Is the underpayment penalty calculated as a percentage of the withholding shortfall?

Here is how the IRS, calculates the underpayment penalty. "The IRS calculates the amount of the Underpayment of Estimated Tax by Individuals Penalty based on the tax shown on your original return or on a more recent return that you filed on or before the due date. The tax shown on the return is your total tax minus your total refundable credits.

We calculate the penalty based on:

• The amount of the underpayment
• The period when the underpayment was due and underpaid
• The published quarterly interest rates for underpayments"

See the link below for more information:

• Underpayment of estimated tax penalty

it's not based on the amount of tax you owe on 4/15 but the amount of tax you underpaid in 2024 relative to the 'safe harbor' amount - which is either 100% of your 2023 tax (110% if your AGI > 150k) or 90% of your 2024 tax whichever is smaller.  The payments have to be timely thru the year either via withholding, or quarterly via estimated tax payments.

so in your example it depends what the $2000 owed with your return represents, and how much you paid in total vs. owed.  let's ignore the "100% of 2023 tax" and assume "90% of 2024 tax" is the smaller amount due.  If your tax liability was $20,000 and you paid $18,000 thru withholding (90%) and have $2000 left to pay, then you won't have a penalty.  If your tax liability was $10,000 and you paid $8,000 thru withholding (only 80% vs. the $9,000 minimum) then you will have an underpayment of $1,000 vs. the 90% safe harbor amount (not $2,000). That underpayment rate is 8% annually, but the underpayment is spread out by quarter so it's calculated based on $250 late from Q1, $500 from Q2, $750 from Q3, $1000 from Q4 - which works out at $50 penalty total (Form 2210 does this calculation).