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Calcimator

Timber Truss Design Calculator

King-post truss member forces, rafter sizing, and bottom chord tension from span, rise, and loading.

About this calculator

This calculator runs simple statics on a symmetric king-post truss to find the force in each member, then checks whether the rafter cross-section you entered can carry its share. Horizontal Thrust at the supports is w x L^2 / (4 x H), where H is Truss Rise -- thrust is inversely proportional to rise, so a steeper truss (taller peak) pushes outward with much less force than a shallow one carrying the identical span and load, which is exactly why traditional roof pitches trade height for less outward spread on the walls. Rafter Axial Force and Bottom Chord Tension are not two independent quantities from the same load path -- Bottom Chord Tension IS the horizontal component of Rafter Axial Force. The rafter carries R / sin(pitch angle) in pure compression (R = the vertical reaction = half the total truss load); resolve that same compression force into horizontal and vertical parts and the horizontal part is R / tan(pitch angle), which is exactly what closes horizontal equilibrium at the heel joint -- the bottom chord's tension exists specifically to cancel the rafter's outward push, so by construction it always equals the rafter's horizontal component, not a separately-derived number that merely happens to match.

Both depend only on Truss Span, Truss Rise, Total Roof Load, and Truss Spacing -- Rafter Width and Rafter Depth never change these force numbers, because member size doesn't affect the statics of a simple triangulated truss, only whether the chosen member can survive the force. That capacity check happens separately: Rafter Compression Capacity is rafter area (width x depth) times the species' compression strength, and Rafter Utilization Ratio compares the two. Wood Species only ever shows up on the capacity side (Rafter Compression Capacity, Min Bottom Chord Size, Min King Post Size) -- it has no effect on the truss's actual internal forces.

Inputs

ft
ft
psf
ft
in
in

Results

Rafter axial force

6,923 lbs

≈ 7 grand pianos

Bottom chord tension

5,760 lbs

≈ 5 grand pianos

King post tension3,840 lbs
Horizontal thrust5,760 lbs
Rafter compression capacity48,000 lbs
Rafter utilization ratio0.14
Min bottom chord size2.9 in
Min king post size2.4 in
Pitch angle33.7°
Pitch (x:12)8:12
Rafter length14.42 ft
Total load on truss7,680 lbs

Figures current as of 2018. Source: American Wood Council, National Design Specification (NDS) for Wood Construction, 2018 Edition, Supplement Table 4D (Reference Design Values for Visually Graded Timbers)

How to Use This Calculator
  1. Enter Truss span, Truss rise, and Total roof load.
  2. Set Truss spacing, Rafter width, and Rafter depth.
  3. Adjust Wood species as needed.
  4. Review Rafter axial force (lbs) and Bottom chord tension (lbs).
  5. Use King post tension (lbs) and Horizontal thrust (lbs) to inform your decision.

How the result changes with Truss span

Truss spanRafter axial forceBottom chord tension
122,400 lbs1,440 lbs
184,335 lbs3,240 lbs
3614,182 lbs12,960 lbs
6037,258 lbs36,000 lbs

What each input means

Truss span
Clear span of the truss from support to support.
Truss rise
Vertical height from the bottom chord to the peak.
Total roof load
Combined dead + live + snow load on the roof (psf of horizontal projection).
Truss spacing
On-center spacing between trusses.
Rafter width
Width of the rafter timber cross-section.
Rafter depth
Depth of the rafter timber cross-section.
Wood species
0 = Douglas Fir-Larch, 1 = Southern Pine.

What each result means

Rafter axial force
Compression force in each rafter.
Bottom chord tension
Tension force in the bottom chord (tie beam).
King post tension
Tension force in the vertical king post.
Horizontal thrust
Outward thrust at each support.
Rafter compression capacity
Axial compression capacity of the chosen rafter section.
Rafter utilization ratio
Rafter force / capacity. Must be ≤ 1.0.
Min bottom chord size
Minimum square member size for the bottom chord (tension).
Min king post size
Minimum square member size for the king post (tension).
Pitch angle
Roof pitch angle from horizontal.
Pitch (x:12)
Roof pitch expressed as rise per 12 inches of run.
Rafter length
Length of each rafter from plate to ridge.
Total load on truss
Total gravity load carried by this truss.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Truss span = 24, Truss rise = 8, Total roof load = 40, Truss spacing = 8 = 7 input(s) provided
  2. Calculate Rafter axial force
    6923 = 6923
  3. Calculate Bottom chord tension
    5760 = 5760
  4. Calculate King post tension
    3840 = 3840
  5. Calculate Horizontal thrust
    Horizontal thrust = (wLbPerFt * spanFt * spanFt) / (4 * riseFt)
    5760 = 5760

Figures and sources

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does a steeper roof pitch (more rise) reduce Horizontal Thrust?

Horizontal Thrust is w x L^2 / (4 x H), so it is inversely proportional to Truss Rise -- doubling the rise for the same span and load halves the outward thrust at the supports. This is a real structural tradeoff traditional timber framers exploit: a steeper truss needs taller rafters and more lumber, but pushes far less outward force into the walls below, which is why very shallow trusses often need a stronger tie beam or steel tension rod instead of relying on the walls alone.

Does choosing a bigger rafter cross-section reduce the force it has to carry?

No. Rafter Axial Force, Bottom Chord Tension, Horizontal Thrust, and King Post Tension are all determined by the truss's geometry and applied load (span, rise, roof load, and truss spacing) through simple statics -- Rafter Width and Rafter Depth never appear in those force calculations. A bigger rafter only raises Rafter Compression Capacity, which lowers Rafter Utilization Ratio by giving the same force more cross-section to resist it with.

Is Bottom Chord Tension really the same force as the rafter's push, just measured differently?

Yes. The rafter carries a single compression force along its length. At the heel joint, that force resolves into a vertical part (balanced by the support reaction) and a horizontal part (the rafter's outward push). The bottom chord's whole structural job is to pull back with exactly enough tension to cancel that horizontal part -- so Bottom Chord Tension is not an independent calculation, it is the rafter's horizontal component by definition of horizontal equilibrium at that joint.

How does wood species affect the truss results?

Wood Species affects only the capacity side of the calculation -- Rafter Compression Capacity (via the species' Fc, compression parallel to grain), Min Bottom Chord Size, and Min King Post Size (via the species' Ft, tension parallel to grain), both taken from the American Wood Council's NDS-2018 reference design value tables for Douglas Fir-Larch and Southern Pine. It has zero effect on the actual internal forces (Rafter Axial Force, Bottom Chord Tension, Horizontal Thrust, King Post Tension), which are purely a function of the truss's geometry and load.

What happens to King Post Tension as the truss span increases?

King Post Tension equals half the total load carried by the truss, and total load is the per-foot roof load times the span -- so King Post Tension rises in direct proportion to Truss Span across its full range, with no plateau or reversal. A longer truss puts proportionally more tension pull on the vertical king post that carries the apex load down to the bottom chord.

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