Footing Bearing Pressure Calculator (Eccentric Load, Middle Third Rule)
Largest and smallest pressure under a rectangular footing carrying a vertical load and a moment, the eccentricity, how much of the base stays in contact, and the area for a pressure you choose.
Results
The dashed line marks the value you entered.
What this tool does
A moment on a footing is the same as moving the load off-centre by e = M ÷ N. As long as the load stays within the middle third (e ≤ B/6) the whole base is pressed on the soil and the pressure varies linearly, N/(BL) × (1 ± 6e/B). Beyond the middle third the soil cannot pull the edge down, so that edge lifts off and the peak pressure rises quickly — the chart shows the take-off. The answer is the pressure on the soil only: comparing it with the allowable bearing capacity and designing the footing itself belong to the geotechnical and structural engineer.
Formula
e = M ÷ N · q = N ÷ (B L) × (1 ± 6e ÷ B) when e ≤ B ÷ 6 · q_max = 2N ÷ [3 L (B ÷ 2 − e)] when e > B ÷ 6 (the base partly lifts off)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
n | Vertical load including the footing's own weight | kN |
m | Moment about the axis across the width B | kN·m |
b | Width B of the footing (in the direction of the moment) | m |
l | Length L of the footing | m |
qt | Soil pressure you want to design for | kPa |
QX | Largest pressure under the footing | kPa |
QN | Smallest pressure under the footing | kPa |
QA | Average pressure (load ÷ area) | kPa |
EC | Eccentricity of the load | m |
CS | Share of the base in contact with the soil | % |
ST | Where the load falls | — |
AR | Footing area for that uniform pressure | m² |
Worked example
- Vertical load including the footing's own weight600 kN
- Moment about the axis across the width B90 kN·m
- Width B of the footing (in the direction of the moment)2 m
- Length L of the footing2.5 m
- Soil pressure you want to design for150 kPa
- Largest pressure under the footing174.0 kPa
- Smallest pressure under the footing66.0 kPa
- Average pressure (load ÷ area)120.0 kPa
- Eccentricity of the load0.150 m
- Share of the base in contact with the soil100 %
- Where the load fallsIn the middle third — the whole base is pressed down
- Footing area for that uniform pressure4.00 m²
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.