Bearing Capacity Calculator for Shallow Foundations

This bearing capacity calculator works out the ultimate bearing capacity q_ult and the allowable bearing pressure for strip, square, rectangular and circular footings. It uses Meyerhof (1963), Vesić/Hansen or EN 1997-1 Annex D, drained or undrained.

It also allows for a water table at any depth. The default 2 m square footing at 1.2 m in sand (φ’ = 30°) gives qult = 975.1 kPa by Meyerhof and 325.0 kPa allowable at FS 3.

How to use it

1. Choose the Method and Footing shape.
2. Enter Width B (or diameter), Founding depth Df and, for a rectangle, Length L (the longer side).
3. Enter Cohesion c’ and Friction angle φ’, or Undrained shear strength cu for the undrained option.
4. Enter Soil unit weight γ (above water table), Saturated unit weight γsat and Depth to water table (blank if deep) from ground level.
5. Set the Factor of safety and read the results.

Factor equations for each method

Drained options: q_ult = c’N_cs_cd_c + q’N_qs_qd_q + 0.5γ’BN_γs_γd_γ. All three use N_q = e^{π tan φ’}tan²(45° + φ’/2) and N_c = (N_q − 1)cot φ’ (π + 2 at φ’ = 0). B/L = 0 for a strip, 1 for a square or circle; K_p = tan²(45° + φ’/2).

Method	Nγ	Shape factors	Depth factors
Meyerhof (1963)	(Nq − 1)tan(1.4φ’)	sc = 1 + 0.2KpB/L; sq = sγ = 1 + 0.1KpB/L	dc = 1 + 0.2√KpDf/B; dq = dγ = 1 + 0.1√KpDf/B
Vesić/Hansen	2(Nq + 1)tan φ’	sc = 1 + (B/L)(Nq/Nc); sq = 1 + (B/L)tan φ’; sγ = 1 − 0.4B/L	dq = 1 + 2tan φ'(1 − sin φ’)²k; dγ = 1; dc = dq − (1 − dq)/(Nctan φ’), or 1 + 0.4k at φ’ = 0
Annex D, drained	2(Nq − 1)tan φ’	sq = 1 + (B/L)sin φ’; sγ = 1 − 0.3B/L; sc = (sqNq − 1)/(Nq − 1)	None

Meyerhof’s s_q, s_γ, d_q and d_γ are 1.0 at φ’ = 0 and rise linearly to the full expressions above at φ’ = 10°; from 10° up the full values apply. In Vesić/Hansen, k = D_f/B up to 1 and arctan(D_f/B) beyond; the N_γ is Vesić’s, not Hansen’s 1.5(N_q − 1)tan φ’.

Undrained Annex D: q_ult = (π + 2)c_us_c + q, with s_c = 1 + 0.2B/L. Here q is the total overburden stress at founding level, using γ above the water table and γ_sat below it.

Water above the base gives q’ = γD_w + (γ_sat − 9.81)(D_f − D_w) and γ’ = γ_sat − 9.81; γ’ is interpolated for water up to B below the base.

Worked example: 2 m square footing, Meyerhof

B = 2 m, D_f = 1.2 m, c’ = 0, φ’ = 30°, γ = 18 kN/m³, no water table, FS = 3.

1. q’ = 18 × 1.2 = 21.60 kPa; K_p = tan²60° = 3.000
2. N_q = e^{π tan 30°} × 3.000 = 18.40; N_c = 17.40/tan 30° = 30.14; N_γ = 17.40 × tan 42° = 15.67
3. s_c = 1 + 0.2 × 3 = 1.600; s_q = s_γ = 1.300. With D_f/B = 0.6, d_c = 1.208 and d_q = d_γ = 1.104
4. q_ult = 21.60 × 18.40 × 1.300 × 1.104 + 0.5 × 18 × 2 × 15.67 × 1.300 × 1.104 = 570.4 + 404.7 = 975.1 kPa
5. Allowable: 975.1/3 = 325.0 kPa gross; (975.1 − 21.6)/3 = 317.8 kPa net
6. Allowable net column load = 317.8 × 2 × 2 = 1,271 kN

Vesić/Hansen gives 977.5 kPa and Annex D drained 849.4 kPa for the same inputs.

Limits of this calculator

• Settlement often governs, so check it separately.
• Loads are vertical and central on level ground, with general shear failure and no inclination, tilt or slope factors.
• Results are sensitive to φ’: at 35° the example’s q_ult is 2,119.1 kPa.
• The Annex D options still use a global FS; Eurocode 7 design needs your National Annex partial factors.

Questions people ask

What is the difference between net and gross allowable bearing capacity?

Gross allowable pressure is qult/FS, while net allowable is (qult − q’)/FS, which removes the overburden already at founding level. For the default footing they are 325.0 and 317.8 kPa.

What factor of safety is used for bearing capacity?

The calculator defaults to FS = 3 on qult. Use the value from your code or geotechnical report; Eurocode 7 uses partial factors instead.

How does the water table affect bearing capacity?

Submerged soil weighs γsat − 9.81 kN/m³, so a high water table cuts both the overburden and the Nγ term. For the default footing, water at founding level reduces qult from 975.1 to 799.5 kPa.

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• Rebar Weight: Weight of reinforcing steel in kg, tonnes or lb, metric and US bars.

Results are for estimating, checking and learning. Design work should be checked against the current code and your project specification, and signed off by a qualified engineer. See all 20 engineering calculators.