overview

When data is compiled for a report or PowerPoint presentation rounding summations in Excel is a frequent problem. It is often desirable but difficult to achieve that rounded totals match the total of the rounded addends.

Let's look at a simple example and a more complex example with row and column sums:

Simple example 1.5 + 2.6 + 3.6 = 7.7

Complex example         Total:   4.3 15.3 21.4 41.0   10.5 7.6 3.7 21.8   17.5 18.3 19.5 55.3   11.5 17.4 20.9 49.8 Total: 43.8 58.6 65.5 167.9

When rounding all numbers to the nearest integer, you get:

2 + 3 + 4 = 8	Total:   4 15 21 41   11 8 4 22   18 18 20 55   12 17 21 50 Total: 44 59 66 168
Totals that appear to be "miscalculated" are in bold.

For some, this is the most desirable outcome, because each number is as close to the unrounded number as possible. In the simple example the largest deviation is 0.5, from 1.5 to 2. You can achieve this result in Excel by using "Format Cell" on each value.

But some people object, because the arithmetic is not correct. They propose to add up the rounded values:

2 + 3 + 4 = 9	Total:   4 15 21 40   11 8 4 23   18 18 20 56   12 17 21 50 Total: 45 58 66 169
Totals that deviate from the original value by 1 or more are in bold.

You can do this in Excel by using =ROUND(x,0) on the addends. The problem is that now in the simple example the largest deviation, from 7.7 to 9, is 1.3, much larger than before.

Is there some middle ground between correct rounding and correct arithmetic? Yes, there is, because you can round as follows:

1 + 3 + 4 = 8	Total:   4 15 22 41   10 8 4 22   18 18 19 55   12 17 21 50 Total: 44 58 66 168
"Tuned" values are in bold.

The sum adds up and in the simple example the maximum deviation is now 0.5, from 1.5 to 1. Rounding in such a way is trivial in this case, but becomes very complicated if you sum over larger two- or even three-dimensional tables. This process is what think-cell round automates.

Using think-cell round, you can achieve consistently rounded totals with minimal "tuning": While most values are rounded to the nearest integer, a few values are rounded in the opposite direction, thus maintaining correct calculations without accumulating rounding error.

Since there are many possibilities to achieve correctly rounded totals by changing values, the software picks a solution that requires the minimum number of values changed and the minimum deviation from the precise values.