You can use jmeter, apache bench, siege to load test your website.
Try increasing the load on your server with these tools. And find the maximum number of clients that your application can handle. Then increase more load to see how more it can take before it breaks.
Recently I did some load testing on a streaming server with flazr. Server were working fine till 400
concurrent connection. After 400
it starts to become slow and when its 450
it breaks. So 400 was the maximum number of connection it supports. But if its near 450 I'll try to decrease load to save my server or increase the hardware capacity like RAM, CPU, NIC
Some links might be usefull
- Bench-marking site performance with apachebench
- Simple is Hard a siege is being used by Rasmus Lerdorf on a Talk
- SQA.SE answer on where can I find good jmeter tutorials