Embedded Post / Pole Depth for Lateral Load (IBC 1807.3)
How deep a post actually goes - the question every fence, sign, deck-rail, and flagpole install starts with.
Example
You enter
- Applied lateral force P (lb) 200
- Height of force above grade h (ft) 4
- Post/footing width b (ft; round dia or square diagonal) 0.5
- Lateral bearing (psf per ft depth, local code) 150
- Restraint at grade nonconstrained
- Isolated pole (1/2-in movement OK, 2x bearing) yes
You get
- Embedment (ft) 4.33332
- Embedment (in) 52
- S pressure (psf) 433.33
Details, formula, and sources
The IBC 1807.3 nonconstrained formula d = 0.5A(1 + sqrt(1 + 4.36h/A)) with the lateral bearing taken at one-third depth (implicit in d, solved iteratively), the constrained slab-at-grade closed form, and the 1806.3.4 isolated-pole 2x increase. A 6-ft fence post with 200 lb of wind at 4 ft sets 52 in deep; a slab at grade cuts it to 34 in. Enter the lateral bearing from your local code - no table shipped.
Nonconstrained (Eq. 18-1): d = 0.5 A (1 + sqrt(1 + 4.36 h/A)), A = 2.34 P/(S1 b), S1 at one-third the embedment (implicit in d, solved iteratively). Constrained (Eq. 18-2): d^2 = 4.25 P h/(S3 b), S3 at the full embedment. Isolated poles: 2x lateral bearing per 1806.3.4.
The IBC Section 1807.3 embedded posts and poles design equations and the 1806.3.4 isolated-pole increase, by name; the formula pair dates to the legacy UBC and is unchanged across the 2018-2024 IBC editions.
The IBC is viewable free through the ICC public-access portal (codes.iccsafe.org) and public code-hosting mirrors; 1807.3 is in every adopted edition.
Estimate. AHJ and licensed professional govern.
Field names used by the API: lateral_force_lb, force_height_ft, post_width_ft, lateral_bearing_psf_per_ft, constraint, isolated, embedment_ft, embedment_in, s_pressure_psf
- Implicit S1 the nonconstrained equation evaluates the lateral bearing at one-third the (unknown) embedment, so the tile solves it by bisection and the fuzzer verifies the root by back-substitutionIBC 1807.3.2.1
- Constrained restraint the closed-form case assumes a rigid floor or pavement restrains the pole at gradeIBC 1807.3.2.2
- Isolated-pole increase 2x tabulated lateral bearing where 1/2 in of grade-level motion is acceptableIBC 1806.3.4
- No code table the psf-per-ft lateral-bearing rate is a user input from the adopted code or geotech reportIBC Table 1806.2 (not reproduced)