I assume that, in SR, both observers moving relative to each other calculate the same relative velocity (v). But I wonder how. If they use clocks and rods, I see two possible methods: (a) combination of the measurements of two frames and (b) only "home-made" measurements. In method (a), Mr A sees Miss B passing by rightwards in a 300,000 km long spacecraft as measured at rest in B's frame. The Front of B's ship passes by at T1 = 0 and the Back at T2 = 1.73205 s. Then if A knew that the relative velocity of B is 0.5c, he would multiply the length of B's spacecraft by sqrt(1-v2/c2), obtain 259,807 km and thus confirm that v is actually 0.5c. But he doesn't know that: v is precisely what he is looking for! In method (b), instead, A would have an assistant located 519,615 km away to the right and with whom he has synchronised clocks following Einstein's method. He would annotate the time when B passes by (T1) and his assistant would do the same T2. Let us imagine that the time interval is again 1.72305 s. So A would conclude that v is again 0.5c. But what if B does the same operation? I confess I get lost when I try to calculate this. Can anyone help? But another question: an alternative way to calculate velocities is measuring the Doppler frequency shift of an electromagnetic signal sent to the other frame and reflected back. The relativistic Doppler formula is frequency of reception = frequency of emission * (1-v/c)/(1+v/c). Sorry but I am so bad at algebra I do not manage to solve for v. What is the relative velocity formula based on frequency of reception versus frequency of emission? And are both parties supposed to get the same result by application of such formula? If so, has this been experimentally proved?