Reciprocal Roof Geometry Calculator
Use this tool to estimate rafter lengths, support spacing, rise, and opening geometry for a circular reciprocal roof with equal rafters.
Plan View Layout (Top View)
What is a reciprocal roof?
A reciprocal roof is a self-supporting roof system where each rafter rests on the next one in sequence, creating a ring of interlocking members. This technique is common in roundhouses, pavilions, natural building projects, and timber frame structures with a central skylight opening.
Unlike a conventional roof that relies on a central ridge beam or trusses, a reciprocal roof distributes loads around the circle. It is both structural and architectural, often producing a striking spiral pattern in the ceiling.
What this calculator gives you
This reciprocal roof calculator is intended for early-stage layout and planning. It estimates:
- Support spacing at the perimeter
- Plan (top-view) run of each rafter
- True sloped rafter length based on pitch
- Rise from wall plate to reciprocal ring
- Approximate roof surface area
- Opening geometry for your center oculus
The geometry assumes equal spacing, equal rafters, and a circular plan. Real-world builds require joinery allowances, timber sizing, species-specific design values, and code checks.
Input guide
Outer roof diameter
This is the diameter across your support points (wall plate or ring beam). If your building is not perfectly round, use the effective diameter of your intended support circle.
Number of rafters
More rafters generally reduce spacing and can create a tighter visual spiral. Typical values are 6 to 14 for small to medium structures.
Roof pitch (degrees)
Pitch controls drainage, snow shedding, and aesthetics. The calculator converts pitch into rise and true length for each rafter.
Center opening diameter
This is your oculus or skylight opening. A larger opening creates shorter rafters and a more dramatic central void; a smaller opening gives more covered area.
How to use the results on site
- Mark support points evenly around your wall plate using the support spacing and angle increment.
- Cut rafters to true length, then leave extra for trial fitting and final trimming.
- Mock up one or two rafters first to verify seat cuts and bearing positions.
- Assemble in sequence so each member bears correctly on the next.
- Confirm bearing lengths and check for twist before final fastening.
Practical build tips for reciprocal roofs
1) Build a full-scale layout template
Draw the plan on plywood or the slab. This quickly reveals fit issues before you cut all rafters.
2) Keep timber dimensions consistent
Even small thickness variations can accumulate around the ring and change your final opening alignment.
3) Plan the final locking sequence
Because the system is interdependent, identify where temporary shoring is needed and how the final piece will be inserted safely.
4) Protect against moisture
Reciprocal roofs often include a central skylight detail. Ensure flashing, membrane continuity, and drainage paths are designed before installation.
Important engineering note
This calculator provides conceptual geometry only. It does not replace structural engineering. For permanent buildings, always verify loads, spans, joinery, fasteners, and local code requirements with a qualified professional.
Related topics
- rafter length calculator
- roof pitch and rise conversion
- timber frame roof geometry
- roundhouse roof framing
- oculus skylight design