King Post Truss Calculator

How This King Post Truss Calculator Works

Every king post truss is the same skeleton: five members and four joints. Two rafters climb from the heels to the apex, two bottom-chord halves run along the tie beam from heel to center, and the king post stands vertically between the apex and the center of the tie. The supports add three reactions — a pin at one heel and a roller at the other. That inventory is what makes this the simplest complete truss: the smallest member count that closes the load loop from ridge to wall and back. Every fancier truss you have ever seen — queen post, Howe, fink, scissor — is this skeleton with extra webs bolted on.

The calculator takes three inputs — span, rise at center, and an apex load P — and resolves everything with two closed-form relations. Geometry comes from Pythagoras: the top-chord length per side is √((span÷2)² + rise²), which for the default 16 ft × 4 ft model gives √(8² + 4²) = 8.944 ft. Forces come from joint equilibrium at the apex: each rafter absorbs P ÷ (2·sinθ) of compression, and the horizontal component each rafter delivers to the heel becomes P ÷ (2·tanθ) of tension in the bottom chord. The king post reads 0.000 kip under an apex-only load — section 2 below shows the load case that wakes it up.

Determinacy check, so you know the hand numbers are exact rather than iterative: for a planar truss, m + r = 2j, where m is members, r is reactions, and j is joints. Here m + r = 2j → 5 + 3 = 8 = 2 × 4. The equation closes perfectly, which means every force has exactly one value — no approximations hide in the table. The whole workflow fits in four steps:

1. 1Set span and rise. Pick the building span and the center rise in the quick calculator above, plus the apex load you want to trace.
2. 2Check the proportions. Read the verdict chip: a rise-to-span ratio between 1:4 and 1:3 is the classic band; below is shallow, above is steep.
3. 3Read the member forces. Chord lengths, slope, and the three force outputs update live — compression in red, tension in blue, the post at 0.000 kip.
4. 4Verify in the analyzer. Open a preloaded deep link and compare the solver’s member-force table, shown to three decimals, against the hand values on this page.

Because the model is statically determinate, the analyzer and the hand formulas must agree to the last decimal. If they ever diverge, the model — not the math — is wrong: usually a load placed on the wrong joint or a support set to pin-pin instead of pin-roller.

King Post Truss Design: Span and Rise Rules

King post truss design starts with one proportion: the rise-to-span ratio. The classic band runs from 1:4 to 1:3 — a 16 ft span wants a rise between 4 and 5.33 ft. Inside that band the rafter angle stays between roughly 27° and 37°, the closed-form forces stay moderate, and the profile looks like the gable people draw when they draw a house. Below 1:4 the chords flatten and forces climb toward −P/1 per rafter pair; above 1:3 forces ease but the gable grows tall enough that wind on the big face starts to dominate the conversation.

Span Table with Rise Proportions

Top-chord lengths are computed at the 1:4 anchor rise (12 ft → 6.708, 16 ft → 8.944, 20 ft → 11.180, 24 ft → 13.416). At the steeper 1:3 end the chords lengthen — for example, a 16 ft span at 5.33 ft rise has 9.613 ft rafters.

Reading the proportions like a designer

• ▸ Force per kip is scale-invariant at a fixed ratio: every 1:4 truss shows sinθ = 0.447, so each rafter carries −2.236 kip per 2 kip of apex load whether the span is 16 ft or 26 ft. Span changes the load, not the leverage.
• ▸ Steepening from 1:4 to 1:3 on the 16 ft model cuts rafter force from −2.236 to −1.803 kip and bottom-chord tension from +2.000 to +1.500 kip per 2 kip — a 19% discount bought with a taller gable.
• ▸ The tie beam is the span-limiter: with an apex-only load nothing supports it at midspan, so its unsupported length is the full span. That is why king post framing gets nervous past the mid-20s in feet.

📐Rafters meet the tie at every heel

Rafters meet the tie at every heelPhoto: Unsplash

Typical Member Starting Points

Published rule-of-thumb practice for light framing gives workable starting points, not final answers. Rafters for small spans commonly begin at 2×6 to 2×8 set at 24 in on center — the same spacing residential roof framing uses everywhere. The king post and the tie beam are often matched in section in light frames, with 4×6 or 4×8 stock doing double duty as tie and post; exposed timber-frame work steps up to heavier sections, where a 6×6 post under an 8×10 tie is a traditional pairing that keeps the joinery face wide enough for the pegs and housings.

Two adjustments move these starting points. First, load: snow country and heavy roof systems push every member up a size or shorten the spacing. Second, the hanging case from section 2 — if anything ever hangs from the bottom-center joint, the post works in tension and its connections (not just its section) become the design item. A tension splice in a 4×6 is a different conversation than a compression bearing.

Verifying the Numbers in the Free Analyzer

Hand formulas earn trust by surviving confrontation with a solver. The analyzer behind this site runs a full stiffness-method solution on any truss you draw, and the deep links on this page skip the drawing entirely — the model, supports, loads, and units rebuild from the link alone on any device. The check takes two minutes:

1. 1Open a deep link. Start with the apex-load model — 16 ft span, 4 ft rise, pin and roller supports, 2 kip down at the peak.
2. 2Read the member-force table. Every axial force shows to three decimals: −2.236 kip in each top chord, +2.000 kip in each bottom-chord half, 0.000 kip in the post.
3. 3Toggle the load. Delete the apex load and add the same 2 kip at the bottom-chord center joint — or open the bottom-load deep link. Watch the chords hold steady and the post jump to +2.000 kip.
4. 4Compare with the hand table. The two-load-case table above is the answer key. Any mismatch means the model changed, not the math — check load placement and supports first.

The units switch matters here too: flip the analyzer between ft and m and the geometry converts while the solution stays consistent, with forces reported in the matching unit system (kip or kN). A 2 kip apex load is about 8.9 kN, so the same 16 ft × 4 ft model in metric reads −9.95 kN in the rafters and +8.90 kN in the tie — the physics does not care which ruler you used.