Selecting the electric motor and battery when building your own electric car can be quite a challenge. There are a few approaches here that can be followed in this post I’ll just touch on the easiest of all, a good look at the alternatives and some educated guessing. This approach is to see what the others are doing and check what power the engines are that are used in similar vehicles. If you plan to convert a sedan like vehicle that is roughly the same size/weight as a Nissan Leaf, check the power that those engines are specified for. (the Nissan Leaf has a motor which is rated at 80kW btw, also check Wikipedia).
The Nissan Leaf, you can learn a lot from the current EVs already out there.
The idea behind it is simple, they did the math, and it works good (they are selling the product). If you want something that can go quicker or accelerate quicker, you’ll want to look for a little bigger engine, but you get a feel of the industry at least and know what you should be aiming for.
Always make sure that the vehicle you are working on and the vehicle you are looking at for the engine specification are reasonably the same. In other words, don’t look at the Tesla Roadster if you want to convert a heavy SUV, the weights are far off, but also the aerodynamics of the two are not comparable.
For the battery a similar approach is viable, check what comparable vehicles have for the battery capacity (the kWh figure!) and ensure that the battery/motor are compatible. An electric motor that runs on 48V will be no good using a single 12V battery. You can check again what the size of for example the Nissan Leaf is (24kWh) and use it as a guideline. The Nissan Leaf can travel around 100 miles / 160 km. If you have a comparable vehicle as the Leaf and put in a 12 kWh battery pack, you will likely get around half the range of the Leaf. This is not entirely a linear scale, but ok for some educated guessing as long as you don’t use a factor 10 bigger or smaller batteries.
Another nice guideline that might help is that the average passenger cars use between 20-30 kWh per 100 miles / 160 km. If you have a relatively light vehicle, you’re bound to be on the low end, if you have a heavier, you’re on the high end of this range (or even higher if it is a really heavy vehicle).
You can save a lot of fuel by converting this one to electric, just don't put in a Leaf-like drive train.
Assume you have a light vehicle, and want to be able to drive 300 miles with it. Assuming a 20 kWh consumption per 100 miles / 160 km, you would need a battery that supplies 60 kWh. Batteries are preferably not fully discharged, and are operated generally in a safe range, so it is more likely you will need 70-80 kWh pack to ensure you have 60 kWh available to drive. The problem that arises is that with battery packs of this size, the weight plays a big factor. If you have to add a battery pack that weighs half that of the original light weight vehicle, your consumption will go up more. This makes for an iterative process where you have to balance the motor and the battery pack versus what you want and what vehicle you have.
Not an easy process and one that can be quite time consuming as well. Luckily there are various companies around, mostly US or Australia based, that offer so called electric car conversion kits. As the name implies, it allows you to convert your petrol vehicle to an electric one. There are even some that are tailored to specific models. The biggest advantage of this: you get a fully matching system that is suitable for your vehicle. Why do the guesswork if they found out and likely the hard way. They know what works and what not.