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Form 8812 is used to calculate the additional child tax credit. If your child tax credit is more than your tax, then use Form 8812 to calculate the refundable additional child tax credit.
Combat pay is tax-exempt and won't be on your tax return. However, Congress didn't want to take away the earned income credit and additional child tax credit for military members in combat situations. When calculating the earned income credit and additional child tax credits, a taxpayer with combat pay will include the combat pay as income just for purposes of these two credits. You calculate your earned income credit and additional child tax credit the regular way without including combat pay, then you calculate your earned income credit and additional child tax credit including your combat pay as income. Then you use the higher of the two calculations for your credits. For example, if the only income you have is combat pay and you have a child who is eligible for the earned income credit, you are going to receive a higher earned income credit by including your combat pay in the earned income credit calculation. If you have other sources of wages and the combat pay decreases the amount of earned income credit, then you would use the regular earned income credit calculation.