So now that we have some ideas as to the etiquette involved, lets look at some simple math ideas to make the calculation simple but effective.
Rule of thumb - standard service - 15%. The most commonly used shortcut to 15% is 10% add a half. This is an easy calculation. Consider a bill for 47.31. First impressions show us 10% is 4.70 and a half of this amount is 2.35 so a tip of 7.00 is reasonable. This is a simplification as we can do the exact math - 4.70 add 2.35 is 7.05 but we are looking for an easy method not an exacting science. Another sound strategy is to work from the highest place value, in other words, if the bill is in the 50's then the tip should be in the 7.50 range. If the bill is 124.00, the logic follows that 12 add 6 =18 so a total of 124 add 18 or 142 is reasonable.
Another very sound strategy is to work from the sales tax. Look at your sales tax rates and devise a strategy based on the amount. In New York city, the tax on a meal is 8.75% so you can just double the amount of tax and your service provider is happy.
There are also some fun and unique answers to the question of how to do the math without straining yourself. Consider the following examples that people have provided:
Great service - bill times 10%, then doubled.
Less then great service - bill times 10%.
For a bill under $50:
Great service - bill times 10% then doubled - you will be over 15 and the appreciation should be noticed.
Good service- somewhere in between great and less then good. Add a little to less then good and you will be safe.
Less then good service - bill times 10% - the message will be conveyed but you are smart enough to realize that it may not be their fault alone.
For a bill over $50:
Make sure you start your calculations based on the pre tax amount of your bill.
Great service - 10% of the bill - doubled - round down.
Less then great -10% round down.
With the exception of those bills where the tip is already included, tipping and how to figure out the tip is a very individualized experience. Estimation and rounding is something I do all the time for tipping as I am not going to worry about a few extra cents here and there. And 'tip-ically' I round up as it's a rare event when I don't feel like being generous when I'm out for a meal.