Run the same hop schedule through both the Tinseth and Rager formulas and the gap between them isn't a fixed percentage or even a fixed direction — it swings from Rager reading noticeably lower than Tinseth to Rager reading dramatically higher, depending mostly on how long the hops were in the boil. Neither formula is right and the other wrong; they're two independently developed models of hop utilization, built from different underlying data and different assumptions about how utilization responds to boil time and wort gravity.
Where the models differ
Boil time response. Tinseth models utilization rising toward a ceiling following an exponential decay curve ((1 - e^(-0.04 x minutes)) / 4.15). Rager uses a hyperbolic tangent curve centred around 31 minutes. The two curves cross twice: Rager starts higher at very short boil times, dips below Tinseth through the middle of the boil, then climbs back above it as boil time gets long. On a single 28 g addition at 6% alpha acid in a 19 L, 1.050-gravity batch, a 15-minute addition puts Tinseth at 10.1 IBU against Rager's 7.3 — Rager reading about 28% lower. A 30-minute addition is close to the crossover point: 15.7 IBU Tinseth against 15.1 Rager, under 4% apart. Push to 60 minutes and Rager has climbed back past Tinseth and kept going: 20.4 IBU Tinseth against 27.3 Rager, now about 34% higher.
Gravity correction. Tinseth applies a gravity correction ("bigness factor") continuously across the whole gravity range. Rager applies no correction at all below 1.050 boil gravity, then applies a step correction above it. This is the single biggest source of disagreement on big beers: a barleywine or imperial stout boiling well above 1.050 gets a meaningfully larger correction under Rager's step function than under Tinseth's continuous one. A 2 oz (56 g), 14% alpha acid addition at 60 minutes in a 19 L, 1.090-gravity batch comes out at 66.4 IBU Tinseth against 106.0 IBU Rager — Rager reading roughly 60% higher, the widest gap this site's calculator produces across its own worked examples.
The shorthand that actually holds
There are two crossovers, not one. The curves cross a first time around the 5-8 minute mark — below that, on very short late additions, Rager reads higher. They cross back a second time around the 28-35 minute mark depending on gravity (roughly 30 minutes at a typical 1.050, earlier at higher gravity, later at lower) — between the two crossovers, through the middle of the boil, Rager typically reads lower than Tinseth, not higher; past the second crossover, on a standard 60-minute bittering addition, Rager is back above Tinseth and pulling further ahead. The one pattern that holds consistently: the gap widens as either boil time or gravity climbs past that second crossover, in both directions.
When the gap is smallest
Additions landing close to the 25-30 minute mark are where the two formulas agree most closely, regardless of gravity — the worked example above puts them under 4% apart at 30 minutes on a moderate-gravity beer. That's specific to timing, not to gravity range on its own; a moderate-gravity beer hopped entirely at 60 minutes still shows a full one-third gap.
When the gap is largest
Big, high-gravity beers with a long boil-length bittering charge show the widest divergence in the "Rager higher" direction — the 1.090-gravity, 60-minute example above at roughly 60% is representative of hop-heavy barleywines and imperial IPAs. This is exactly the situation where knowing both numbers — rather than trusting whichever one your brewing software happens to default to — is most useful, because a single-number IBU estimate on a big beer can be misleadingly precise-looking for a value that's genuinely uncertain by a wide margin.
What to actually do with this
Neither formula is "the truth" — IBU itself is a laboratory measurement of dissolved iso-alpha acid concentration, and both formulas are estimates of what that lab measurement would show. Use the IBU calculator's side-by-side output as a range rather than a single target, and lean more on your own tasting notes than either formula once you've brewed a style a few times and know how a given calculated IBU actually translates to perceived bitterness in your own process.