Footing Bearing Capacity Calculator (Terzaghi): Ultimate and Allowable Bearing Pressure
A first estimate of the pressure a soil can carry under a footing.
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How this calculator works
Choose the footing shape and enter its width, the depth of its base, the cohesion and friction angle of the soil, the unit weight and the factor of safety.
The calculator finds the bearing capacity factors, the surcharge at the footing level, and the ultimate bearing pressure as the sum of the cohesion term, the depth term and the width term.
It then divides by the factor of safety for the allowable pressure and gives the allowable load on a metre of strip footing or on a pad.
Formulas used
- q_u = c N_c + q N_q + \tfrac12\gamma B N_\gamma
- N_q = e^{\pi\tan\phi}\tan^2(45^\circ + \phi/2)
- N_c = (N_q - 1)\cot\phi
- q_a = q_u / FS
Worked example
With the default numbers in the calculator above:
- Bearing capacity factors: Nq = 18.40, Nc = 30.14, Ngamma = 22.40
- Pressure of the soil at the level of the base of the footing (the surcharge): 18.00 kPa
- Ultimate bearing pressure (the three parts: cohesion, depth, and the width of the footing): 633.65 kPa
- Allowable bearing pressure: 211.22 kPa
- Allowable load on each metre length of strip footing: 316.83 kN per metre
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
Is this enough to design a footing?
No. It is a preliminary check. The design soil values come from a geotechnical report, and settlement often governs.
What are the three terms?
One for the soil cohesion, one for the weight of the soil above the base of the footing, and one for the weight of the soil under the footing, which grows with the width.
What factor of safety should I use?
About 3 on the ultimate pressure for a hand check. A limit state design uses a geotechnical reduction factor from AS 2159.
What happens with groundwater?
It reduces the effective unit weight of the soil and so reduces the bearing capacity a lot. This calculator does not include it.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Terzaghi, Theoretical Soil Mechanics; Das, Principles of Foundation Engineering; AS 2870 Residential slabs and footings; AS 2159 Piling.
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