Based on your facts of $10K in net income (if this is gross, keep in mind to deduct expenses from this number), the SE (social security and medicare) tax would be roughly 15.3% x 10,000 = 1,530. It's approximate because you get a deduction off the gross of 7.65%. Then you must calculate your income tax. If you're filing single, it appears you're in the 22% tax bracket and your total for tax on self-employed earnings would be $2,200 plus $1,530 = $3,730.
If you withhold extra tax from your W2 job, you would need to cover $3,730 /4 for the remaining months left in the year. That would be $932.50 in extra federal tax per month. You can see why it might make sense to mail in or electronically deposit one or two ES payments.
The IRS has some form 2210 penalty avoidance safe harbors. If you pay in at least 100% of the prior year's tax liability (110% if you make over $150K), or 90% of your current year liability, you will not owe a penalty. This is what form 2210 is actual for - to calculate any penalty.
Other factors can come in to play such as deductions from your self employment income, tax credits or other passive income or if you're filing married join. However, it would be advised to make the remaining ES payments for September and January of 2025. You may also need to pay state estimates. Some states penalize you for not paying quarterly just like the IRS and some states do not. You will need to check with the revenue department of your state.
Cheers
