Proportionally distributing attributes from one layer to another

I have some experience with ArcMap but only on a relatively superficial level. Right now, I'm trying to perform an action and I'm not sure to get it done. I've tried Googling and documentation but I'm just not exactly sure what function I'm looking for.

I have two layers. One is a grid of equally sized squares, the other is a layer with administrative units. These administrative units all have a value for a particular feature (say no. toilets per household).

Now, I would like to record this feature for the grid layer. When a cell is completely within one of the administrative units, this is straightforward. However, I am not sure how to perform this action when multiple administrative units are contained in a grid cell.

I would like to perform an action that proportionally 'transfers' these values from the administrative units to the grid cells. E.g., say 60% of a grid cell is in administrative unit A, and 40% is in B, with A having 0.5 toilets per household and B having 0.6. I would then like this value for the grid cell to be 60%*0.5 + 40%*0.6 (0.54).

How would I be able to do this?

I have tried spatial join but this does not seem to be able to deal with the proportional nature of my problem.

• Only Intersect or Union can determine fractions for pro-rating attributes. – Vince Dec 11 '19 at 19:43
• ArcGIS can calculate fractions in the Intersect and Union tools? That's useful. I wish QGIS had that in a built-in tool. I'm sick of calculating `new area divided by original area`. – csk Dec 11 '19 at 19:50
• @Vince would you be able to elaborate? I'm not sure how to do that with the standard Intersect tool. – J. Collins Dec 11 '19 at 19:55
• Intersect (vice spatial join, which doesn't split the feature) is only the first step. Then you need to join back to the whole by the preserved key field, to compute the fraction (lengh or area) by which to pro-rate the intersected features. – Vince Dec 11 '19 at 20:02
• Alright, I'm gonna give it a try. Thanks. – J. Collins Dec 11 '19 at 20:09