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My current springs have a rate of 360lbf/in and unfitted 420cm in length. Fitted to the car they are 350cm in length. What lbf/in do i need so that the car sits 3" lower ?
I'm considering a spring at 413cm in length rated at 225lbf/in but not sure what the height difference will be ?
When installing lowering springs that reduce the ride height of a car by more than ~1 inch, you'll want to increase the spring rate to avoid bottoming out (body scraping the ground or shocks reaching maximum stroke). You'll also need to replace your shocks if you change the spring rate more than ~10%.
If you want to lower the car by using a lighter spring, you'll need to know the corner weights of the car, but for a rough estimation you can take the GVW (gross vehicle weight) and divide it by 4.
From the information you provided, your car has an approximate weight of 3200 lbs, so the weight on each spring is ~800 lbs (assuming 50/50 front/rear weight distribution) To lower the car by 3", you'd need a spring rate of 154 lb/in.
Given the calculated 3200lb GVW, a spring rate of 225 lb/in will cause the car to sit 1.3" lower than stock, but since the springs are (assuming you meant mm instead of cm) 7mm shorter (unloaded free length), the overall drop will be roughly 1.6".
Again, I advise against using lower rate springs to lower the car. Good lowering springs will be shorter in free length and higher in rate, so that the shocks do not bottom out when you go over bumps etc. I would search some internet forums for your specific car and ask around about lowering springs, in the US you can usually find a set for ~350USD.
Do NOT use lower rate springs to lower the car!!! You will be riding the bumpstops all the time! You want shorter springs, with adjustable perches (aka coil-over sleeves). This will allow you to adjust the ride height exactly at each corner of the car. You do not need to get threaded body shocks (aka 'real' coilovers), just the sleeves that go over your shocks/struts. Use a higher rate spring that is recommended for lowering your vehicle. It's hard to recommend a rate exactly without knowing your ride, because everyone's suspension curve is different. Most are non-linear.
