Passer rating calculator

Passer rating squeezes a quarterback's passing into one number. The NFL version was designed to run from 0 to 158.3, and the college version is a separate formula with no ceiling. Both use the same five counts from the box score, so a stat line you find on any league site is enough.

How is NFL passer rating calculated?

Four numbers are worked out from a passer's attempts (ATT), completions (CMP), yards (YDS), touchdown passes (TD) and interceptions (INT): a = (CMP ÷ ATT − 0.3) × 5, b = (YDS ÷ ATT − 3) × 0.25, c = (TD ÷ ATT) × 20 and d = 2.375 − (INT ÷ ATT × 25). Each is held between 0 and 2.375, then the rating is (a + b + c + d) ÷ 6 × 100. The calculator shows all four parts, both before and after the limit.

What is a perfect passer rating, and what is the lowest?

158.3 is the top: all four parts at the 2.375 limit. Working the formulas backwards (our arithmetic) that takes a completion rate of 77.5%, 12.5 yards per attempt, touchdowns on 11.875% of attempts and no interceptions. Zero needs a completion rate of 30% or lower, 3.0 yards per attempt or fewer, no touchdowns and an interception on at least 9.5% of attempts. Because of the limits, extra yards past 12.5 per attempt earn nothing.

Why does a college rating look so much higher than an NFL rating?

The NCAA uses a different formula: (8.4 × yards + 330 × touchdowns + 100 × completions − 200 × interceptions) ÷ attempts, and nothing is capped. Its scale runs from about −731.6 to 1,261.6 on paper, so college ratings above the NFL maximum of 158.3 are possible. The same stat line gets 168.6 under the NCAA formula but only 113.9 under the NFL one (the 1997 UCLA season used in the example below). The two numbers must not be compared with each other.

What counts as a good passer rating?

There is no official grade. The scale runs from 0 to 158.3, and Wikipedia reports that the NFL built the formula around league figures from 1960 to 1970, so ratings have drifted upward as passing improved. We do not store league averages here, because they change every season and we would have to cite the year. Compare a rating with the league leaders and the league average for the same season on NFL.com or Pro Football Reference, and with the quarterback's own career line.

Does passer rating include rushing, sacks or fumbles?

No. The formula only uses attempts, completions, yards, touchdown passes and interceptions. A quarterback's rushing, sacks taken, fumbles, drops by receivers and the situation of the game are all left out, and so are yards after the catch versus air yards. That is why measures built on every play can disagree with it. Use the rating as a compact summary of passing efficiency, not a full measure of a player.

Can the rating be worked out for one game or a few passes?

Yes. The formula works for any line with at least one attempt, and the limits make short lines swing hard: one completed 40-yard touchdown pass in one attempt scores a perfect 158.3, and one incompletion scores 39.6. The calculator rejects impossible lines, such as more completions than attempts or more touchdowns than completions, because the formula would still return a number but it would not describe real football.

Worked example: Aaron Rodgers, 2011

Rodgers completed 343 of 502 passes for 4,643 yards, 45 touchdowns and 6 interceptions. Completions: (343 ÷ 502 − 0.3) × 5 = 1.916. Yards: (4,643 ÷ 502 − 3) × 0.25 = 1.562. Touchdowns: 45 ÷ 502 × 20 = 1.793. Interceptions: 2.375 − 6 ÷ 502 × 25 = 2.076. The yardage and touchdown parts are held at the 2.375 limit where the raw numbers are 1.562 and 1.793. The sum is 7.348, divided by 6 and multiplied by 100: 122.5. That matches the published 122.5, the highest single-season mark on Guinness World Records' list. The same line under the NCAA formula is 173.2.

Common mistakes and limits

Forgetting the limits. Without the 0 to 2.375 limit on each part, a 600-yard day on 20 attempts would add so much that it hid a bad completion rate; the limit is also why the NFL scale tops out at 158.3 and why it can be reached on few attempts. Mixing the scales. A college rating of 160 and an NFL rating of 100 can describe similar play. Treating the number as a verdict. It leaves out rushing, sacks, fumbles and the quality of the receivers and the offensive line, and it counts a short completion on third-and-ten the same as one that moves the chains. Typing completions over attempts or interceptions that overlap completions. An intercepted pass is not a completion, so completions plus interceptions cannot exceed attempts; the calculator checks that.

Related sports math: baseball stats calculator for AVG, OPS and ERA, true shooting calculator for basketball efficiency, and Elo rating calculator for head-to-head strength.

Sources: Wikipedia, “Passer rating” (NFL and NCAA formulas, and the conditions for 158.3 and 0.0), which cites NFL.com’s “QB Rating Formula” and the Pro Football Hall of Fame; the NFL.com and Pro Football Reference pages could not be opened from our tools, so the formula is confirmed against Wikipedia and independent calculator write-ups, and the 122.5 figure against Guinness World Records and StatMuse. NCAA formula and the 1997 UCLA example: football.stassen.com, “NCAA and NFL Passing Efficiency computation”. How we check our calculators.