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.