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PaceSplit

Formulas & Methodology

Every PaceSplit calculator stands on a published formula. Below is the complete list, with the academic source for each one and links to the calculators that use it.

Formula index

ID Formula Source Used by
F1 Pace = Time ÷ Distance Fundamental kinematic identity.
F2 Speed ↔ Pace conversion Unit conversion identity.
F3 Treadmill incline-adjusted pace Jones, A.M. & Doust, J.H. (1996). A 1% treadmill grade most accurately reflects the energetic cost of outdoor running. Journal of Sports Sciences, 14(4), 321–327.
F4 Treadmill elevation gain Trigonometric small-angle approximation (valid for grades ≤ 15%).
F5 Riegel race-time prediction Riegel, P.S. (1981). Athletic Records and Human Endurance. American Scientist, 69, 285–290.
F6 Cameron race-time prediction Cameron, D. (1999). Cameron's model for predicting race times across distances.
F7 VDOT (Daniels & Gilbert) — training paces from race performance Daniels, J. & Gilbert, J. (1979). Oxygen Power: Performance Tables for Distance Runners. Updated in Daniels (2013), Daniels' Running Formula, 3rd ed.
F8 VO2max from race performance (simplified) Derived from F7 — VDOT approximates VO2max for trained runners.
F9 Maximum heart rate (Haskell & Fox; Tanaka; Inbar; Nes) Fox, S.M., Naughton, J.P. & Haskell, W.L. (1971). Tanaka, H., Monahan, K.D. & Seals, D.R. (2001). Inbar, O. et al. (1994). Nes, B.M. et al. (2013).
F10 Karvonen heart-rate zones Karvonen, M.J., Kentala, E. & Mustala, O. (1957). The effects of training on heart rate. Annales Medicinae Experimentalis et Biologiae Fenniae, 35(3), 307–315. ACSM method.
F11 Age grading (WMA tables) World Masters Athletics age-grading tables, Alan Jones 2023 revision.
F12 Negative split modelling Santos-Lozano, A. et al. (2014). Marathon split-pace analysis informs the conservative / moderate / aggressive bands.
F13 Race split generation Derived from F1 + F12.
F14 Stride length / cadence identity Fundamental biomechanical identity.
F15 Equivalent pace across distances Derived from F5 (Riegel).

Formulas are reproduced and explained in detail on each calculator’s methodology section. Where multiple formulas are appropriate (max-HR estimators, race-time predictors), each calculator lets you choose which one to apply.