Exact arithmetic
Pace, race-distance calculators, the pace–speed converter, and even splits are definitions, not models. Pace is finish time divided by distance. Distance is time divided by pace. Time is pace multiplied by distance. Speed is the inverse of pace. Splits divide the target time evenly across each kilometer or mile.
These tools do not estimate fitness, terrain, or weather. If the inputs are correct, the output is the same number you would get with a stopwatch and a measured course.
Rounding
Displayed times round to the nearest second. Displayed speed rounds to one decimal place. Internal arithmetic uses seconds and kilometres so rounding happens once, at display, not at every intermediate step.
Race prediction — Riegel
Equivalent race times use Peter Riegel’s power-law model with exponent 1.06:
T2 = T1 × (D2 ÷ D1)^1.06
T1 and D1 are a recent race time and distance. T2 is the predicted time at distance D2. The formula assumes similar training, similar conditions, and that both distances sit in a range where endurance scales smoothly. It does not account for heat, hills, tactics, or a jump from a 5K to an undertrained marathon. Treat the result as a planning estimate.
Training paces — Jack Daniels VDOT
Training paces come from Jack Daniels’ VDOT system. A recent race distance and time estimate VDOT, an index of current endurance fitness. That value is converted to velocities at percentages of VO2 for recovery, easy, tempo, threshold, and interval running.
The bands are training estimates, not prescriptions. They assume the race you entered is representative. They do not replace coaching, and they do not know your injury history.
Heart rate — Tanaka, %HRmax, and Karvonen
If you do not enter a known maximum heart rate, the calculator estimates it with Tanaka’s formula:
Estimated max HR = 208 − 0.7 × age
Percentage-of-max zones use that maximum. Karvonen zones use heart-rate reserve: (max − rest) × percent + rest. Age-predicted max HR is a population estimate. Individual maximums vary. Heart-rate numbers on this site are training guidance, not medical advice.
Grade-adjusted pace — Minetti 2002
Grade-adjusted pace uses Minetti’s energy-cost polynomial for running versus gradient. Flat-equivalent pace is actual pace multiplied by (flat cost ÷ grade cost). Uphill running costs more energy, so the flat-equivalent pace is faster than the watch pace. Downhill costs less, so the equivalent is slower.
This is an energy-cost estimate, not a GPS measurement and not a prediction of race time on a hilly course.
Age grading — interpolated WMA 2015 factors
“How good is my running time?” compares a result with interpolated World Masters Athletics (WMA 2015) age-grading factors for 5K, 10K, half marathon, and marathon. Age-grade percentage is the statistically elite standard for your age and comparison category divided by your time.
Factors for ages between tabulated points are interpolated. Distances other than those four are not invented. The output is labeled an estimate. It is not an official WMA ranking, not a qualifying standard, and not a statement about talent.
Uneven splits
Negative and positive split tables use two constant paces, switching at halfway. For a drop of 2% (0.02), first-half time is total ÷ (2 − drop) and the second half is the remainder. A positive drop makes the second half faster. Progressive pace interpolates interval pace from the first kilometre or mile to the last, then scales so the finish still matches the goal time.
Kilometre-split and mile-split pages lock the interval. Pace bands print both columns for the official half marathon or marathon distance.
Race equivalents — VDOT versus Riegel
The race time predictor uses Riegel with exponent 1.06. Required race performance is the same formula with distances swapped: the time you need at a known distance to hit a goal. Race equivalents invert Jack Daniels VDOT so other distances match the same fitness index. The two models will not agree exactly. That is expected.
Marathon potential is Riegel locked to 42.195 km. Goal feasibility compares a Riegel prediction with a goal clock and labels the gap close, stretch, or outlier. Those labels are conventions, not a training plan.
Cooper 1968 and 12-minute arithmetic
The Cooper test estimates VO2max from 12-minute distance: (metres − 504.9) / 44.73. Cite Cooper, K. H. (1968), JAMA. The 12-minute run calculator does not estimate VO2; it only converts pace and distance in 720 seconds. VO2 from a race reports Daniels VDOT as an ml·kg⁻¹·min⁻¹ index.
Reverse age grading
Forward age grading reports percent, age-graded time (clock × factor), and the open-class standard. Reverse age grading starts from a target percent and returns the clock time. Running “percentile” on this site is the same WMA band mapping — not a rank in a results database.
Track, intervals, and Yasso 800s
Track tools assume a 400 m lane-1 oval. Lap time is pace per kilometre × 0.4. Interval session time is work × reps plus rest × (reps − 1). Yasso 800s map a marathon goal of H:MM onto 800 m times of MM:SS. That mapping is a named heuristic popularised by Bart Yasso, not a peer-reviewed predictor.
What results are not
Nothing on this site is medical advice, nutritional advice, a coaching plan, or an official ranking. Exact-arithmetic tools answer a definition. Model-based tools answer a published formula with the inputs you typed. Use them for training guidance, then apply judgement.
Browse the calculators or read about the lab.
Citations
- Riegel, P. S. (1977). Time predicting. Runner's World. See also Riegel, P. S. (1981). Athletic records and human endurance. American Scientist, 69(3), 285–290.
- Daniels, J. Daniels' Running Formula. Human Kinetics.
- Tanaka, H., Monahan, K. D., & Seals, D. R. (2001). Age-predicted maximal heart rate revisited. Journal of the American College of Cardiology, 37(1), 153–156.
- 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.
- Minetti, A. E., Moia, C., Roi, G. S., Susta, D., & Ferretti, G. (2002). Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology, 93(3), 1039–1046.
- World Masters Athletics. Age-grading factors, 2015 tables. This site uses an interpolated subset for 5K, 10K, half marathon, and marathon only.
- Cooper, K. H. (1968). A means of assessing maximal oxygen intake. JAMA, 203(3), 201–204.
- Yasso 800s as popularised by Bart Yasso / Runner's World. A workout heuristic, not a marathon prediction model.