BrickCore · Masonry explained

Arch radius, rise and setting-out centre explained

Calculate a segmental arch radius from span and rise. Locate its centre, draw the intrados and understand why brick spacing follows the arc, not the opening.

Start an arch drawing with two springing points and the required height above their connecting line. For a circular segmental arch with level springings, these dimensions determine the circle. Other arch shapes need different constructions.

1 000 mm1 600 mm400 mm600 mm
The worked example

Measure span and rise

Span is the straight distance between the springing points. Rise is measured perpendicular to that line up to the crown of the inner curve. Do not confuse it with the thickness of the arch ring or the brick depth through the wall.

Calculate a segmental arch radius

Multiply the span by itself. Divide by eight times the rise, then add half the rise. For a 1600 mm span and a 400 mm rise: 1600² ÷ 3200 + 200 = 1000 mm. This formula applies to a circular arc, not every arch shape.

1 600² ÷ (8 × 400) + 400 ÷ 2 = 1 000 mm

Locate the centre and draw the intrados

Draw the opening centreline. In this example the circle centre lies 1000 − 400 = 600 mm below the springing line. Measure 1000 mm from this point to both springings and the crown. Use that radius to draw the intrados. For a constant arch ring, draw the outer curve with the radius plus the ring thickness.

Divide along the curve, not the clear span

The curved line is longer than the straight opening. Brick and joint dimensions belong to the chosen reference line. Basket-handle and Tudor arches use multiple centres; an ellipse does not have one fixed circular radius. Use each shape’s own calculator and setting-out instructions.