The starting point, one race result
Everything here starts from a single data point: a 5K finished in 25:00. The pace calculator converts that into a rate — 5:00 per km, or 12 km/h — which becomes the input for everything that follows.
Predicting other race distances from that pace
Riegel's formula uses the 5K result to predict times at other distances: a 10K in about 0:52:07, and a half marathon in 1:55:00. Both predictions come from the same 25:00-for-5K starting point, adjusted for each target distance's own ratio to the original 5K.
Deriving training paces from the same result
The training pace calculator takes that runner's race pace — 5:00 per km — and applies fixed multipliers to generate a full set of training paces: easy pace 6:30 per km (30% slower, for comfortable-effort runs), long-run pace 6:00 (20% slower), tempo pace 5:24 (8% slower, a "comfortably hard" effort), and interval pace 4:30 (10% faster than race pace, for short hard efforts).
One number, several different answers
A single race result doesn't just describe how fast someone ran on one day — run through the right formulas, it also describes how fast they'd likely finish other race distances, and what pace they should target on easy days, long runs, tempo runs, and intervals in between races. Each calculator answers a different question, but they all start from the exact same underlying number.