\[{\text{actual raise = }\frac{\text{new salary}}{\text{old salary * (1 + inflation rate)}}} - 1\]

Where does this come from? It's maybe easiest to think of this in terms of units. Say you make $50,000 now, and you made $40,000 last year. You make 20% more right? Not exactly. What the $ there really represents is some purchasing power. Inflation is a drop in purchasing power, so what you really need to do is convert the $ before and after to the same unit. To determine the value of $ in the current year in terms of the $ in the previous year, you just divide it by 1 + inflation rate. That gives you the equation above.

Plugging in the numbers in the initial question then, the actual raise is:

\[{\frac{\text{new salary}}{\text{old salary * (1 + inflation rate)}}} - 1\]

\[{\frac{\text{old salary * (1 + 0.10)}}{\text{old salary * (1 + 0.06)}}} - 1\]

Which is just 0.038, so the actual raise is 3.8%.

It is very important to understand your raise in terms of local inflation. If you get a 5% raise but your area gets 10% more expensive, you actually got a paycut (4.5% paycut given those numbers).