Rowing 2K Time Predictor

Paul’s Law, rowing’s own rule of thumb

Paul’s Law says that every time the distance doubles, your 500m split gets about 5 seconds slower. Written out:

split_2 = split_1 + 5 × log₂(distance_2 ÷ distance_1)

It is credited to a rower called Paul Smith and lives on the Concept2 forums rather than in any journal. Smith reportedly meant it less as a forecast than as a way to compare a rower’s speed with their endurance, and that is still the best use of it (see below).

What the predictions actually look like

For a 1:34.5 over 500m, Paul’s Law predicts a 2K of about 6:58. Going from 500m to 2,000m is two doublings, so the split slows by 10 seconds: 1:34.5 + 10 = 1:44.5, and four of those make 6:58.0.

The calculator also prints a second opinion, Riegel’s formula, which runners use: time grows with distance to the power 1.06. From the same 500m it says 6:50.8. On a 7:30 2K the two agree within about three seconds anywhere from 500m to 6,000m. For faster rowers they drift apart. From a 6:30 2K, Riegel’s 5K is 17:10 and Paul’s is 17:21, because Riegel slows you by a percentage of your split and Paul by a flat five seconds.

This table lists the test times that are all worth the same 2K under Paul’s Law. Read across a row: a rower who does any one of these is, on paper, the same rower.

If your 5K comes in faster than the row predicts, your 2K is the piece leaving something behind, usually at the top end. If your 5K is slower, the gap is aerobic.

Notice how modest the pace change is across that range. A 7:30 2K is a 1:52.5 split, and the equivalent 5K is only 1:59.1. Six and a bit seconds per 500m separates a piece lasting seven and a half minutes from one lasting twenty.

Where the formula breaks

Paul’s Law assumes the rower is trained and pacing well. It overestimates 2K from a 500m if the sprint was a redline all-out PR. Short pieces include alactic and creatine-phosphate energy that won’t carry to 2000m. It underestimates 2K from a long aerobic piece if pacing was conservative.

Five seconds is also an average. A sprint-built rower loses more than that per doubling and an aerobic diesel loses less, which is exactly the comparison Smith had in mind. Row two tests at different distances, count the seconds you actually lose per doubling, and you know which side of the line you sit on.

What to do with the number

Predict your 2K, then train the gap. If the predictor says 6:45 and you can only hold 7:00 in a race, the gap is mental, pacing, or race-day taper, not fitness. If the predictor says 6:45 and your last 2K was 6:30, you have improved between tests, so re-test soon to update the baseline.

The Concept2 logbook keeps a “best of all time” by distance which makes for a built-in Paul’s Law audit.