In the US I think you'll find that most of these "V" speeds are "defined," and not necessarily calculated. For what it's worth, here are a few of the "takeoff" V speed definitions:
Vmcg. (Minimum control speed on the ground): The minimum speed at which an aircraft is defined to be “controllable” (lateral excursion lower than 30 feet) with aerodynamic controls only after an engine failure on the ground.
Vef – (Engine failure speed): the speed that the critical engine is assumed to fail. It may not be less than Vmcg.
V1 (often referred to as “Decision Speed”): Must not be less than Vef plus the speed gained between when the engine failed and the pilot recognized the failure. This means that this speed is the minimum speed at which an engine failure may occur and the pilot may continue the takeoff. At the same time, V1 speed must not be greater than the speed at which a rejected takeoff can be initiated and stop the airplane within the calculated accelerate-stop distance.
Vmu (Minimum unstick speed): Minimum airspeed at which airplane can safely lift off ground and continue take-off. Because of the way this speed is determined, lift-off is not possible prior to reaching this speed.
Vr (Rotation speed): Must be greater than V1 and greater than 1.05 Vmca and may not be less than the speed that would allow reaching V2 before reaching a height of 35 feet above the takeoff surface. This speed is selected so that the rotation begins at Vr and provides that Vlo occurs at a speed greater than VMU The rotation is continued at approximately 3 degrees per second until reaching the desired pitch attitude.
Vlo (Lift-off speed): Must be greater than 1.1 Vmu with all engines, or 1.05 Vmu with engine out.
Vmca (Minimum control speed in the air): Minimum airspeed at which, when the critical engine is made inoperative, it is still possible to maintain control of the airplane and maintain stable, controlled flight. [The rudder is used to compensate for the yaw moment caused by thrust asymmetry. There is a minimum speed at which full rudder will be necessary, in order to fly a constant heading with level wings. To reduce sideslip, this speed can be reduced even more, if the aircraft is banked on the live engine’s side. The lower the speed, the greater the necessary bank angle. The speed that corresponds to a 5-degree bank angle is defined as Vmca.]
V2min (Minimum take-off safety speed): Must be greater than 1.1 Vmca and 1.2 Vs, the stalling speed in the take-off configuration.
V2 (Take-off safety speed): May not be less than V2min and may not be less than Vr plus the speed gained before reaching a height of 35 feet above the takeoff surface. [If one engine is lost before reaching V2, then the initial climb is flown at V2. If thrust is lost at a speed between V2 and V2+10, then the current speed is maintained, to ensure the most efficient climb speed. It is not necessary to increase pitch, in order to reduce the speed to V2, when a higher speed has already been reached.]
I think when you read through these definitions, you can see that V1 speed is selectable and may represent several different factors, depending on the airplane and the runway. For example, a very light airplane on a very long runway might combine to allow you to have a relatively low Vef – where you could experience an engine failure (as long as this speed is not less than Vmcg) and have enough runway to continue to accelerate with the remaining engine(s) and make a safe takeoff. At the same time, you might be able to accelerate to a relatively high Vef – where you could experience an engine failure, and have enough runway to bring the airplane to a safe stop within the confines of that runway. Here you would have two “selections” of V1, with different points along the runway and different values for the term.
AirRabbit