How NFL Passer Rating Works: The QB Rating Formula and the 158.3 Ceiling

Passer rating is the number a broadcast slaps on the screen the moment a quarterback walks off the field, and it is the one football statistic that almost everybody quotes and almost nobody can compute from memory. It sits on a scale that runs from 0 to a strange-looking 158.3, with no obvious midpoint and a ceiling that reads like a typo. Once you see how it is built, though, the whole thing makes sense: passer rating combines four capped components into a single 0 to 158.3 scale, and 158.3 is what a perfect game looks like.

This guide walks through the formula, the four parts it averages, why the maximum is 158.3 instead of a round 100 or 150, and what numbers like 100 and 120 actually mean. We will work one real stat line all the way through so you can see the math move.

The four components the formula is built from

The NFL rating does not look at a quarterback as one blob of production. It splits the day into four rates and scores each one separately:

Completion percentage — how often the throws connect.
Yards per attempt — how far the ball travels per throw, on average.
Touchdown percentage — the share of attempts that end in the end zone.
Interception percentage — the share of attempts handed to the defense.

Each of those four feeds its own little sub-formula, and each sub-formula produces a value that is then clamped to the 0 to 2.375 band before anything is averaged. That clamp is the heart of the system, and it is the detail people get wrong most often.

Here is each part, written the way the league defines it:

a = (completion rate − 0.3) × 5
b = (yards per attempt − 3) × 0.25
c = touchdown rate × 20
d = 2.375 − (interception rate × 25)

After each of a, b, c and d is capped to the 0 to 2.375 range, the rating is:

rating = ((a + b + c + d) / 6) × 100

That is the entire formula. Four capped rates, summed, divided by six, multiplied by 100.

Why the ceiling is 158.3 and not 100

The 158.3 maximum looks arbitrary until you trace where it comes from. Each of the four components tops out at exactly 2.375. Max all four at once and the sum is 4 × 2.375 = 9.5. Divide 9.5 by 6 and you get about 1.5833. Multiply by 100 and you land on 158.333, which the league reports as 158.3.

So the ceiling is not a round number somebody chose. It is a structural result of capping the four parts at 2.375 each. The 2.375 cap exists for a reason worth understanding: it stops one freakish input from running away with the whole score. Without it, a quarterback who completes 90 percent of his throws would push the completion component into absurd territory and drown out the other three. Capping each part keeps the rating balanced, and the side effect of that balance is the odd-looking 158.3 at the top.

A floor of 0 works the same way from the other direction. Throw enough interceptions and the d component bottoms out at 0, but it cannot go negative, so the NFL rating never drops below zero no matter how ugly the game gets.

A worked example: 27 of 38, 312 yards, 3 TDs, 1 INT

Let us run a realistic line all the way through — a good-not-perfect afternoon under center: 27 completions on 38 attempts for 312 yards, 3 touchdowns, 1 interception.

First, the four rates:

Completion rate = 27 / 38 = 0.7105 (about 71.1 percent)
Yards per attempt = 312 / 38 = 8.21
Touchdown rate = 3 / 38 = 0.0789
Interception rate = 1 / 38 = 0.0263

Now the four components:

a = (0.7105 − 0.3) × 5 = 2.053 → within range, stays 2.053
b = (8.21 − 3) × 0.25 = 1.303 → stays 1.303
c = 0.0789 × 20 = 1.579 → stays 1.579
d = 2.375 − (0.0263 × 25) = 2.375 − 0.658 = 1.717 → stays 1.717

None of the four hit the 2.375 cap, which already tells you this was a solid game rather than a historic one. Sum them: 2.053 + 1.303 + 1.579 + 1.717 = 6.652. Divide by 6 to get 1.109, then multiply by 100. The rating is about 110.8 — a strong, winning performance, the kind of number that anchors a clean Sunday.

When I first tried to do this by hand during a game, I made the classic blunder: I plugged in 71 for the completion rate instead of 0.71, which instantly pinned the a component to its cap and gave me a nonsense score. That is exactly the mistake the calculator is built to remove — you hand it raw completions and attempts, and it works the rates out for you so the decimal point never bites. If you want to verify any single rate by hand, the percentage calculator will turn 27 of 38 into 71.1 percent in one step, and the passer rating calculator will then carry all four components, apply the clamps and show you which bar is holding the score back.

What a perfect rating actually requires

To hit 158.3 you have to max all four capped components at the same time. That means clearing four thresholds in one game:

Completion rate at or above 77.5 percent
Yards per attempt at or above 12.5
A touchdown on at least 11.875 percent of attempts
Zero interceptions

A textbook perfect line is 20 completions on 20 attempts for 400 yards with 5 touchdowns and no picks, which maxes every part. In practice, many real perfect games arrive on smaller attempt counts — a quarterback who throws 12 times, completes 10, racks up 200 yards and 3 scores can clear all four bars without ever looking like he had a monster volume day. The cap is what lets a tidy, efficient outing reach the same ceiling as a 400-yard explosion.

Reading the number: what 100 and 120 mean

Because the scale is unfamiliar, the milestones are worth memorizing. League average across a full season in the modern passing era sits in the high 80s to low 90s. A rating of 100 over a whole season is a strong, often Pro Bowl level body of work; a single game at 100 is a comfortable win. Elite seasons push past 110, and the all-time single-season records land around 120 to 122, which is roughly the practical edge of what a human plays across sixteen-plus games.

One caution worth keeping: passer rating ignores sacks, rushing, fumbles and drops, and it quietly rewards short, safe throws that prop up completion percentage. A checkdown-heavy afternoon can post a pretty number while the offense barely moves. Treat the rating as one signal next to yards per attempt and total touchdowns rather than a final verdict, the same way you would never judge a player on a single column.

College football, for what it is worth, uses a different math entirely — an uncapped passer-efficiency formula that can sail past 158.3 or even go negative — which is why an NFL rating and an NCAA efficiency number should never be pasted into the same sentence without a label.

That is passer rating end to end: four rates, four caps, one average, and a ceiling of 158.3 that is less mysterious than it looks once you know where it comes from.

Made by Toolora · Updated 2026-06-13