# Bearing Capacity Calculator

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

- Page: https://jianzhujisuan.com/en/bearing-capacity
- Category: Foundations (https://jianzhujisuan.com/en/c/foundations)
- Chinese version: https://jianzhujisuan.com/zh/bearing-capacity.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Friction angle φ 30 °, Cohesion c 0 kPa, Unit weight γ 18 kN/m³, Embedment depth Df 1.5 m, Footing width B 2 m, Factor of safety 3): **Allowable bearing pressure 300 kPa**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Friction angle φ | number | 30 | ° |  |
| Cohesion c | number | 0 | kPa |  |
| Unit weight γ | number | 18 | kN/m³ |  |
| Embedment depth Df | number | 1.5 | m |  |
| Footing width B | number | 2 | m |  |
| Factor of safety | number | 3 | — |  |

## Formula

- **Nq**: Nq = exp(π tanφ)·tan²(45+φ/2)
- **Nc**: Nc = (Nq − 1)/tanφ (5.14 when φ = 0)
- **Nγ**: Nγ = 2(Nq + 1) tanφ (Vesic)
- **Ultimate**: qu = c·Nc + γ·Df·Nq + 0.5·γ·B·Nγ
- **Allowable**: qa = qu / FS
- **Total load**: P = qa × B² (square footing)

## Worked example

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.

## Questions

### 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.

## Related tools

- [Pile Capacity Calculator](https://jianzhujisuan.com/en/pile-capacity): N value for sand, cu for clay: shaft and base worked separately, then divided by a factor of safety.
- [Retaining Wall Stability Calculator](https://jianzhujisuan.com/en/retaining-wall): Soil and surcharge produce moments at different heights; both factors of safety must pass.
- [Earth Pressure Calculator](https://jianzhujisuan.com/en/earth-pressure): All three coefficients at once; the gap between active and passive is where the money is.

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