SOLVETUTORMATH SOLVER

Instrument MI-11-098 · Sports

Training Pace Calculator

Enter a recent race distance and time — this returns your VDOT fitness score and the five training paces Jack Daniels' method derives from it, tuned to your current fitness rather than generic pace charts.

Instrument MI-11-098
Sheet 1 OF 1
Rev A
Verified
Type 11 — Running SER. 2026-11098

VDOT (Daniels & Gilbert running-fitness score)

45.3

VDOT = VO2(race pace) / %VO2max sustainable for race duration (Daniels & Gilbert 1979)

332 Easy pace (sec/km, ~70% VDOT)
291 Marathon pace (sec/km, ~82.5% VDOT)
279 Threshold pace (sec/km, ~87% VDOT)
255 Interval pace (sec/km, ~97.5% VDOT)
231 Repetition pace (sec/km, ~110% VDOT)
The working Every figure verified twice
  1. vdot = (−4.6 + 0.182258·(10000 ⁄ 45) + 0.000104·pow(10000 ⁄ 45, 2)) ⁄ (0.8 + 0.189439·exp(−0.012778·45) + 0.298956·exp(−0.193261·45)) = 45.3
  2. paceEasySecKm = 60000 ⁄ ((−0.182258 + √(pow(0.182258, 2) + 4·0.000104·(4.6 + 0.7·45.263003))) ⁄ (2·0.000104)) = 332
  3. paceMarathonSecKm = 60000 ⁄ ((−0.182258 + √(pow(0.182258, 2) + 4·0.000104·(4.6 + 0.825·45.263003))) ⁄ (2·0.000104)) = 291
  4. paceThresholdSecKm = 60000 ⁄ ((−0.182258 + √(pow(0.182258, 2) + 4·0.000104·(4.6 + 0.87·45.263003))) ⁄ (2·0.000104)) = 279
  5. paceIntervalSecKm = 60000 ⁄ ((−0.182258 + √(pow(0.182258, 2) + 4·0.000104·(4.6 + 0.975·45.263003))) ⁄ (2·0.000104)) = 255
  6. paceRepSecKm = 60000 ⁄ ((−0.182258 + √(pow(0.182258, 2) + 4·0.000104·(4.6 + 1.1·45.263003))) ⁄ (2·0.000104)) = 231
Worksheet log
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How this instrument works

VDOT is a single fitness number developed by coach Jack Daniels and exercise physiologist Jimmy Gilbert, first published in their 1979 monograph and later refined in Daniels' Running Formula. It works by modeling the actual oxygen cost of running at any given speed, then combining that with a second equation estimating what percentage of your maximum oxygen uptake you can realistically sustain for a race of that duration. The result is a fitness score that lets you compare performances across completely different distances on equal footing — a strong 5K and a strong marathon performance can both map to a similar VDOT if they represent comparable fitness.

Once your VDOT is known, the same underlying equations run in reverse to generate training paces: each pace zone targets a specific percentage of VDOT that exercise science associates with a specific physiological adaptation. Easy pace sits around 70% VDOT and builds aerobic base without excess fatigue; marathon pace around 82.5% trains race-specific endurance; threshold pace around 87% pushes your lactate clearance capacity; interval pace around 97.5% develops VO2max; and repetition pace, faster than 100% VDOT, sharpens running economy and speed through short, well-recovered efforts.

The method's accuracy depends heavily on the quality of the race result you feed it. A genuinely maximal recent effort — not a comfortable training run — gives training paces that actually match your current fitness. A stale time from months ago, or a race run conservatively rather than all-out, will understate your fitness and hand you training paces that are easier than what you're currently capable of.

VO2=4.60+0.182258v+0.000104v2VO_2 = -4.60 + 0.182258v + 0.000104v^2%VO2max(t)=0.8+0.1894393e0.012778t+0.2989558e0.1932605t\%VO_{2max}(t) = 0.8 + 0.1894393e^{-0.012778t} + 0.2989558e^{-0.1932605t}VDOT=VO2(vrace)%VO2max(trace)VDOT = \dfrac{VO_2(v_{race})}{\%VO_{2max}(t_{race})}
v = race velocity in meters per minute; t = race duration in minutes; each training pace is found by inverting the VO2 equation at that zone's published %VDOT target (Easy ~70%, Marathon ~82.5%, Threshold ~87%, Interval ~97.5%, Repetition ~110%), per Jack Daniels & Jimmy Gilbert's published formulas.
  • Enter the distance of a recent race, in meters.
  • Enter your finishing time for that race, in decimal minutes.
  • Read your calculated VDOT fitness score.
  • Read the five training paces: easy, marathon, threshold, interval, and repetition, each in seconds per kilometer.

Worked example — a recent 10K in 45:00

A recreational runner recently raced a 10K (10,000 meters) in 45 minutes flat and wants updated training paces for their next block. Running that distance and time through the VDOT equations gives a fitness score of approximately 45.3 — a solid recreational-competitive level of fitness.

From that VDOT, the five training paces come out to roughly 5:32 per kilometer for easy runs, 4:51 per kilometer for marathon-pace efforts, 4:39 per kilometer for threshold work, 4:15 per kilometer for VO2max intervals, and about 3:51 per kilometer for short repetition efforts. Rather than guessing at workout paces or copying a generic chart, this runner now has five numbers specifically calibrated to their current fitness, ready to plug into their next training block.

Questions

What is VDOT, and why not just train off my actual race pace directly?

VDOT is an intensity-normalized fitness score that lets the same underlying formula generate appropriate paces across every training zone, from easy runs to short repetitions, rather than just describing one single pace. Your race pace alone tells you how fast you can race that one distance; VDOT translates that into a complete, physiologically grounded set of training paces for entirely different types of workouts.

Which race result should I actually use as input?

Use your most recent maximal-effort race, ideally somewhere between 1500 meters and marathon distance — the range the underlying formulas were originally calibrated against. A training run, a conservatively paced race, or a result from many months ago will all tend to understate your current fitness and produce training paces that are too easy.

Why does this method generate five different training paces instead of just one?

Each pace zone targets a distinct physiological system: easy pace builds aerobic base and recovery capacity, marathon pace trains race-specific fueling and endurance, threshold pace raises your lactate clearance ceiling, interval pace develops VO2max, and repetition pace sharpens speed and running economy. A well-rounded training plan draws on all five rather than training at just one intensity.

Do these training paces change as my fitness improves?

Yes — recompute your VDOT and training paces with a fresh race result every few weeks or after a key workout or race during an active training cycle. Fitness genuinely shifts over that timeframe, and paces calculated from a stale result will lag behind where you actually are, either underchallenging or overreaching depending on the direction your fitness has moved.

Is repetition pace supposed to feel faster than my current mile race pace?

It's typically close to, or slightly faster than, your current 1500m-to-mile race pace, since it targets roughly 110% of VDOT — an intensity above what you can sustain for a full VO2max effort. It's meant for short intervals with generous recovery, focused on speed and mechanics rather than sustained aerobic effort.

References