You are in the right ballpark, but the tax rate will be 30% or more.
I would do it this way:
If you also have a regular job, we will assume that your W-4 already takes into account your marital status and dependents. So you only need to pay tax on the freelance job.
Take your net profit (income minus expenses) for the quarter (June 1 -Aug 31). Multiply x 4. Add your other income to find the highest tax percentage you will pay (15%, 22%, 24%, or higher, see this link https://www.irs.com/articles/2020-federal-tax-rates-brackets-standard-deductions/). Determine the tax on the freelance job, and add an extra 15% for self-employment tax (the freelance version of social security and medicare tax withholding). Take the total tax and divide by 4. That's your payment due Sept. 15.
If your only employment is freelance, then do this instead:
Take your net profit (income minus expenses) for the quarter (June 1 -Aug 31). Multiply x 4 to get the annual figure. Multiply by 15% to get the self-employment tax amount, then divide by 4 to get this quarter's payment. Separately, take your annualized income and subtract your standard deduction for your marital status. Subtract an additional $8000 for each dependent who is your child under the age of 17, and subtract $2000 for each dependent who is not your child or is over age 16. When you get that income figure, look it up on the tax bracket table. Figure the total tax as shown on the table, and then divide by 4 to get the quarterly amount. Add the quarterly income tax amount to the quarterly SE tax amount and make one combined payment.
If you just estimated 30% of your net profit for total income under $100,000 and 35% for income over $100,000, you'll probably be close.
You can also use this IRS calculator.
https://www.irs.gov/individuals/tax-withholding-estimator
The reason you take the quarter x 4 (annualized) instead of estimating your full year income, is that if your income varies, you can get hit with a penalty for underpayment even if you pay in full. For example, if you are mainly a landscaper and earn most of your income in quarter 2 and 3, but make 4 equal payments, you will be under-paid for quarters 2 and 3. If you take each quarter x 4, calculate the tax and divide by 4, you will pay more in q2 and q3 when your income is higher and you will pay less in q4 and q1 when your income is lower.
