Bought house for $130k, divorced later, refinanced to remove ex and took out some cash, new mortgage $250. Sold for $440. Profit $170. Do I have to pay cap gains tax?

mortgages and refinancing have no effect on your gain.  your gain is the selling price of $440K less selling costs less your tax basis which would seem to be the sum of the purchase price and closing costs plus the cost of any capital improvements. the institution handling the closing will issue a 1099-S (on or before 1/31/2023) showing the full sales price. and that's what you'll have to use on your tax return.  if it's been your principal residence for at least 730 days during the period that starts 5 years before the sale you are entitled to exclude for federal purposes up to $250K of the gain. I'm assuming you haven't remarried)

@cindeadlee = the profit is not $170k.  Appears you took the $440k selling price and subtracted the mortgage to get to the profit.  The mortgage balance has nothing to do with it. 

The profit is

the selling price of $440k,

less any selling expenses (for example, the commission),

less any improvements you made during the time you owned it,

less how much you paid for it ($170k - despite the divorce, the cost basis remains the same). 

From that result, you can exclude $250k as long as YOU lived in the home at least 2 of the past 5 year.

So $440k- $170k is $270k

As long as your selling expenses and any improvements you made to the house exceed $20k AND you lived in the home for 2 of the past 5 years, there is not going to be any capital gains tax. 

Bought house for $130k, divorced later, refinanced to remove ex and took out some cash, new mortgage $250. Sold for $440. Profit $170.

Just using your numbers and information alone with no other facts to work with, your profit/gain is $310k. The refi has nothing to do with the cost basis of the property. However, there is a difference between refinancing, and buying the ex out. A buyout changes the cost basis. But only for the half you purchased. The cash out adds another wrinkle into the equation also when it comes to deductible interest on SCH A.

As far as paying tax on the gain, that depends on when purchased, when sold, how long it was y our primary residence, and the "ex" may qualify for the capital gains tax exclusion on the half they sold to you assuming this was in fact a buy out.

Of course, the wrinkles aren't over yet if you live in a community property state. Potential complexity abounds here. Lesson I learned many moons ago; if it was easy, you did it wrong.