Flight Crew Instrument; Flight Crew Commercial
Flight Crew Last 90 Days 30; Flight Crew Total 2600; Flight Crew Type 550
Communication Breakdown; Time Pressure; Situational Awareness
Airspace Violation All Types; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert
Environment - Non Weather Related; Human Factors
I was instructed by the ZZZ1 Tower after taking off on Runway XR to follow another small aircraft who had taken off before me before turning right downwind to depart to the north east. I was expecting to get clearance through the [ZZZ] Class B because the Tower had indicated so. The aircraft I was following never turned crosswind; so I initiated my turn and was a little faster than normal climb because I was trying to stay below 1;800 feet which was the bottom of the Class B airspace straight ahead. In turning right to depart to the east; I clipped the corner of the Class B surrounding ZZZ2 just to the north of ZZZ1. The Tower asked if I was familiar with the airspace around ZZZ1 and I stated that I am and that I had clipped the corner of the Class B and was expediting turning south. I thought the bottom at that point was 1;800 feet and I remained below 1;800 feet before getting south of that corner; however; after landing at home ZZZ3; I checked my actual track and saw that at that point where I briefly went in to the Class B it exists from ground to 10;000 feet; not 1;800  feet to 10;0000 as I had thought. In this particular area the Class B just to the west of me showed 1;800 feet to 10;000 feet which is what I saw on my chart. Tower thanked me for getting out quickly and handed me off to ZZZ Departure who gave me an unrestricted climb to 10;500 feet; my filed encounter altitude. Departure never specifically cleared me through the Class B to the east which has a base of 4;800 feet and top of 10;000 feet; but they did give me an unrestricted climb to 10;500. It's possible that I was above 4;800 feet; on my climbout which also would have been flight in to the Class B without a specific clearance which I failed to ask for.I have flown down to ZZZ1 3 times in the past few months and because of the reduced traffic during COVID I've been cleared through the Class B and even offered it by ATC without asking; which is unusual. ATC is very pleasant in that area; but I thought I should report this to help others with this type of potential confusion. ZZZ1 gets a lot of local flights and the Tower issues quite a few follow another aircraft instructions as well as 'stay south of highway XXX that only locals would know; I presume to stay away from the nearby Class B airspace from the ground to 10;000 feet.
GA pilot reported a Class B airspace violation.