h5k

Methods and sources

Every number on this site comes from one of the formulas below. This page says which, what each one assumes, and where each one stops being trustworthy.

Arithmetic, not models

Two of the calculators involve no modelling at all and cannot be wrong except by typo:

The splits calculator is nearly in this category. Even splits are pure division. Negative and positive splits use a linear pace ramp whose average is pinned to the target time: asking for the second half to be s faster than the first gives a half-amplitude of d = s × average / (1 − s/2) around the average pace. That is a modelling choice about the shape of the fade, not a claim about physiology.

VDOT — Daniels and Gilbert

Used by the VDOT calculator, the plan generator, and as one of three race prediction models. Two fitted curves:

VDOT is the first divided by the second. Training paces run the pair backwards at a fixed fraction of VDOT: 59–74% easy, 75–84% marathon, 86–88% threshold, 95–100% interval, 105–110% repetition.

Where it drifts. The sustainable-fraction curve exceeds 1.0 for efforts under about five minutes, because short races draw on anaerobic capacity that the model folds into the same number. A VDOT from a 1500 m result therefore reads high for a runner with good basic speed and a thin aerobic base. The model also assumes a trained runner: for someone very new to running, the easy-pace range in particular comes out faster than is useful.

Source: Jack Daniels and Jimmy Gilbert, Oxygen Power: Performance Tables for Distance Runners (1979), and Daniels, Daniels' Running Formula.

Race prediction — three models

The predictor shows all three rather than averaging, and reports the spread between them as the honest uncertainty.

Riegel (1977)

T₂ = T₁ × (D₂/D₁)^1.06. Peter Riegel fitted the exponent across a broad set of race results. Transparent and easy to check by hand. Its weakness is structural: a single exponent applies the same penalty per doubling however far you extrapolate, so it grows optimistic over large jumps in distance. The exponent is adjustable on that page; 1.07–1.10 better reflects a runner whose weekly volume is modest relative to the target race.

Cameron

t₂ = (t₁/d₁) × (a(d₁)/a(d₂)) × d₂ where a(x) = 13.49681 − 0.048865x + 2.438936/x^0.7905, distances in miles. Fitted to the best times of its era. Because it is not a power law, it bends in a way Riegel cannot, and it is usually the most realistic of the three from 5K to the marathon.

Daniels VDOT

VDOT from the known race, then the unknown race read back off that VDOT. Physiologically grounded rather than curve-fitted, but it assumes equivalent training for both distances, which is the assumption that fails when a 5K runner asks about a marathon.

What none of them know. Your weekly mileage, your longest recent run, the course, the weather, or your fuelling. Every one of those can only make you slower than the prediction.

Incline — Minetti et al. (2002)

The treadmill converter's equivalent-flat-pace figure uses the measured energy cost of running on gradients:

Cr(i) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6 joules per kilogram per metre, for gradient i between −0.45 and +0.45. Flat running costs Cr(0) = 3.6, so the flat speed with the same energy cost per second is v × Cr(i)/3.6.

What this is and is not. It is an energy-cost equivalence, the same family of correction as grade-adjusted pace in training apps. It is not a racing equivalence: sustained racing is limited by lactate clearance and fuel as well as by energy cost, and those do not scale with gradient the same way. One useful property of the curve is that cost is lowest around −10% to −20% and rises again on steeper descents, because braking is expensive.

The separate "set the treadmill to 1%" convention comes from Jones and Doust (1996), who found that 1% matched treadmill oxygen cost to outdoor running above about 8 km/h. It corrects for absent air resistance and is unrelated to the effect of a real hill.

Source: A. E. Minetti, C. Moia, G. S. Roi, D. Susta, G. Ferretti, "Energy cost of walking and running at extreme uphill and downhill slopes", Journal of Applied Physiology 93(3), 2002.

Heart rate

Maximum heart rate defaults to Tanaka (2001): 208 − 0.7 × age, from a meta-analysis of 351 studies. Also shown for comparison are Nes (211 − 0.64 × age), Gellish (207 − 0.7 × age) and the familiar Fox (220 − age), which was never derived from a regression and is the least accurate of the four.

The caveat that matters more than the formula. Every age formula is a population average with a standard deviation of 10–12 bpm. For an individual runner that is wider than a whole training zone. If you know your real maximum from a hard race finish, use it.

When a resting heart rate is supplied, zones use Karvonen heart rate reserve: target = resting + (max − resting) × intensity. Reserve tracks percentage of VO2max considerably better than raw percentage of maximum, and it adapts as your resting rate falls with training.

Couch to 5K

The Couch to 5K generator is the one page here with no formula behind it. The walk/run format comes from a 1996 article by Josh Clark and has been reproduced everywhere since. It has never been tested as a protocol, and no published version cites evidence for its particular ladder of intervals. It is a convention.

What this page generates is the progression, not any published table. The longest jog grows geometrically from the starting interval to the graduation figure. Total jogging and total walking follow their own geometric curves, jogging up and walking down, so both move monotonically week to week and every session lands between about 20 and 40 minutes. Repeats fall out of those totals, which is what makes the last session a single unbroken run without a special case.

Two consequences are intended. Progression is per session, not per week, because a weekly ladder from 30 seconds to 30 minutes in six weeks implies roughly doubling the longest jog every week; here no step exceeds about 25%. And a six-week plan graduates at 20 minutes of continuous running, not 30, because six weeks from a standing start does not reach half an hour. The principles are well supported: progress gradually, and keep beginner running easy. The specific numbers are ours, and they are arithmetic, not evidence.

The 5K plan

The plan generator derives all paces from your VDOT. The structure around them reflects mainstream distance-running practice rather than any single published plan: volume ramping with a cutback every fourth week, one or two quality sessions per week depending on days available, a long run of roughly 30% of weekly volume, threshold work emphasised early because it has the largest effect on 5K time, VO2max intervals through the middle, short repetitions for economy late, and a two-week taper that cuts volume while holding intensity.

The projected improvement assumes a plausible VDOT gain per week by experience level, weighted toward the conservative end. It is an estimate of what a completed block could produce, not a prediction of your race.

Corrections

If something here is wrong, please say so. The formulas are stated above so they can be checked.

Not medical advice

Everything on this site is general information about training and racing. It is not medical advice, it does not account for your health history, and it is not a substitute for a doctor or a coach who knows you. If you have a cardiac condition, are returning from injury, or are new to vigorous exercise, get proper advice before following a training plan.