Coronal shocks are important structures, but there are no direct observations of them in solar and space physics. The strength of shocks plays a key role in shock-related phenomena, such as radio bursts and solar energetic particle (SEP) generation. This paper presents an improved method of calculating Alfven speed and shock strength near the Sun. This method is based on using as many observations as possible, rather than one-dimensional global models. Two events, a relatively slow CME on 2001 September 15 and a very fast CME on 2000 June 15, are selected to illustrate the calculation process. The calculation results suggest that the slow CME drove a strong shock, with Mach number of 3.43 - 4.18, while the fast CME drove a relatively weak shock, with Mach number of 1.90 - 3.21. This is consistent with the radio observations, which find a stronger and longer decameter-hectometric (DH) type II radio burst during the first event, and a short DH type II radio burst during the second event. In particular, the alculation results explain the observational fact that the slow CME produced a major solar energetic particle (SEP) event, while the fast CME did not. Through a comparison of the two events, the importance of shock strength in predicting SEP events is addressed.