First a few points:
- Most employers have a 401(k), 403(b), 457(b), TSP or similar plan. They don't generally get involved with an IRA.
- The total employee contribution to the 401(k) in 2021 is $19,500; for 2022 it is $20,500. If you are 50 or over and your employer plan allows a catch-up contribution, then the you can contribute an additional $6,500 each year.
- If an employer plan has a Roth component to the 401(k) you can split that $19,500 anyway you like across the traditional and Roth components.
- In an IRA the total amount you can put into the combination of traditional and Roth is $6,00 for 2021 and 2022. If you are 50 or older you can add an additional $1,000
Now on to your questions:
Do companies match proportionally?
Say I put in 5% Roth and 1% [Traditional] 401k. Employer match is 4%. Would that
mean that the match is 3.33% Roth and .66% 401k?
From a tax perspective all company match money is considered a pre-tax contribution. It is not considered part of the $19500/$20500 limit, but when you pull it out of the retirement account in the future it will be taxable income. It doesn't matter if the employee contribution to the 401(k) was pre-tax, post-tax, or Roth the employer contribution is all pre-tax. Therefor the split in in question is incorrect.
What is the correct way to find Roth contribution?
Roth contribution = (gross income * Roth %) + (gross income * Roth employer match % * ratio)
Roth contribution = (net income * Roth %) + (gross income * Roth employer match % * ratio)
Some other black magic or perhaps dependent on company/plan?
Employers either let you decide how much you contribute each check by the percent of gross or a set number of dollars each check. There is debate regarding the rule of thumb of a retirement contribution of 10% -15% of gross. Does it include the employer match.
You have to decide that if the company 401(k) plan allows Roth, do you want some or all of your contribution to be Roth? If there is no Roth 401(k) option, then do you want to put the amount to get the maximum company match into the traditional 401(k), and then more into a Roth IRA?