The calculator needs the width as it affects the impedance. Therefore you should not change the width of the track mid-way if you want the impedance to be continuous.
Any discontinuity will cause reflections. Every time you change the width, a discontinuity is created, unless you change something else too, to compensate for the change.
Other important factor is that the reference plane (often GND) needs to be continuous in geometry too. You can't for example cut the plane underneath the track without affecting the impedance.
So the answer is you need to calculate the impedance for each width along the track.
Also, widths below 0.1 mm become trickier to manufacture, check with your circuit board manufacturer what the design rules should be.