Count essentials, not your whole budget
An emergency fund pays for the months when income stops or a large bill arrives. In those months you cut back, so size the fund on essentials only: rent or EMI, food, utilities, insurance, transport, and minimum debt payments. Leave out holidays, eating out and new purchases.
How many months of cover you need
Three months suits a stable salaried job in a household with a second income. Six months is the usual default. Nine months or more makes sense for freelancers, business owners, single earners, and anyone in an industry where finding new work takes a while.
A worked example
Essentials of 2,200 a month with six months of cover give a target of 13,200. With 4,000 already saved, the gap is 9,200. Setting aside 500 a month closes it in 19 months. Raising that to 800 cuts the wait to 12 months.