and the load and backing carried above the arch are not inputs, and every one of them changes how a given shape behaves. Two arches with the same rise-to-span ratio can be sound and unsound.
- The answer assumes rise is measured vertically from the springline to the underside of the crown, and span is the clear opening between abutments. Measuring rise from a sill or floor, or span to the outside of the jambs, shifts the ratio and can move it into a different band.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-10-04 · v1.0.2
Regulatory standards & verification citations1
- Arch classification by rise-to-span ratio: flat/jack arch ≈ 1/8 or less, segmental arch ≈ 1/8 to 1/2, semicircular arch = 1/2
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