Started a new job and suspect I'm having too much withheld?

I started a new job recently with a 12.5% increase in pay from my last job, but my take home pay is less than I expected. I noticed my federal withholding seemed higher and did the IRS withholding calculator, which predicted I will pay almost double the amount of what I owe next year. I filled out my W-4 correctly, so I don't understand why such a big refund and how to adjust my withholding?