Hi,
Both a good and tough question. As someone who has heard this question hundreds of time before (from startups that I worked with), I think that I can help:
There are 2 options / solutions to calculate the value/equity: the financial solution (cold numbers) one, and the psychological one.
From a financial aspect, you can calculate the current value of the business (if need be, I'm happy to explain how this is commonly done). This is the value/worth of your hard work over the last 2 years. Once you've added a number to it, you can now know (more or less) how much equity/shares your new partner 'should' get in return for his/her investment.
The problem with this option, is that we are not robots - we have feelings, egos and independent thoughts. This means that no matter how accurate your calculations might be, your partner might still value the business differently (if higher - then no problem. If less = arguments arise). This leads me to the second option: the psychological calculation.
You are taking on board a partner. Assuming you're not only bringing this person into the business for his/her investment, this means that you have reached the conclusion that you want this person with you, and/or or that you need them for their skills. If so, this means that your future partner has value - in addition to the money he/she is bringing in. In which case, the best option is to decide with yourself how much you are willing to give for this 'value'. Then, invite the person for coffee, and ask them how much they would expect in return: if they say a lower number than you thought of - great (you'll both be happy). If they ask for more than you thought, explain and pursued why you are offering that specific amount. There are numerous methods to reaching 'middle ground' - usually through means of vesting. For example: your partner would get X% equity, and every Y months/years they would get Z% more (alternatively he/she could get more only if they achieve certain milestones or goals).
2 last tips:
1. It is better having 50% (for example) of a bigger cake, than having 100% of no cake (or 70% of a much smaller cake).
2. whatever you do, make sure that you have a decent founders agreement. Fall outs between founders/business partners is one of the top 3 reasons that startups/businesses fail.
I am happy to prepare you for the meeting, help you analyze the percentage you should offer, and/or draft the founders agreement should you need one.
Best of luck.