FORMULAS / EVIDENCE / LIMITS
RunFasta's browser tools are deterministic and run locally. This page separates arithmetic, research-informed choices and product heuristics so that a useful estimate is never presented as physiological truth.
Last reviewed: 22 July 2026. These tools support training decisions; they do not diagnose fitness, injury, heat illness or medical suitability. Symptoms, conditions and direct effort always override a calculated target.
01 / PACE
pace = elapsed time ÷ measured distance
Miles use exactly 1.609344 kilometres. Display values are rounded only after calculation. This is unit arithmetic, not a performance model.
Average pace hides grade, pauses, GPS error, wind and within-run variation. It does not imply that every split should be identical.
02 / TRAINING RANGES
A recent 5K is first projected to 10K with the commonly used Riegel power-law exponent of 1.06. RunFasta then applies a 0.98 adjustment to create a threshold anchor. Easy, tempo and 4×4 ranges are fixed offsets from that anchor.
Those offsets are RunFasta product heuristics, not clinically validated individual thresholds. The calculator deliberately exposes them so they can be tested and revised.
A stale or unrepresentative 5K, hills, trail surface, heat, wind, altitude, fatigue and the talk test. The 4×4 range is a conservative starting cue; it is not a command to reach a heart-rate number immediately.
03 / PR ATTEMPT
The selected goal time is divided by distance. Four equal-distance quarters use +9, +3, −3 and −9 seconds per kilometre around goal pace. The warm-up and cooldown sit outside the timed attempt.
The quarter offsets sum to zero, so the nominal target remains unchanged before rounding. The progression is designed to discourage an overly fast opening, but it does not establish that the chosen goal is achievable.
Course grade, turns, GPS accuracy, wind, heat, current fitness and whether a negative split is appropriate for this runner and distance.
04 / CADENCE
The tool multiplies observed cadence by the requested change, rounds to a whole step per minute and displays a ±2 spm trial band. A one-click-per-step metronome uses the same BPM; music with two steps per beat uses half that BPM.
The default 3% change is intentionally modest. Evidence indicates that changing step rate can alter several biomechanical variables, but a 2022 systematic review found insufficient evidence to determine injury and performance effects conclusively. It does not support prescribing one cadence to every runner.
Anderson et al., 2022 — systematic review and meta-analysis
Comfort, pain, pace, terrain and natural mechanics. Treat a cue as a short experiment; stop if it worsens pain or form.
05 / HEAT CONTEXT
Dew point uses the Magnus approximation with constants 17.625 and 243.04. RunFasta then assigns a broad qualitative band from air-temperature and dew-point thresholds, with a small categorical increase for mixed or full-sun exposure.
The severity bands are cautious product heuristics. They are not a validated heat index, WBGT measurement, percentage slowdown or safety threshold. Research supports that temperature, humidity, wind and solar load affect endurance performance, but weather alone has limited power to predict an individual's result.
Mantilla et al., 2021 — 1,258 endurance races
El Helou et al., 2012 — environmental parameters and marathon performance
Measured radiant heat, wind, clothing, duration, acclimatization, hydration, medication, health and individual response. Prefer an official local heat warning and measured WBGT where available.
06 / GPX GEOMETRY
Distance is the sum of WGS84 latitude/longitude point-to-point haversine distances inside each GPX track segment. Segment gaps are not joined. Elevation gain and loss use a five-point moving median and ignore changes smaller than 0.5 m. “Near flat” is the share of assessed 30 m windows whose absolute elevation grade is at most 2%.
These smoothing and flatness thresholds are RunFasta inspection heuristics, not a survey-grade elevation model. Flatness is withheld when fewer than 60% of points contain elevation or less than 100 m can be assessed.
The browser rejects DTD/entity declarations, files over 20 MB, more than 100,000 points and invalid coordinates. No coordinates or filename are displayed or uploaded. GPS/barometric elevation may still be noisy. Standard GPX normally does not establish pavement, trail, sand, traffic, lighting, legal access, closures or personal safety.
07 / REPRODUCIBILITY
The calculator implementation is a small JavaScript module with deterministic boundary tests. Shared golden fixtures check that Android and web formulas agree. Inputs stay in the browser; only an aggregate campaign label is placed on a Play link.
Versioned formulas are preferable to invisible adaptation: if a method changes, the tests and this page must change together. A calculator result is still an estimate even when perfectly reproducible.