The formula
area = load ÷ allowable bearing pressure
Where it comes from
A footing is nothing more than a spread so the column load reaches enough ground for the ground to carry it. The arithmetic is a division, and what decides the size is a figure we do not calculate: the allowable bearing pressure of the soil, which runs from 0.5 kg/cm² in made ground to over 4 in rock. The self-weight of the footing also bears on the ground, so it is estimated first and checked afterwards against the real depth.
How to work it out by hand
- Convert the allowable pressure to kilonewtons per square metre: one kg/cm² is 98 kN/m²
- Divide the column load by that pressure
- Add around 10 % for the self-weight of the footing
- The square root of that area is the side if you make it square
- Check with the real depth that the pressure is still below the allowable value
What is worth knowing
Depth has a practical minimum of around forty centimetres, because below that there is no room to lap the reinforcement and anchor the column starter bars, and a footing that shallow works in punching shear rather than bending. The reinforcement figure is a typical rate and is there for pricing, not for detailing: the real bars depend on the projection and the cover. And if the utilisation comes out well below a hundred per cent the footing is oversized; if it comes out above, it does not work and has to grow.