Formulas for Solving Word Problems

Clarity is the first rule of persuasion. If our customers don’t understand what we’re saying, they’re not going to reach for their wallets and offer us wads of cash. When people are confused, they slow down the buying process or shut it off completely. So it’s in our best interests to make sure our message is easy to understand. That’s our topic this time.

I was working with a group of engineers recently and mentioned that many editors use mathematical formulas to determine if a piece of text is readable. Their faces lit up like children who just saw grandma and grandpa pull up in a car full of presents.

“Formulas?” they asked. “There are formulas to show us how to write better? Why didn’t anyone tell us this before? We understand formulas.”

So we spent the next half hour looking at readability formulas, why they work, and how they can serve as a rough but reliable guide to the clarity of your writing. I honestly believe those engineers will now write better, because they have a tool to help them measure how well they’re doing.

Most readability formulas (and there are lots of them) measure how long your sentences are and how many big words you use. The underlying assumption is that long sentences and big words are harder to decode. Obviously, long words aren’t always hard to understand. And long sentences aren’t always difficult to read. There are exceptions. However, as a rough guideline, these underlying assumptions work pretty well.

The easiest way to calculate readability is to let your computer do it for you. There are two other formulas that are simple enough you can do the calculations in your head.

Measuring Readability with Your Word Processor

If you use Microsoft Word, open the “Tools: Options: Spelling and Grammar” box and select “Show Readability Statistics.” Now the word processor will calculate your readability each time you run a spelling check. If you want to check the readability on just a portion of a document, simply highlight the portion you want to check and click on the spell check icon. When it asks if you want to check the rest of the document, select “No.”

Microsoft Word presents your readability in a chart titled “Readability Statistics” that gives you lots of useful information. (WordPerfect users have a similar tool that also yields a Flesch-Kincaid Grade Level index.)

There’s a lot of useful information here. I can see that my average sentence length is about right (around 15 to 17 words is a good average sentence length for adult readers), and I see that I’ve completely avoided passive voice constructions. But what about the Flesch Reading Ease and Flesch-Kincaid Grade Level numbers? Are they good or bad?

The Reading Ease score is based on a standard of 100. The higher the number, the easier the writing is to understand. In business writing, which includes proposals, of course, a good score would be somewhere between 50 and 70. Based on that score, my paragraph is all right, but it could be simpler.

The Flesch-Kincaid Grade Level measurement correlates the complexity of the writing with the equivalent U.S. grade level of education the reader needs to read the particular passage easily. (Note that this is strictly a measurement of the complexity of the writing. It does not mean the content is appropriate for someone at that level. Readability and content are different issues.)

What is the right level for your proposal? For your executive summary, aim for a grade level equivalent of 10 or less. That’s approximately the level of front page articles in the Wall Street Journal and the New York Times, which are clearly intended for well educated adults. Other parts of the proposal could creep a little higher than 10, but 12 is the danger line. If the grade level is higher than 12, you must simplify the writing. Unfortunately, I’ve seen executive summaries that had readability scores above 20!

Sometimes you can’t use the word processor to calculate readability. Maybe you have hard copy only, or maybe the text is stored in Adobe Acrobat. Retyping an entire passage just to measure its readability is not a task most of us would gladly undertake. The good news is that you can still calculate readability easily by using either of two simple techniques: Gunning’s Fog Index or the SMOG Index.

Gunning's Fog Index

Robert Gunning first published his measure of readability in 1952. Half a century later, people still produce “foggy” prose, so his tool is still relevant. To calculate the Fog Index, follow these three steps:

1. Choose a passage of about 100 words and determine the average sentence length for that passage. (You just divide the number of sentences into the total number of words.)

2. In the same passage, count the number of big words—which, by definition, means words with three syllables or more. Do not include proper nouns (like Cincinnati), words that are combinations of short, easy words (compound words like bookkeeper and understand), or verb forms that acquire three syllables by the addition of -ed, or -es or -ing (like created, trespasses, traveling).

3. Add together the average sentence length and the number of big words. Then, to determine the Fog Index, multiply this sum by .4. This will produce a number that is a grade level equivalent, just as you got from the Flesch-Kincaid index.

The Smog Index

Like the Fog Index, the Smog Index measures the murkiness inherent in a piece of writing. It uses a slightly different method to arrive at the final answer, which is again a school-grade level that indicates the relative difficulty or ease of reading the given passage.

To use the Smog Index, count the number of big words (same definition applies) in a passage of 30 consecutive sentences. Then find the square root of that number. Add 3 and you’ll have a grade level equivalent.

I know these formulas probably sound goofy to you if you’ve never heard or them or tried them before. But if you try them a couple of times, you’ll see that they’re both easy and helpful.

Another way to improve the readability of your writing, of course, is to hire people who can write clearly to do it for you. That’s where the Sant Corporation can help. We have writers trained in persuasive communication principles who know how to produce clear, simple prose for your proposals and presentations.