Well, it's a little more complex than just the number of characters in a noun compared to English, for instance, Japanese also has a different grammatical structure compared to English, so certain sentences would use MORE words in Japanese, and others would use LESS words. I don't really know Japanese, so please forgive me for using Korean as an example.
In Korean, a sentence is often shorter than an English sentence, due mainly to the fact that they are cut short by using context to fill in the missing words. For instance, saying "I love you" could be as short as 사랑이 ("sarangi", simply the verb "love"), or as long as the fully qualified sentence 저는 당신이 살앙이예요 (I [topic] you [object] love [verb + polite modifier]. In a text how it is written depends on context, which is usually set by earlier sentences in the paragraph.
Anyway, having an algorithm to actually KNOW this kind of thing would be very difficult, so you're probably much better off, just using statistics. What you should do is use random samples where the known Japanese texts, and English texts have the same meaning. The larger the sample (and the more random it is) the better... though if they are truly random, it won't make much difference how many you have past a few hundred.
Now, another thing is this ratio would change completely on the type of text being translated. For instance, highly technical document is quite likely to have a much higher Japanese/English length ratio than a soppy novel.
As for simply using your dictionary of word to word translations - that probably won't work to well (and is probably wrong). The same word does not translate to the same word every time in a different language (although much more likely to happen in technical discussions). For instance, the word beautiful. There is not only more than one word I could assign it to in Korean (i.e. there is a choice), but sometimes I lose that choice, as in the sentence (that food is beautiful), where I don't mean the food looks good. I mean it tastes good, and my option of translations for that word changes. And this is a VERY common circumstance.
Another big problem is optimal translation. Something that human's are really bad at, and something that computers are much much worse at. Whenever I've proofread a document translated from another text to English, I can always see various ways to cut it much much shorter.
So although, with statistics, you would be able to work out a pretty good average ratio in length between translations, this will be far different than it would be were all translations to be optimal.