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Bearing Capacity Calculator

The three bearing factors follow from the friction angle; divide the ultimate value by a factor of safety.

Also known as allowable bearing pressure · safe bearing capacity · soil bearing pressure

Quick answer

With the default inputs: Friction angle φ 30° · Cohesion c 0 kPa · Unit weight γ 18 kN/m³ etc.Allowable bearing pressure 300 kPa

Use your own dimensions ↓

Inputs

°
kPa
kN/m³

Result

Allowable bearing pressure
300kPa
Nc30.14
Nq18.40
N-gamma22.40
Cohesion term0.0kPa
Surcharge term496.8kPa
Width term403.2kPa
Ultimate capacity900kPa
Allowable load on footing1200kN
How this is worked out

The bearing factors are not a memorised table of integers, they are functions of the friction angle: Nq = exp(pi tan phi) x tan²(45 + phi/2), Nc = (Nq - 1)/tan phi, and N-gamma from Vesic, 2(Nq + 1) tan phi. A table is only valid at the angles printed on it, so interpolating between rows adds error that the formula avoids. The three terms mean different things: c Nc is cohesion and for saturated soft clay with phi near zero it is the entire capacity, giving qu = 5.14 cu, which is what governs in soft ground; gamma Df Nq is the surcharge from embedment, so deeper footings carry more; and 0.5 gamma B N-gamma is the width term, which is not truly linear because wide footings fail in a shallower mechanism than the formula assumes, so practice caps B (often at 3 m). Groundwater matters: below the water table use the submerged unit weight, roughly gamma minus 9.8 kN/m³, or you will over-predict capacity by 30% or more.

Next up: Pile Capacity Calculator · Retaining Wall Stability Calculator

Formula

NqNq = exp(π tanφ)·tan²(45+φ/2)
NcNc = (Nq − 1)/tanφ (5.14 when φ = 0)
NγNγ = 2(Nq + 1) tanφ (Vesic)
Ultimatequ = c·Nc + γ·Df·Nq + 0.5·γ·B·Nγ
Allowableqa = qu / FS
Total loadP = qa × B² (square footing)
φ = 30°, c = 0, γ = 18 kN/m³, 1.5 m embedment, 2 m wide footing, factor of safety 3: Nq = 18.40, Nc = 30.12, N-gamma = 22.39, giving 0, 496.7 and 403.1 kPa, 900 kPa ultimate and 300 kPa allowable — a 2×2 m footing carries 1200 kN.

Basis

FAQ

How do I calculate soil bearing capacity?
Work out Nc, Nq and N-gamma from the friction angle, put them into qu = c Nc + gamma Df Nq + 0.5 gamma B N-gamma, then divide by a factor of safety of 2 to 3. For example, phi 30 degrees, c zero, gamma 18, 1.5 m embedment and a 2 m footing give about 900 kPa ultimate and 300 kPa at FS 3. Note the formula is a plane-strain strip footing case; square and circular footings carry more, commonly taken as 1.3 times.
What if the water table is high?
Switch every term to the effective unit weight. Below the water table use gamma-prime, gamma-sat minus 9.8, roughly 45% of the dry value. For sand at 18 kN/m³ with the water table at base level, gamma-prime falls to 8.2 and the width term drops from 403 to 184 kPa, taking the allowable pressure from 300 to 227 kPa. That is why isolated footings settle after a pit floods — the soil did not change, its effective stress did. Upward seepage reduces effective stress further and can reach a quick condition.

What to calculate next

These jobs are done back to back on site — follow the steps to work through the whole sequence.

Foundations: when bearing capacity is not enoughStep 1 of 4

  1. 1Bearing Capacity Calculator
  2. 2Pile Capacity Calculator
  3. 3Pile Cap Calculator
  4. 4Bored Pile Concrete and Rebar Calculator

Cite this page

Use this format in reports, method statements or coursework. The link is permanent.

Building Calculator. Bearing Capacity Calculator. 2026-10-25. https://jianzhujisuan.com/en/bearing-capacity

Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.