Calculate a quarterback’s TD to INT ratio from passing touchdowns and interceptions, or find the touchdowns needed to reach a target TD/INT ratio.
TD-to-INT Ratio Formula
A football passer’s touchdown-to-interception ratio divides passing touchdowns by interceptions thrown:
Official 2020 NFL club game notes report a 2.65 touchdown-to-interception ratio for 106 passing touchdowns and 40 interceptions: 106 divided by 40 equals 2.65.
Decimal and Whole-Number Formats
The calculator shows the decimal touchdowns-per-interception value and simplifies the entered count pair with its greatest common divisor. For example, 28 touchdowns and 10 interceptions equal 2.8 to 1 and simplify from 28:10 to 14:5.
What Happens With Zero Interceptions?
Division by zero has no finite numeric result. If touchdowns are positive and interceptions are zero, the calculator preserves the descriptive count line, such as 10:0, and labels the quotient non-finite. If both totals are zero, 0 divided by 0 is undefined. It is mathematically incorrect to force either case to a numeric ratio of zero.
Touchdowns Needed for a Target Ratio
With a positive interception count, target mode rearranges the formula:
The result rounds upward to the minimum whole passing touchdown count and verifies the achieved ratio. Decimal targets are evaluated exactly before rounding; a target of zero requires zero touchdowns with the entered positive interception count.
Example
For a hypothetical stat line of 153 touchdowns and 56 interceptions, 153 divided by 56 is about 2.73 touchdowns per interception. A target of 3.5 with eight interceptions requires exactly 28 passing touchdowns.
Interpretation
A higher ratio reflects more passing touchdowns relative to interceptions, but it does not measure total passing volume, sacks, completion percentage, yardage, or game situation. A quarterback with a favorable ratio in a small sample should not automatically be ranked above one who sustained a slightly lower figure across much greater volume.
Assumptions and Limitations
- Use passing touchdowns and interceptions from the same official player, team, and game scope.
- Rushing, receiving, and return touchdowns do not belong in the numerator.
- The ratio does not normalize for attempts; interception percentage and passer-efficiency formulas provide additional context.
- Target mode is a count requirement, not a forecast.
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Sources
National Football League club game notes, 2020, touchdown-to-interception ratio table (page 20). These historical figures illustrate the statistic and are not a current ranking.
