Web app pricing in EUR or USD?

You should have prices in EUR and US. Some payment processors have mechanisms to auto-detect the visitor country and show the prices in appropriate currency. Another option is to have drop down selection to choose the currency and recalculate the prices.

Charge in US $, and also have a Price in € and £ if appropriate.

If you don't have a dollar price directly you will have purchase resistance, just as in the UK you have resistance for a non Sterling price.

How much resistance will depend on the demographic and target customers.

If you want to smooth out daily currency fluctuations you can always assess every month or something and come up with a new "nice" price $8.99 $9.99 etc.

If most of your market is US based and you're in the EU you're going to have to be subject to exchange rate fluctuations to some extent - if you're charging a monthly fee it will seem strange to many customers if that price changes every month.

You say "I don't want my income to depend on the exchange rate this much". So you want your customers to take the risk? You can want that but I promise you Americans will not sign up for a recurring fee in a currency other than dollars. So the bottom line is it doesn't matter what you want, what matters is what the market will tolerate. If you expect 70% of your business to come from the US, you will be putting 70% of your business at risk to not quote prices in USD.

You should geo-locate so as to not show both (ie if from non-EU address, show in $), and have some sort of pricing engine that takes the fluctuations over time but only adjusts in normal increments so as to not look weird.

I agree with Ross that you should offer prices in both Euro and USD. US customers will most likely not sign up for a subscription fee in a currency other than dollars so, no matter what, if you expect 70-80% of your customers to be from the US I would definitely recommend putting their "comfort" first.

With an online accounting software like E-conomic, you can easily invoice your customers in different currencies depending on their needs. Exchange rates are updated in E-conomic daily, or you can set your own fixed exchange rates if you would like. You can find out more on our website, or by giving us a call.

No matter what you choose, good luck with your new venture!

Just update the dollar prices manually on a regular basis if that is possible. It is at least better than charging americans in Euros. Ross's answer, is of course the more advanced answer.