summing a series of cells where one of the cells = zero

In a simple (shopping list like) spread sheet I want to calculate a total value.

so it might be:

a1*b1 = c1

a2*b2 = c2

a3*b3 = c3

total of c1+c2+c3 in c4

This works fine is there are entries in all of the a and b cells - giving a numeral in all of the c cells.

But if, for example, a1 is zero or if a1 has no entry, then it won't calculate c4.

I use in c1 =if(a1*b1>0,a1*b1,"") because I only want to see "non-blank" cells

I could use in c1 =if(a1*b1>0,a1*b1,0) but then i get a heap of "0" cells throughout the sheet

The above example is simplified.

Any help gratefully received!

Thanks

Bill