Raked Seating Sightline Calculator: Riser Height for Every Row (C-Value)

How it works

D_i = first-row distance + (i − 1) × row depth · E_i = F + (E_{i−1} + C − F) × D_i ÷ D_{i−1} (equivalently riser N = (R + C)(D + T) ÷ D − R) · floor_i = E_i − seated eye height · C achieved = (E_i − F) × D_{i−1} ÷ D_i − (E_{i−1} − F) · staggered seats: check over row i − 2 instead of i − 1

Every spectator should see the focal point (the front edge of the stage, the bottom of the screen or the near touchline) over the head of the person in front. The C-value is the vertical gap between that sightline and the eye of the spectator in front; head height above the eye is roughly 100–120 mm, so 60 mm lets you see between heads, 90 mm is the recommended minimum and 120 mm gives a clear view over heads. Working back from the first row, similar triangles give each row's required eye height, and because the rows recede from the focal point the risers grow row by row: the ideal floor is a gentle curve. Built seating approximates that curve. "Flights" splits the rows into bands with one riser each (the smallest that still gives every row in the band the target C), and "One riser" uses a single step everywhere, which is simplest but wastes height at the front. The calculator reports the C-value each row really gets, so you can see the effect of a riser cap, rounding or staggered seats. It works in a 2D section through the centre of the seating; side seats with curved rows see the focal point at an angle and get slightly more clearance. Aisle steps follow the US IBC stepped-aisle limits (risers 4–8 in, uniform within a flight); other codes differ.

Worked example

Ten rows at 0.9 m, the first 4 m from a stage floor 1.0 m above the first-row floor, seated eye height 1.12 m, target C = 90 mm, ideal curve. Row 2 needs eye height 1.0 + (1.12 + 0.09 − 1.0) × 4.9 ÷ 4.0 = 1.257 m, a 137 mm riser. Repeating row by row, risers grow to 224 mm at row 10, and the back-row floor sits 1,678 mm (5 ft 6.1 in) above the front-row floor, an average rake of 11.7° over 8.1 m. The back row is 12.2 m from the stage edge and looks down 8.5°. Building it with one uniform riser is far less efficient: because every raised row also raises the requirement for the rows behind it, the smallest single riser that keeps 90 mm everywhere is 299 mm, for a rise of 2,693 mm. The 224 mm risers are over 203 mm, so each aisle needs 2 steps of about 112 mm per row.

Sources: Sightline (architecture): C-values and step heights (Wikipedia) · C-value formula for stadium tiers (Barça Innovation Hub) · Stepped-aisle riser limits, IBC/NCBC 1029.13.2.2 (NC Office of State Fire Marshal)

Frequently asked questions