Door Swing Clearance Calculator
Calculate the floor area swept by a door and the minimum clearance space required based on door width and swing angle.
Formulas Used
Swept Area (Annular Sector):
A = (θ / 2) × (Router² − Rinner²)
where Router = door width, Rinner = door thickness, θ = swing angle in radians.
Arc Length (outer edge):
L = Router × θ
Chord Length:
C = 2 × Router × sin(θ / 2)
Clearance Bounding Box (θ ≤ 90°):
Width = Router × sin(θ)
Depth = Router × (1 − cos(θ))
Clearance Bounding Box (90° < θ ≤ 180°):
Width = Router
Depth = Router × (1 − cos(θ))
Assumptions & References
- The hinge is modeled as a fixed point at one edge of the door.
- The outer radius equals the full door width (hinge to latch edge).
- The inner radius equals the door thickness (the door body itself).
- Standard interior door widths range from 24 in (610 mm) to 36 in (914 mm); exterior doors up to 42 in (1067 mm).
- ADA / ICC A117.1 requires a minimum 32 in (813 mm) clear opening width and 18 in (457 mm) latch-side clearance for accessible doors.
- IBC Section 1010 requires doors in means of egress to swing in the direction of egress travel when serving occupant loads ≥ 50.
- Standard door thickness is 1-3/8 in (35 mm) for interior and 1-3/4 in (44 mm) for exterior doors.
- The bounding box represents the minimum rectangular floor area that must remain clear for the door to operate freely.
- Reference: Architectural Graphic Standards, 12th Edition; IBC 2021; ADA Standards for Accessible Design.