Sum Range Based on Values in another Column

I've got a table with several hundred rows each representing a different entry however several rows will share the same value in one particular column.

I'm trying to create a column (Column C) where the values equal the sum of all values in Column B for which the values in Column A are equal. In other words, I'm trying to define the range of a SUM Function as "all cells in a column where the cells in another column are equal"

chart 1.jpg

Any ideas on how I can approach this?

Thanks.