Footing Soil Bearing Pressure Calculator

How is the bearing pressure under a footing calculated?

A footing spreads the load above it onto the ground. If the load acts through the centre of the footing the pressure is uniform: q = N / (B × L). When a moment acts as well, the pressure rises at one edge and falls at the other: q = N / A ± M / W. For a rectangular base W = L × B² / 6, so the same relation reads q = N / (B × L) × (1 ± 6 × e / B), where e = M / N is the eccentricity.

The kern rule: e ≤ B / 6

As long as the eccentricity stays within B / 6, the whole base is in compression. This zone is called the kern, or the middle third. At e = B / 6 the pressure at one edge drops to zero. Beyond that the formula gives negative pressure, but soil cannot carry tension: part of the base lifts off.

The distribution then becomes triangular. The length in compression is x = 3 × (B / 2 − e) and the maximum pressure is q_max = 2 × N / (L × x). Pressure rises quickly once the resultant leaves the kern.

Example

A 2 m × 2 m footing carries 600 kN vertical load and a moment of 100 kN·m. The average pressure is 600 / 4 = 150 kPa and the moment adds 100 / (2 × 2² / 6) = 75 kPa. The maximum pressure is 225 kPa and the minimum 75 kPa. The eccentricity is 0.167 m against a kern limit of 0.333 m, so the whole base is in compression. With an allowable bearing pressure of 250 kPa the utilisation is 90 percent.

Bending in two directions

With moments in both directions the corner pressures are q = N / A × (1 ± 6 × e_B / B ± 6 × e_L / L). For the whole base to stay in compression, 6 × e_B / B + 6 × e_L / L must not exceed 1.

Limits

The tool calculates the pressure, not how much the ground can carry. The allowable pressure comes from the ground investigation and should already account for settlement. Remember to add the weight of the footing and the fill above it. For seismic design and for standards based on limit states the form of the check is different.