The name of current kalpa is Swetha Varaha Kalpa.
How many years has been completed till now from the starting point of the Swetha Varaha Kalpa?
Taking the units of time from this link, Let's try to calculate it.
Each Kalp has 14 Manwantara and 15 SandhiKal, and SandhiKal is only equal to a Satyug. (The other answer here says there are 72 ChaturYug in one Manwantara, but as per this link let's keep it to 71, it could be actually 72, let me know if I am mistaken.)
We are in 7th Manwantara, it means 7 SandhiKal (1,728,000 each) and 6 Manwantara(306,720,000 each) has passed
7 * 1,728,000 (SandhiKal) = 12,096,000
6 * 306,720,000 (Manwantara) = 1,840,320,000
And we are in 28th ChaturYug, it means 27 ChaturYug (4,320,000) already passed
27 * 4,320,000 = 116,640,000
and We are living in Kalyug, so other 3 are passed it gives
1,728,000 + 1,296,000, + 864,000 = 3,888,000
Now, Kalyug started on 18 February 3102 BCE, that gives
3102 + 2019 = 5121
Adding all the above we get
12,096,000 + 1,840,320,000 + 116,640,000 + 3,888,000 + 5121 = 1,972,949,121 years passed in this Kalp.
Let me know if I missed something, and thanks for the question, I hadn't done so much maths for a long while.