Methodology

All conversions go through the exact international mile of 1,609.344 metres and pure multiplication or division, so round-trips carry no drift beyond float epsilon — converting min/mile → mph → min/km → min/mile returns the value you started with.

A marathon is 42.195 km — 26.219 miles, not 26.2. Mile splits are therefore 26 full miles of 1,609.344 m plus a final partial split of 352.056 m (0.219 mi); kilometre splits are 42 full kilometres plus 195 m. Distances that are exact multiples — a 5K in kilometres, a 10K in kilometres — produce no partial split.

Each split’s raw time is its share of the goal time weighted by length; the partial final split gets exactly its proportional share. The raw times are then converted to whole seconds with largest-remainder rounding: every split is floored, and the leftover seconds are handed out to the splits with the largest fractional remainders. The result: every split is a whole number of seconds, and the splits always sum exactly to the goal time — the cumulative clock lands on your goal to the second, never 3:59:58 or 4:00:01.

The even / −1% / −2% options apply a linear drift across the splits: split i gets weight 1 + d·(c − i), where c is the middle split and d = f/(n−1) for a target first-to-last differential f. The first split is the slowest, the last the fastest, and the differential between them is about f (1% or 2%). Times are then scaled to the goal and apportioned exactly as above — a negative-split plan never changes your finish time, only its shape.

5K, 10K and halfway times within a longer race are interpolated from the split list: the clock time at any course point is the previous split boundary plus the proportional share of the split in progress, assuming even effort within each split. At split boundaries the value is exact.

The treadmill chart’s effective flat pace uses the running energy-cost curve fitted by Minetti, Ardigò and Saibene (2002), “Energy cost of walking and running at extreme uphill and downhill slopes” (Journal of Applied Physiology 93: 1039–1046). The paper fits gross energy cost C(i), in joules per kilogram per metre, to treadmill grade i expressed as a fraction:

Goal pages show two kinds of context, both labelled as rules of thumb. Implied training paces use standard coaching offsets from race pace (easy running 90–210 s/mi slower depending on distance, tempo 10–30 s/mi either side, long runs 30–150 s/mi slower). Prerequisite performances use the equivalences runners actually plan with: marathon ≈ 2 × half + ~12 minutes, half ≈ 2.2 × 10K, 10K ≈ 2 × 5K + ~90 seconds. These frame whether a goal is realistic today — they are not race predictions, and we deliberately do not build a predictor or a training plan around them.

No VO₂max modelling, no race prediction beyond the rules of thumb above, no training plans, no accounts and no email gates. The product is the chart, the splits and the printable band; everything on this page exists so you can trust those numbers.